Question 2 :
Use Euclid's division lemma to find the HCF of the following<br/>16 and 176
Question 3 :
State whether the following statement is true or false.The following number is irrational<br/>$6+\sqrt {2}$
Question 4 :
Determine the HCF of $a^2 - 25, a^2 -2a -35$ and $a^2+12a+35$
Question 5 :
According to Euclid's division algorithm, HCF of any two positive integers a and b with a > b is obtained by applying Euclid's division lemma to a and b to find q and r such that $a = bq + r$, where r must satisfy<br/>
Question 6 :
State whether the following statement is True or False.<br/>3.54672 is an irrational number.
Question 8 :
In a division sum the divisor is $12$  times the quotient and  $5$  times the remainder. If the remainder is  $48$  then what is the dividend?
Question 9 :
H.C.F. of $x^3 -1$ and $x^4 + x^2 + 1$ is
Question 10 :
State whether the following statement is true or false.The following number is irrational<br/>$7\sqrt {5}$
Question 12 :
State True or False:$4\, - \,5\sqrt 2 $ is irrational if $\sqrt 2 $ is irrational.
Question 13 :
Euclid's division lemma states that for two positive integers a and b, there exist unique integers q and r such that $a = bq + r$, where r must satisfy<br>
Question 14 :
To get the terminating decimal expansion of a rational number $\dfrac{p}{q}$. if $q = 2^m 5^n$ then m and n must belong to .................
Question 15 :
............. states that for any two positive integers $a$ and $b$ we can find two whole numbers $q$ and $r$ such that $a = b \times q + r$ where $0 \leq r < b .$
Question 17 :
$2\times 2\times 2\times 3\times 3\times 13 = 2^{3} \times 3^{2} \times 13$ is equal to
Question 20 :
What is the HCF of $4x^{3} + 3x^{2}y - 9xy^{2} + 2y^{3}$ and $x^{2} + xy - 2y^{2}$?
Question 21 :
The number of possible pairs of number, whose product is 5400 and the HCF is 30 is<br>
Question 23 :
Use Euclid's division algorithm to find the HCF of :$196$ and $38220$
Question 25 :
Assertion: $\displaystyle \frac{13}{3125}$ is a terminating decimal fraction.
Reason: If $q=2^n \cdot 5^m$ where $n, m$ are non-negative integers, then $\displaystyle \frac{p}{q}$ is a terminating decimal fraction.
Question 26 :
Let $x=\dfrac { p }{ q } $ be a rational number, such that the prime factorization of $q$ is of the form $2^n 5^m$, where $n, m$ are non-negative integers. Then $x$ has a decimal expansion which terminates.
Question 27 :
State whether the following statement is true or not:$\left( 3+\sqrt { 5 }  \right) $ is an irrational number. 
Question 28 :
Without actually performing the long division, state whether the following rational number will have a terminating decimal expansion or non -terminating decimal expansion$\displaystyle \frac{7}{210}$
Question 30 :
The statement dividend $=$ divisor $\times$ quotient $+$ remainder is called 
Question 31 :
State whether the given statement is True or False :<br/>$2\sqrt { 3 }-1 $ is an irrational number.
Question 33 :
A number $x$ when divided by $7$  leaves a remainder $1$ and another number $y$ when divided by $7$  leaves the remainder $2$. What will be the remainder if $x+y$ is divided by $7$?
Question 34 :
Euclids division lemma can be used to find the $...........$ of any two positive integers and to show the common properties of numbers.
Question 35 :
Without actually dividing find which of the following are terminating decimals.
Question 36 :
Assertion: The denominator of $34.12345$ is of the form $2^n \times 5^m$, where $m, n$ are non-negative integers.
Reason: $34.12345$ is a terminating decimal fraction.
Question 37 :
If $a=107,b=13$ using Euclid's division algorithm find the values of $q$ and $r$ such that $a=bq+r$
Question 41 :
A rectangular veranda is of dimension $18$m $72$cm $\times 13$ m $20$ cm. Square tiles of the same dimensions are used to cover it. Find the least number of such tiles.
Question 42 :
Euclids division lemma, the general equation can be represented as .......
Question 44 :
The greatest number that will divided $398, 436$ and $542$ leaving $7,11$ and $14$ remainders, respectively, is
Question 45 :
The ........... when multiplied always give a new unique natural number.
Question 49 :
The LCM of 54 90 and a third number is 1890 and their HCF is 18 The third number is
Question 51 :
Use Euclid's division lemma to find the HCF of the following 65 and 495.
Question 52 :
State whether the given statement is True or False :<br/>$3+\sqrt { 2 } $ is an irrational number.
Question 53 :
Assuming  that x,y,z  are positive real numbers,simplify the following :<br/>$ (\sqrt{x})^{-2/3}\sqrt{y^{4}}\div \sqrt{xy^{-1/2}} $<br/>
Question 54 :
If $x=6+2\sqrt {6}$, then what is the value of $\sqrt { x-1 } +\cfrac { 1 }{ \sqrt { x-1 } } $?
Question 57 :
In a division sum, the divisor is $10$ times the quotient and five times the remainder. What is the dividend, if the remainder is $46?$
Question 58 :
If a = 0.1039, then the value of $\sqrt{4a^2-4a+1}+3a$ is :<br>
Question 60 :
$HCF$ of two or more number may be one of the numbers.
Question 61 :
A number when divided by $114$ leaves the remainder $21.$ If the same number is divided by $19$ the remainder will be
Question 62 :
Which of the following irrational number lies between 20 and 21
Question 63 :
The greatest number which divides $134$ and $167$ leaving $2$ as remainder in each case is
Question 66 :
Use Euclid's division lemma to find the HCF of the following<br/>27727 and 53124
Question 67 :
State whether the given statement is True or False :<br/>The number $6+\sqrt { 2 } $ is irrational.
Question 68 :
Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.<br/>$\dfrac { 13 }{ 3125 } $
Question 69 :
State whether the given statement is True or False :<br/>$4-5\sqrt { 2 } $ is an irrational number.<br/>
Question 70 :
The value of $\sqrt { 1+2\sqrt { 1+2\sqrt { 1+2+.... } } }$ is
Question 71 :
 The square of any positive odd integer for some integer $ m$ is of the form <br/>
Question 72 :
The decimal expansion of the rational number $\displaystyle\frac{23}{2^{3}5^{2}}$, will terminate after how many places of decimal?
Question 74 :
Find the HCF of $92690,7378$ and $7161$ by Euclid's division algorithm.
Question 75 :
Mark the correct alternative of the following.<br>The HCF of $100$ and $101$ is _________.<br>
Question 79 :
In a division sum a student took  $63$  as divisor instead of  $36$. His answer was  $24$. What is the correct answer? 
Question 81 :
State true or false. $\sqrt { 3 } + \sqrt { 4 }$ is an rational number.
Question 82 :
$n$  is a whole number which when divided by  $4$  gives  $3 $ as remainder. What will be the remainder when  $2n$  is divided by $4$ ?<br/>
Question 83 :
The H.C.F. of two expressions is x and their L.C.M is $ \displaystyle x^{3}-9x  $  IF one of the expression is $ \displaystyle x^{2}+3x  $  then,the other expression is 
Question 84 :
If the H.C.F. of $A$ and $B$ is $24$ and that of $C$ and $D$ is $56,$ then the H.C.F. of $A, B, C$ and $D$ is
Question 88 :
Sum of digits of the smallest number by which $1440$ should be multiplied so that it becomes a perfect cube is
Question 89 :
If HCF of $210$ and $55$ is of the form $(210) (5) + 55 y$, then the value of $y$ is :<br/>
Question 90 :
According to Euclid's division algorithm, using Euclid's division lemma for any two positive integers $a$ and $b$ with $a > b$ enables us to find the<br/>
Question 91 :
If the square of an odd positive integer can be of the form $6q + 1 $ or  $6q + 3$ for some $ q$ then q belongs to:<br/>
Question 94 :
Find the dividend which when a number is divided by $45$ and the quotient was $21$ and remainder is $14.$
Question 95 :
State whether the following statements are true or false . If a statement is false , justify your answer.<br>HCF of an even number and odd number is always $ 1$.
Question 96 :
State true or false of the following.<br>If a and b are natural numbers and $a < b$, than there is a natural number c such that $a < c < b$.<br>
Question 97 :
State true or false of the following.<br>The predecessor of a two digit number cannot be a single digit number.<br>
Question 98 :
The divisor when the quotient, dividend and the remainder are respectively $547, 171282$ and $71$ is equal to 
Question 99 :
Use Euclid's division lemma to find the HCF of $40$ and $248$.
Question 100 :
If these numbers form positive odd integer 6q+1, or 6q+3 or 6q+5 for some q then q belongs to:<br/>
Question 101 :
When a natural number x is divided by 5, the remainder is 2. When a natural number y is divided by 5, the remainder is 4. The remainder is z when x+y is divided by 5. The value of $\dfrac { 2z-5 }{ 3 } $ is
Question 102 :
For what value of k does the system of equations$\displaystyle 2x+ky=11\:and\:5x-7y=5$ has no solution?
Question 103 :
Equation of a straight line passing through the point $(2,3)$ and inclined at an angle of $\tan^{-1}\dfrac{1}{2}$ with the line $y+2x=5$, is:
Question 104 :
The survey of a manufacturing company producing a beverage and snacks was done. It was found that it sells orange drinks at $ $1.07$ and choco chip cookies at $ $0.78$ the maximum. Now, it was found that it had sold $57$ food items in total and earned about $ $45.87 $ of revenue. Find out the equations representing these two. 
Question 105 :
Choose the correct answer which satisfies the linear equation: $2a + 5b = 13$ and $a + 6b = 10$
Question 107 :
A choir is singing at a festival. On the first night $12$ choir members were absent so the choir stood in $5$ equal rows. On the second night only $1$ member was absent so the choir stood in $6$ equal rows. The same member of people stood in each row each night. How many members are in the choir?
Question 108 :
The unit digit of a number is $x$ and its tenth digit is $y$ then the number will be 
Question 110 :
In a zoo there are some pigeons and some rabbits. If their heads are counted these are $300$ and if their legs are counted these are $750$ How many pigeons are there?
Question 111 :
The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point
Question 113 :
The graph of the linear equation $2x -y = 4$ cuts x-axis at
Question 115 :
What is the equation of the line through (1, 2) so that the segment of the line intercepted between the axes is bisected at this point ?
Question 116 :
Assem went to a stationary shop and purchased $3$ pens and $5$ pencils for $Rs.40$. His cousin Manik bought $4$ pencils and $5$ pens for $Rs. 58$. If cost of $1$ pen is $Rs.x$, then which of the following represents the situation algebraically?
Question 118 :
The number of pairs of reals (x, y) such that $x =x^2+y^2$ and $y =2xy$ is
Question 119 :
If $p+q=1$ andthe ordered pair (p, q) satisfies $3x+2y=1$,then it also satisfies
Question 120 :
What is the equationof Y-axis? Hence, find the point of intersection of Y-axis and the line $y\,=\, 3x\, +\, 2$.
Question 122 :
If the system of equation, ${a}^{2}x-ay=1-a$ & $bx+(3-2b)y=3+a$ possesses a unique solution $x=1$, $y=1$ then:
Question 123 :
The solution of the equation $2x - 3y = 7$ and $4x - 6y = 20$ is
Question 124 :
Solve the following equations:<br/>$x + \dfrac {4}{y} = 1$,<br/>$y + \dfrac {4}{x} = 25$.Then $(x,y)=$
Question 125 :
If $2x + y = 5$, then $4x + 2y$ is equal to _________.
Question 126 :
State whether the given statement is true or false:Every point on the graph of a linear equation in two variables does not represent a solution of the linear equation.<br/>
Question 127 :
If x and y are positive with $x-y=2$ and $xy=24$ , then $ \displaystyle \frac{1}{x}+\frac{1}{y}$   is equal to
Question 128 :
The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$ has a non-zero solution, is ________.
Question 129 :
If the equations $4x + 7y = 10 $ and $10x + ky = 25$ represent coincident lines, then the value of $k$ is
Question 130 :
What is the equation of straight line passing through the point (4, 3) and making equal intercepts on the coordinate axes ?
Question 131 :
Examine whether the point $(2, 5)$ lies on the graph of the equation $3x\, -\, y\, =\, 1$.
Question 132 :
If $(a, 3)$ is the point lying on the graph of the equation $5x\, +\, 2y\, =\, -4$, then find $a$.
Question 133 :
The linear equation $y = 2x + 3$ cuts the $y$-axis at 
Question 134 :
State whether the given statement is true or false:The graph of a linear equation in two variables need not be a line.<br/>
Question 135 :
Two perpendicular lines are intersecting at $(4,3)$. One meeting coordinate axis at $(4,0)$, find the coordinates of the intersection of other line with the cordinate axes.
Question 136 :
Let PS be the median of the triangle with vertices $P\left( 2,2 \right), Q\left( 6,-1 \right), R\left( 7,3 \right).$The equation of the line passing through $\left( 1,-1 \right)$and parallel to PS is
Question 137 :
Five tables and eight chairs cost Rs. $7350$; three tables and five chairs cost Rs. $4475$. The price of a table is
Question 138 :
The solution of the simultaneous equations $\displaystyle \frac{x}{2}+\frac{y}{3}=4\: \: and\: \: x+y=10 $ is given by
Question 141 :
The  linear equation, such that each point on its graph has an ordinate $3$ times its abscissa is $y=mx$. Then the value of $m$ is<br/>
Question 145 :
The sum of two numbers is $2$ and their difference is $1$. Find the numbers.
Question 146 :
Equation of a straight line passing through the origin and making an acute angle with $x-$axis twice the size of the angle made by the line $y=(0.2)\ x$ with the $x-$axis, is:
Question 147 :
If $x + y = 25$ and $\dfrac{100}{x + y} + \dfrac{30}{x - y} = 6$, then the value of $x - y$ is
Question 148 :
The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be
Question 149 :
What is the nature of the graphs of a system of linear equations with exactly one solution?
Question 150 :
$\dfrac{1}{3}x - \dfrac{1}{6}y = 4$<br/>$6x - ay = 8$<br/>In the system of equations above, $a$ is a constant. If the system has no solution, what is the value of $a$
Question 151 :
A line which passes through (5, 6) and (-3. -4) has an equation of
Question 152 :
What is the value of $a$ for the following equation: $3a + 4b = 13$ and $a + 3b = 1$? (Use cross multiplication method).<br/>
Question 153 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{a}{4}\, -\, \frac{b}{3}\, =\, 0\,;\, \frac{3a\, +\, 8}{5}\, =\, \frac{2b\, -\, 1}{2}$
Question 154 :
The solution of $64^{2x - 5} = 4 \times 8^{x - 5}$ is<br>
Question 155 :
If $2^{2x - y} = 32$ and $2^{x + y} = 16$ then $x^{2} + y^{2}$ is equal to<br>
Question 156 :
Solve the set of equations: $3\left ( 2u+v \right )= 7uv$ and $3\left ( u+3v \right )= 11uv$
Question 157 :
Solve the equations using elimination method:<br>$x + 3y = 8$ and $x + 2y = 8$<br>
Question 158 :
Find the value of x and y using cross multiplication method: <br>$x - 6y = 2$ and $x + y = 4$
Question 159 :
Solve the equations using elimination method:<br>$3x + 2y = 7$ and $4x - 3y = -2$
Question 160 :
Solve: $4x+\displaystyle \frac{6}{y}= 15$ and $6x-\displaystyle \frac{8}{y}= 14$. Hence find the value of $k$, if $y= kx-2$.
Question 161 :
Let the equation $x + y +z = 5, x + 2y + 2z = 6, x + 3y + \lambda z = \mu$ have infinite solution then the value of $\lambda \mu $ is$10$
Question 162 :
Solve the following simultaneous equations by the method of equating coefficients.$\displaystyle \frac{x}{2}+3y=11; \, \, x+5y=20$
Question 163 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\displaystyle \frac {2}{\sqrt x}+\frac {3}{\sqrt y}=2, \frac {4}{\sqrt x}-\frac {9}{\sqrt y}=-1$<br/>
Question 164 :
Solve the equations using elimination method:<br>$x - y = 2$ and $-x y = -10$
Question 165 :
Solve the equations using elimination method:<br/>$x + y = 2$ and $2x- y = 7$
Question 166 :
Solve the following pairs of equations by reducing them to a pair of linear equations:<br>$\displaystyle \dfrac {7x-2y}{xy}=5, \dfrac {8x+7y}{xy}=15$<br>
Question 167 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\dfrac{2x-3y}{xy}=4$ and $\dfrac{15x+3y}{xy}=30$
Question 168 :
Solve : $\displaystyle \frac{9}{x}\, -\, \displaystyle \frac{4}{y}\, =\, 8$ and $\displaystyle \frac{13}{x}\, +\, \displaystyle \frac{7}{y}\, =\, 101$
Question 169 :
Solve: $4x\, +\, \displaystyle \frac{6}{y}\, =\, 15$ and $6x\, -\,  \displaystyle \frac{8}{y}\, =\, 14$<br/>Hence, find 'a' if $y\, =\, ax\, -\, 2$
Question 170 :
Solve the following pair of equations:<br/>$\displaystyle \frac{1}{5}\left ( x-2 \right )=\displaystyle \frac{1}{4}\left ( 1-y \right )$, $26x+3y+4= 0$
Question 171 :
Solve: $\displaystyle \frac{3}{x}\, -\, \displaystyle \frac{2}{y}\, =\, 0$ and $\displaystyle \frac{2}{x}\, +\, \displaystyle \frac{5}{y}\, =\, 19$<br/>Hence, find 'a' if $y\, =\, ax\, +\, 3$
Question 172 :
Solve the following pair of simultaneous equations:$\displaystyle \frac{8}{x}\, -\, \frac{9}{y}\, =\, 1;\,\frac{10}{x}\, +\, \frac{6}{y}\, =\, 7$
Question 173 :
Solve the following pair of simultaneous equations:$8a\, -\, 7b\, =\, 1$<br/>$4a\, =\, 3b\, +\, 5$
Question 175 :
Solve: $3\left ( 2x+y \right )= 7xy$ and $3\left ( x+3y \right )= 11xy$;  where, $x\neq 0, y\neq 0$
Question 176 :
If 10y = 7x - 4 and 12x + 18y = 1; find the values of 4x + 6y and 8y - x.
Question 178 :
Find the value of $x$ and $y$ using cross multiplication method: <br/>$6x + y = 18$ and $5x + 2y = 22$
Question 179 :
Determine the values of a and b for which the following system of linear equation has infinite solutions.<br>$2x-(a-4)y=2b+1$<br>$4x-(a-1)y=5b-1$<br>
Question 180 :
Solve the following pair of equations by reducing them to a pair of linear equations:$6x + 3y = 6xy, 2x + 4y = 5xy$<br/>
Question 181 :
If $\displaystyle \frac{x+y-8}{2} = \frac{x+2y-14}{3}=\frac{3x-y}{4}$, then the values of $x$ and $y$ is
Question 182 :
If $y=a+\dfrac { b }{ x } $, where $a$ and $b$ are constants and if $y=1$ when $x=-1$, and $y=5$ when $x=-5$, what is the value of $a+b$?
Question 183 :
Solve: $4x\, +\, \displaystyle \frac{6}{y}\, =\, 15$ and $6x\, -\, \displaystyle \frac{8}{y}\, =\, 14$
Question 184 :
If $(3)^{x + y} = 81$ and $(81)^{x - y} = 3$, then the values of $x$ and $y$ are<br>
Question 185 :
Find the value of x and y using cross multiplication method: <br/>$x-  2y = 1$ and $x + 4y = 6$
Question 186 :
Solve the following pair of simultaneous equations:$\displaystyle\, 4x\, +\, \frac{3}{y}\, =\, 1\,; 3x\, -\, \frac{2}{y}\, =\, 5$
Question 189 :
The number of solutions for the system of equations $2x + y = 4, 3x + 2y = 2$ and $x + y = - 2$ is
Question 190 :
Solve the following pair of equations by reducing them to a pair of linear equations:<br/>$\dfrac {1}{(3x+y)}+\dfrac {1}{(3x-y)}=\dfrac {3}{4},\  \dfrac {1}{2(3x+y)}-\dfrac {1}{2(3x-y)}=\dfrac {-1}{8}$
Question 191 :
Find the value of x and y using cross multiplication method: <br>$3x - 5y = -1$ and $x + 2y = -4$
Question 192 :
Solve the following pair of linear (simultaneous) equations by the method of elimination:<br/>$0.2x+0.1y= 25$<br/>$2\left ( x-2 \right )-1.6y= 116$
Question 193 :
If$\displaystyle \frac{x+y}{x-y}=\frac{5}{3}\: and\: \frac{x}{\left ( y+2 \right )}=2$ the value of (x , y) is
Question 194 :
If $y=a+\cfrac { b }{ x } $, where $a$ and $b$ are constants, and if $y=1$ when $x=-1$, and $y=5$ when $x=-5$, then $a+b$ equals.
Question 195 :
Find the value of x and y using cross multiplication method: <br>$3x + 4y = 43$ and $-2x + 3y = 11$
Question 196 :
Solve the following simultaneous equations by the method of equating coefficients.$x-2y=-10; \, \, 3x-5y=-12$
Question 198 :
Given that $3p + 2q = 13$ and $3p - 2q = 5$, find the value of $p + q$
Question 199 :
Solve the following pair of simultaneous equations:$\displaystyle\, y\, -\, \frac{3}{x}\, =\, 8\, ;\, 2y\, +\, \frac{7}{x}\, =\, 3$
Question 200 :
If $2x + y = 23$ and $4x - y = 19$; find the values of $x - 3y$ and $5y - 2x$.<br/>
Question 201 :
Solve: $4x+\displaystyle \frac{6}{y}= 15$ and $6x-\displaystyle \frac{8}{y}= 14$. Hence, find $a$ if $y= ax-2$
Question 202 :
What must be subtracted from $4x^4 - 2x^3 - 6x^2 + x - 5$, so that the result is exactly divisible by $2x^2 + x - 1$?
Question 203 :
What is $\dfrac {x^{2} - 3x + 2}{x^{2} - 5x + 6} \div \dfrac {x^{2} - 5x + 4}{x^{2} - 7x + 12}$ equal to
Question 204 :
State whether True or False.Divide : $a^2 +7a + 12 $ by $  a + 4 $, then the answer is $a+3$.<br/>
Question 206 :
If $P=\dfrac {{x}^{2}-36}{{x}^{2}-49}$ and $Q=\dfrac {x+6}{x+7}$ then the value of $\dfrac {P}{Q}$ is:
Question 207 :
If $\alpha , \beta$ are the zeros of the polynomials $f(x) = x^2+x+1 $ then $\dfrac{1}{\alpha}+\dfrac{1}{\beta}=$________.
Question 208 :
If $x\ne -5$ , then the expression $\cfrac{3x}{x+5}\div \cfrac {6}{4x+20}$ can be simplified to
Question 210 :
If $\alpha$ and $\beta$ are the zeroes of the polynomial $4x^{2} + 3x + 7$, then $\dfrac{1}{\alpha }+\dfrac{1}{\beta }$ is equal to:<br/>
Question 212 :
If $a\ne 2$, which of the following is equal to $\cfrac { b\left( { a }^{ 2 }-4 \right) }{ ab-2b } $?
Question 213 :
If $\alpha , \beta $ are the roots of the equation $ax^{2}+bx+c=0$, find the value of $\alpha ^{2}+\beta ^{2}$.
Question 214 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$\displaystyle x^2-\frac{1}{4x^2}; x-\frac{1}{2x}$
Question 217 :
Factorise the expressions and divide them as directed.$4yz(z^2 + 6z-  16)\div  2y(z + 8)$<br/>
Question 219 :
Simplify:Find$\ x(x + 1) (x + 2) (x + 3) \div  x(x + 1)$<br/>
Question 220 :
If the roots of ${ x }^{ 2 }-2mx+{ m }^{ 2 }-1=0$ lie between $-2$ and $4$, then
Question 221 :
Work out the following divisions.<br/>$96abc(3a -12) (5b +30)\div  144(a-  4) (b+  6)$<br/>
Question 222 :
If a polynomial $p(x)$ is divided by $x - a$ then remainder is<br/>
Question 223 :
If $\alpha , \beta$ are the roots of equation $x^2 \, - \, px \, + \, q \, = \, 0,$ then find the equation the roots of which are $\left ( \alpha ^2  \, \beta ^2 \right )  \,  and  \,  \,  \alpha \, + \,\beta $.
Question 226 :
State whether the following statement is true or false.After dividing $ (9x^{4}+3x^{3}y + 16x^{2}y^{2}) + 24xy^{3} + 32y^{4}$ by $ (3x^{2}+5xy + 4y^{2})$ we get<br/>$3x^{2}-4xy + 8y^{2}$
Question 227 :
Find the value of a & b, if  $8{x^4} + 14{x^3} - 2{x^2} + ax + b$ is divisible by $4{x^2} + 3x - 2$
Question 228 :
State whether true or false:Divide: $4a^2 + 12ab + 91b^2 -25c^2 $ by $ 2a + 3b + 5c $, then the answer is $2a+3b+5c$.<br/>
Question 229 :
Work out the following divisions.$10y(6y + 21) \div 5(2y + 7)$<br/>
Question 231 :
Find the expression which is equivalent to : $\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $?
Question 232 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$a^2-b^2 ; a-b$
Question 233 :
Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and their coefficients.$49x^2-81$<br/>
Question 234 :
State whether True or False.Divide: $x^2 + 3x -54 $ by $ x-6 $, then the answer is $x+9$.<br/>
Question 237 :
State whether True or False.Divide: $12x^2 + 7xy -12y^2 $ by $ 3x + 4y $, then the answer is $x^4+2x^2+4$.<br/>
Question 238 :
The degree of the remainder is always less than the degree of the divisor.
Question 239 :
Apply the division algorithm to find the remainder on dividing $p(x) = x^4 -3x^2 + 4x + 5$ by $g(x)= x^2 +1 -x.$
Question 243 :
Factorise the expressions and divide them as directed.$12xy(9x^2-  16y^2)\div  4xy(3x + 4y)$
Question 245 :
Divide:$\left ( 15y^{4}- 16y^{3} + 9y^{2} - \cfrac{1}{3}y - \cfrac{50}{9} \right )$ by $(3y-2)$Answer: $5y^{3} + 2y^{2} - \cfrac{13}{3}y + \cfrac{25}{9}$
Question 246 :
Simplify:$20(y + 4) (y^2 + 5y + 3) \div 5(y + 4)$<br/>
Question 247 :
Choose the correct answer from the alternatives given.<br>If the expression $2x^2$ + 14x - 15 is divided by (x - 4). then the remainder is
Question 248 :
$\alpha $ and $\beta $ are zeroes of polynomial $x^{2}-2x+1,$ then product of zeroes of a polynomial having zeroes $\dfrac{1}{\alpha }$  and    $\dfrac{1}{\beta }$ is
Question 250 :
What must be added to $x^3-3x^2-12x + 19$, so that the result is exactly divisible by $x^2 + x-6$?
Question 253 :
Let $P(x) = 1 + x + x^2 +x^3+x^4+x^5$. What is the remainder when $P(x^{12})$ is divided by $P(x)$?
Question 255 :
The roots of the equation $\displaystyle x^{2}+Ax+B=0$ are 5 and 4. The roots of $\displaystyle x^{2}+Cx+D=0$ are 2 and 9. Which of the following is a root of $\displaystyle x^{2}+Ax+D=0$?
Question 256 :
The condition that the equation $x^2 + px + q = 0$, whose one root is the cube of the other root is :
Question 257 :
If $\alpha$ and $\beta$ be two zeros of the quadratic polynomial $ax^2+bx+c$, then $\dfrac {\alpha^2}{\beta}+\dfrac {\beta^2}{\alpha}$ is equal to<br/>
Question 259 :
Find the product of roots if the quadratic equation $ax^2+bx+c=0$ has exactly one non-zero root.
Question 261 :
If the roots of the equation $\dfrac{x^{2}-bx}{ax-c}=\dfrac{m-1}{m+1}$ are equal but opposite in sign, then the value of $m$ will be
Question 262 :
Divide the following and write your answer in lowest terms: $\dfrac{x^2-36}{x^2-49}\div \dfrac{x+6}{x+7}$
Question 263 :
$mx^2+(m-1)x +2=0$ has roots on either side of x=1 the m $\in$
Question 264 :
If $\alpha$ and $\beta$ are the roots of $x^2-pX +1=0$ and $\gamma$ is a root of $X^2+pX+1=0$, then $(\alpha+\gamma)(\beta+\gamma)$ is
Question 265 :
If $\alpha$ and $\beta$ be two zeros of the quadratic polynomial $ax^2+bx+c$, then evaluate:$\alpha^3+\beta^3$<br/>
Question 266 :
Find the zeros of the quadratic polynomial $f(x) = x^2-3x -28$ and verify the relationships between the zeros and the coefficients.
Question 267 :
If $3{p}^{2}=5p+2$ and $3{q}^{2}=5q+2$, where $p\ne q$, then $pq$ is equal to
Question 268 :
Divide the following and write your answer in lowest terms: $\dfrac{3x^2-x-4}{9x^2-16}\div \dfrac {4x^2-4}{3x^2-2x-1}$
Question 270 :
If ${(5{x}^{2}+14x+2)}^{2}-{(4{x}^{2}-5x+7)}^{2}$ is divided by ${x}^{2}+x+1$, then the quotient $q$ and the remainder $r$ are given by:
Question 271 :
Evaluate: $96 abc (3a -12)(5b -30) \div 144 (a -4) (b -6)$
Question 272 :
$\left[2x\right]-2\left[x\right]=\lambda$ where $\left[.\right]$ represents greatest integer function and $\left\{.\right\}$ represents fractional part of a real number then 
Question 273 :
The value of $m$ for which the equation $\dfrac { a }{ x+a+m } +\dfrac { b }{ x+b+m } =1$ has roots equal in magnitude but opposite in sign is<br>
Question 274 :
If $\alpha, \beta$ are the roots of the quadratic equation $ax^2+bx+c=0$ and $3b^2=16ac$ then
Question 275 :
Divide :$\displaystyle \left[ { x }^{ 4 }-{ \left( y+z \right)  }^{ 4 }\right] \ by \left[{ x }^{ 2 }+{ \left( y+z \right)  }^{ 2 }\right]$
Question 276 :
There are $x^{4} + 57x + 15$ pens to be distributed in a class of $x^{2} + 4x + 2$ students. Each student should get the minimum possible number of pens. Find the number of pens received by each student and the number of pens left undistributed $(x\epsilon N)$.
Question 277 :
If $\displaystyle \alpha$ and$\displaystyle \beta$ are roots of$\displaystyle { x }^{ 2 }-2x-1=0$, find the value of$\displaystyle { a }^{ 2 }\beta +{ \beta }^{ 2 }\alpha$.
Question 279 :
If $\alpha $ and $\beta$ are the roots of a rational function $\dfrac{2}{\alpha+1}-\dfrac{\alpha}{6}=0$. What is the sum of $\alpha+\beta$?<br/>
Question 280 :
Workout the following divisions<br/>$11a^3b^3(7c - 35) \div 3a^2b^2 (c - 5)$
Question 282 :
If $\alpha$ and $\beta$ are the roots of $x^2 - ax + b^2 = 0$, then $\alpha^2 + \beta^2$ is equal to
Question 284 :
If the ratio of the roots of ${x}^{2}+bx+c=0$ is equal to the ratio of the roots of ${x}^{2}+px+q=0$ then ${p}^{2}c-{b}^{2}q=$
Question 285 :
If $\alpha, \beta$ are the root of quadratic equation $ax^2+bx+c=0$,then $\displaystyle \left ( a\alpha +b \right )^{-3}+\left ( a\beta +b \right )^{-3}=$
Question 289 :
If a and b are the rootsof the quadratic equation $\displaystyle { 6x }^{ 2 }-x-2=0$from an equation whose roots are$\displaystyle { a }^{ 2 }$ and$\displaystyle { b }^{ 2 }$?
Question 290 :
If$\displaystyle \alpha $ and<b></b>$\displaystyle \beta $ are the roots of $\displaystyle 4x^{2}+3x+7=0$ the value of$\displaystyle \frac{1}{\alpha ^{3}}+\frac{1}{\beta ^{3}}$ is
Question 291 :
Simplify: $\displaystyle 7\left( 4x+5 \right) \left( 2x+6 \right) \div \left( 4x+5 \right) $
Question 292 :
If $\alpha, \beta$ are real and $\alpha^2, -\beta^2$ are the roots of $a^2 x^2 + x+1-a^2=0;\ (a  >  1)$, then $\beta^2=$
Question 293 :
If $\displaystyle \alpha $ and $\displaystyle \beta  $ are roots of the polynomial $\displaystyle f\left ( x \right )= x^{2}-5x+k$ such that $\displaystyle \alpha -\beta = 1$, then value of $k$ is equal to<br/>
Question 294 :
Suppose the quadratic function $f\left( x \right) =a{ x }^{ 2 }+bx+c$ is such that $f\left( -2 \right) =0\quad and\quad \dfrac { -b }{ 2a } =1$. Solve $f\left( x \right)=0$
Question 295 :
Workout the following divisions<br/>$54lmn (l + m) (m + n) (n + 1) \div 81mn (l + m) (n + l)$
Question 298 :
Find the Quotient and the Remainder when the first polynomial is divided by the second.<br/>$(x^3+1) $ by $(x+1)$
Question 299 :
(64x$^3$ + y$^3$) $\div$ (16x$^2$ - 4xy + y$^2$) is equal to
Question 301 :
Find all values of a for which the equation $x^4+(a−1)x^3+x^2+(a−1)x+1=0$ possesses at least two distinct negative roots.
Question 302 :
If the equation<br>$\displaystyle\left( { p }^{ 2 }+{ q }^{ 2 } \right) { x }^{ 2 }-2\left( pr+qs \right) x+{ r }^{ 2 }+{ s }^{ 2 }=0$ has equal rootsthen<br>
Question 303 :
Check whether $2x^2 - 3x + 5 = 0$ has real roots or no.<br/>
Question 306 :
The least integer $'c'$ which makes the roots of the equation $x^2+3x+2c$ imaginary is
Question 307 :
In a rectangle the breadth is one unit less than the length and the area is $12$ sq.units. Find the length of the rectangle.
Question 308 :
If the roots of the equation $ax^2+bx+c=0$ are all real equal then which one of the following is true?
Question 309 :
Find $ p \in R $ for $x^2 - px + p + 3 = 0 $ has<br/>
Question 310 :
Say true or false.If $2y^{2}\, =\, 12\, -\, 5y$, then solution is $\displaystyle \frac{3}{2}\, or\, -4$.<br/>
Question 311 :
Roots of the equation $\sqrt {\dfrac {x}{1-x}}+\sqrt {\dfrac {1-x}{x}}=2\dfrac {1}{6}$ are
Question 312 :
If $f(x)$ is a quadratic expression such that $f(1) + f(2) = 0$, and $-1$ is a root of $f(x) = 0$, then the other root of $f(x) = 0$ is :
Question 313 :
State the following statement is True or False<br/>The sum of a natural number $x$ and its reciprocal is $\displaystyle \frac{37}{6}$, then the equation is $x\, +\, \displaystyle \frac{1}{x}\, =\, \displaystyle \frac{37}{6}$.<br/>
Question 316 :
Choose the best possible option.<br>$\displaystyle{ x }^{ 3 }-5x+2{ x }^{ 2 }+1=0$ is quadraticequation.<br>
Question 317 :
Check whether the given equation is a quadratic equation or not.<br/>${ x }^{ 2 }+2\sqrt { x } -3$
Question 318 :
If $x^2-36=0$, which of the following could be a value of $x$?
Question 320 :
Solve the following quadratic equation by factorization :<br>$a(x^2 \, + \, 1) \, - \, x \, (a^2 \, + \, 1) \, = \, 0$
Question 321 :
STATEMENT - 1 : $(x-2)(x+1)$ $=$ $(x-1)(x+3)$ is a quadratic equation.<br/>STATEMENT - 2 : If $p(x)$ is a quadratic polynomial, then $p(x)$ $=$ $0$ is called a quadratic equation.<br/>
Question 322 :
Check whether the following is a quadratic equation.$(x - 3) (2x + 1) = x (x + 5)$<br/>
Question 323 :
If $C > 0$ and the equation $3 a x ^ { 2 } + 4 b x + c = 0$ has no real root, then
Question 326 :
Applying zero product rule for the equation $x^{2}- ax - 30 = 0$ is $x = 10$, then $a =$ _____.<br/>
Question 328 :
If roots of $(a - 2b + c)x^2 + (b - 2c +a)x + (c - 2a +b) = 0$ are equal, then :
Question 329 :
If $y=\cfrac { 2 }{ 3 } $ is a root of the quadratic equation $3{ y }^{ 2 }-ky+8=0$, then the value of $k$ is ..................
Question 330 :
The difference between the product of the roots and the sum of the roots of the quadratic equation $6x^{2} - 12x + 19 = 0$ is
Question 331 :
Which point satisfies the linear quadratic system y=x+3 and y=5-x$\displaystyle ^{2}$?
Question 336 :
The mentioned equation is in which form?<br/>$m^{3}\, +\, m\, +\, 2\, =\, 4m$
Question 337 :
Check whether the given equation is a quadratic equation or not.<br/>$\quad { x }^{ 2 }+\cfrac { 1 }{ { x }^{ 2 } } =2\quad $<br/>
Question 338 :
The sum of a number and its reciprocal is$ \displaystyle \frac{125}{22} $ The number is
Question 340 :
Which of the following equations has two distinct real roots ?<br>
Question 346 : <p>If the value of '$b^2-4ac$' is less than zero, the quadratic equation $ax^2+bx+c=0$ will have</p><br/>
Question 347 :
If c is small in comparision with l then ${\left( {\frac{l}{{l + c}}} \right)^{\frac{1}{2}}} + {\left( {\frac{l}{{l - c}}} \right)^{\frac{1}{2}}} = $
Question 348 :
The number of solutions of the equation,$2\left\{ x \right\} ^{ 2 }+5\left\{ x \right\} -3=0$ is
Question 349 :
Is the following equation quadratic?$(x\, +\, 3) (x\, -\, 4)\, =\, 0$
Question 350 :
Determine whether the equation $\displaystyle 5{ x }^{ 2 }=5x$ is quadratic or not.
Question 351 :
The difference of two natural numbers is $4$ and the difference of their reciprocals is $\dfrac{1}{3}$. Find the numbers.
Question 353 :
The quadratic equation whose roots are the A.M. and H.M. between the roots of the equation,$2x^2- 3x + 5 = 0$is
Question 354 :
If the roots of the quadratic equation $x^2+6x+b=0$ are real and distinct and they differ by atmost $4$ then the least value of $b$ is-
Question 355 :
The value of $a$ for which one root of the quadratic equation $(a^2-5a+3) x^2+(3a-1)x+2=0 $ is twice as large as the other, is :<br/>
Question 356 :
The altitude of a right triangle is $7$ cm less than itsbase. If the hypotenuse is $13$ cm, find the other twosides.
Question 357 :
If $x=1$ is common root of equations $ax^{2} +ax+3=0$ and $x^{2}+x+b=0$, then value of $ab$ will be:
Question 358 :
A man is walking at a speed of 15 km per hour. After every kilometre, he takes rest for 3 minutes. How much time will he take to cover a distance of 4 km?
Question 359 :
The roots of the equation $ax^2 + bx + c = 0$ will be imaginary if
Question 360 :
Consider quadratic equation $ax^2+(2-a)x-2=0$, where $a \in R$.Let $\alpha ,\beta $ be roots of quadratic equation. If there are at least four negative integers between $\alpha$ and $\beta$, then the complete set of values of $a$ is
Question 361 :
If $x=5+2\sqrt{6}$, then the value of ${ \left( \sqrt { x } -\cfrac { 1 }{ \sqrt { x } } \right) }^{ 2 }$ is _____
Question 362 :
If the discriminant of quadratic equation ${ b }^{ 2 }-4ac=0$ then the roots are 
Question 364 :
Find the discriminant of the equation and the nature of roots. Also find the roots.$2x^2 + 5 \sqrt 3x + 6 =0$
Question 365 :
If $x^2 - 4x + \log_{\frac{1}{2}}A = 0$ does not have two distinct real roots, then maximum value of $A$ is:
Question 366 :
A trader bought an article for Rs. $x$ and sold it for Rs. $52$, thereby making a profit of $(x-10)$ per cent on his outlay. Calculate the cost price.
Question 368 :
The ______ product rule says that when the product of two terms is zero, then either of the terms is equal to zero.<br>
Question 369 :
Find the values of $k$ for the following quadratic equation, so that they have two real and equal roots:$4x^2 - 2(k + 1)x + (k + 4) = 0$
Question 370 :
Assertion: If roots of the equation $ x^{2}-b x+c=0 $ are two consecutive integers, then $ b^{2}-4 c=1 $
Reason: If $ a, b, c $ are odd integer, then the roots of the equation $4 abc<br>x^{2}+\left(b^{2}-4 a c\right) x-b=0 $ are real and distinct.
Question 371 :
$kx^2-2\sqrt 5x +4 = 0$For what value of $k$ will the quadratic equation have real and equal roots ?
Question 372 :
The quadratic equations $x^{2}-6x+a=0$ and $x^{2}-cx+6=0$ have one root in common. The other roots of the first and second equations are integers in the ratio $4: 3$. Then the common root is<br><br>
Question 373 :
The given equation has real roots. State true or false: $8x^2 + 2x -3 = 0$<br/>
Question 374 :
$\alpha$ and $\beta$ are the roots of the equation $ax^{2}+bx+c=0$ and $\alpha^{4}, \beta^{4}$ are the roots of the equation $lx^{2}<br>+mx+n=0(\alpha, \beta$ are real and distinct.) Let $f(x)=a^{2}lx^{2}-4aclx+2c^{2}l+a^{2}m=0$, then<br>Roots of $f(x)=0$ are<br>
Question 375 :
Minimum possible number of positive root of the quadratic equation${x^2} - (1 + \lambda )x + \lambda - 2 = 0, \in R:$
Question 376 :
If the roots of the equation $\displaystyle x^{2}+px-6=0$ are $6$ and $-1$ then the value of $p$ is
Question 378 :
The factors of the equation, $(x + k)\left (x + \dfrac{1}{2}\right) = 0$, find the value of $k$.<br/>
Question 379 :
$x^2-(m-3)x+m=0\:\:(m \in R)$ be a quadratic equation. Find the value of $m$ for which both the roots are greater than $2$
Question 382 :
if x be real and 0 < b< c then $ \dfrac { { x }^{ 2 }-bc }{ 2x-b-c } $<br/><br/>
Question 383 :
If $a(p+q)^{2}+2 b p q+c=0$ and $a(p+r)^{2}+2 b p r+c=0$ <br> $(a \neq 0),$ then,
Question 384 :
If difference of roots of the equation$\displaystyle x^{2}+px+8= 0$ is $2$, then $p$ is equal to
Question 385 :
If $a, b$ and $c$ are non-zero real numbers and $a{z}^{2}+bz+c+i=0$ has purely imaginary roots, then $a$ is equal to
Question 386 :
If both a and b belong to the set $\displaystyle \left\{ 1,2,3,4 \right\}$ then the number of equations of the form $ ax^{2}+bx+1=0$ having real roots is :<br>
Question 387 :
If the roots of the equation $ax^2+ bx + c = 0$ arereciprocal to each other, then
Question 388 :
If the roots of the equation $a{ x }^{ 2 }+bx+c=0$ are reciprocal of each other, then
Question 389 :
If k be the ratio of the roots of the equation$ \displaystyle x^{2}-px+q=0 $ , the value of$ \displaystyle \frac{k}{1+k^{2}} $ is
Question 390 :
If the absolute value of the difference of roots of the equation $\displaystyle x^{2}+px+1=0$ exceeds $\sqrt{3p}$
Question 391 :
If the ratio of the roots of equation$\displaystyle x^{2}+px+q=0$ be equal to the ratio of the roots of$\displaystyle x^{2}+lx+m=0$ then
Question 392 :
The least value of $a$ for  which roots of the equation $x^2-2x-\log_4 a=0$ are real is
Question 393 :
In each of the following, determine whether the given values are solutions of the given equation or not :<br/> $x^2 \, - \, 3\sqrt{3x} \, + \, 6 \, = \, 0, \, x \, = \, \sqrt{3}, \, x \, = \, -2\sqrt{3}$
Question 394 :
The roots of $a{ x }^{ 2 }+bx+c=0$, where $a\neq 0,b,c\epsilon R$ are non real complex and $a+c<b$. Then <br><br>
Question 395 :
The value of k for which the roots are real and equal of the following equation<br/>$x^2$ - 4kx + k = 0 are k = 0, $\dfrac{1}{4}$
Question 396 :
If $p, q$ are odd integers, then the roots of the equation $2px^{2} + (2p + q) x + q = 0$ are
Question 398 :
In the following, determine whether the given quadratic equation have real roots and if so, find the roots :<br/>$\sqrt{3}x^2 \, + \, 10x \, - \, 8\sqrt{3} \, = \, 0$
Question 399 :
$x^2-(m-3)x+m=0\:\:(m \in R)$ be a quadratic equation. Find the value of $m$ for which, at least one root is greater than $2$.
Question 401 :
Which of the following is correct, if the roots of quadratic equation are equal?
Question 403 :
If $m_1$ and $m_2$ are the roots of the equation $x^2+\left(\sqrt{3}+2\right)x+\left(\sqrt{3}-1\right)=0$, then the area of the triangle formed by the lines $y=m_1x,y=m_2x$ and $y=2$ is :
Question 404 :
If the equations ${x}^{2}+ax+12=0$, ${x}^{2}+bx+15=0$ and ${x}^{2}+(a+b)x+36=0$ have a common root then the possible values of $a,b$ is (are)
Question 405 :
If $\alpha$ and $\beta$ are roots of the equation $a{ x }^{ 2 }+bx+c=0$ then the equation whose roots are $\alpha +\frac { 1 }{ \beta }$ are $\beta +\frac { 1 }{ \alpha }$ is
Question 406 :
The equation $\displaystyle 9y^{2}(m+3)+6(m-3)y+(m+3)=0 $, where $m$ is real has real roots then 
Question 407 :
If one of the roots of $x^2-bx+c=0,\:(b,c)\:\epsilon\:Q$ is $\sqrt{7-4\sqrt 3}$ then:
Question 408 :
Given expression is $x^{2} - 3xb + 5 = 0$. If $x = 1$ is a solution, what is $b$?
Question 411 :
If $x^2-10ax-11b=0$ has roots $c$ and $d$, then, $x^2-10x-11d=0$ has roots $a$ and $b$, then $a+b+c+d=$
Question 412 :
Find the values of $K$ so that the quadratic equations $x^2+2(K-1)x+K+5=0$ has atleast one positive root.
Question 413 :
If $b_1b_2=2(c_1+c_2)$, then at least one of the equations $x^2+b_1x+c_1=0$ and $x^2+b_2x+c_2=0$ has<br>
Question 414 :
If both the roots of the equation ${ x }^{ 2 }-32x+c=0$ are prime numbers then the possible values of $c$ are
Question 415 :
If one of the roots of the quadratic equation $a{ x }^{ 2 }-bx+a=0$ is $6$, then the value of $\cfrac { b }{ a } $ is equal to
Question 416 :
If both the roots of the equation$\displaystyle x^{2}-6ax+2-2a+9a^{2}=0$ exceed $3$, then
Question 417 :
If $|2x + 3|\le 9$ and $2x + 3 < 0$, then
Question 418 :
Let $f(x)\, =\, x^2\, +\, ax\, +\, b,$ where a, b $\epsilon$ R. If $f(x) = 0$ has all its roots imaginary, then the roots of $f(x) + f' (x) + f" (x) = 0$ are
Question 419 :
The total cost price of certain number of books is $450$. By selling the books at $50$ each, a profit equal to the cost price of $2$ books is made. Find the approximate number of books.<br/>
Question 420 :
If $\displaystyle r_{1}\:$ and $ r_{2}$ are the roots of $\displaystyle x^{2}+bx+c=0$ and $\displaystyle S_{0}=r_{1}^{0}+r_{2}^{0}$, $\displaystyle S_{1}=r_{1}+r_{2}$ and $\displaystyle S_{2}=r_{1}^{2}+r_{2}^{2}$, then the value of $\displaystyle S_{2}+bS_{1}+cS_{0}$ is
Question 421 :
Let $f: R\rightarrow R $ be the function $f(x) = (x - a_{1}) (x - a_{2}) + (x - a_{2}) (x - a_{3})+ (x - x_{3})(x-x_{1})$ with $a_{1}, a _{2}, a_{3}\in R $ Then $f(x)=\geq 0 $if and only if<br>
Question 422 :
The quadratic equation $p(x) =0$ with real coefficients has purely imaginary roots. Then the equation $p(p(x)) =0$ has
Question 423 :
The condition that the roots of the equation $\displaystyle ax^{2}+bx+c=0$ be such that one root is $n$ times the other is 
Question 424 :
$\alpha ,\beta $ are roots of the equation $2{x^2} - 5x - 6 = 0$ then
Question 425 :
A tradesman finds that by selling a bicycle for Rs. 75, which he had bought for Rs. $x$, he gained $x$%. Find the value of $x$.
Question 426 :
Assertion: If the roots of the equations $x^2-bx+c=0$ and $x^2-cx+b=0$ differ by the same quantity, then $b+c$ is equal to $-4$
Reason: If $\alpha,\beta$ are the roots of the equation $Ax^2+Bx+C=0,$ then $\displaystyle \alpha -\beta =\frac { \sqrt { { B }^{ 2 }-4AC }  }{ A } $
Question 429 :
The number of values of $\displaystyle k$for which$\displaystyle \left ( x^{2} - \left ( k - 2 \right )x + k^{2} \right ) \left ( x^{2} + kx + \left ( 2k - 1 \right ) \right )$is a perfect square
Question 430 :
Find the term independent of x in the expansion of $\left(2x^2-\dfrac{3}{x^3}\right)^{25}$.
Question 431 :
 If  the sum of the roots of the quadratic  equation $ax^2+bx+c=0$  is equal to the sum of the square of their reciprocals, then  $\dfrac{a}{c},\dfrac{b}{a}$ and $\dfrac{c}{b}$ are in<br/>
Question 432 :
Equation $x^2 - x + q = 0$ has imaginary roots if 
Question 433 :
If $\alpha$ and $ \beta$ are the roots of the equation $ { x^{ 2 } }-ax+b=0$ and $ { v }_{ n }={ \alpha  }^{ n }+{ \beta  }^{ n }$, then<br/>
Question 434 :
If the roots of the equation ${ x }^{ 2 }-2ax+{ a }^{ 2 }+a-3=0$ are real and less than $3$, then
Question 435 :
If $a < b < c < d$, then for any real non-zero $\lambda$, the quadratic equation $(x-a)(x-c)+\lambda (x-b)(x-d)=0$ has<br>
Question 436 :
The value of $a$ for which the equation $a ^ { 2 } + 2 a + \csc ^ { 2 } \pi ( a + x ) = 0$ has a solution, is/are
Question 437 :
If $x^2-(a+b+c)x+(ab+bc+ca)=0$ has imaginary roots, where $a,b,c\in R^+,$ then $\sqrt { a } ,\sqrt { b } ,\sqrt { c } $
Question 438 :
The real number $k$ for which the equation $2x^ {3}+3x+k=0$ has two distinct real roots in $[0,1]$
Question 439 :
If $x = 3t, y = 1/ 2(t + 1)$, then the value of $t$ for which $x = 2y$ is
Question 440 :
If one root of the equation $a{ x }^{ 2 } + bx + c = 0$ be the square of the other, then the value of${ b }^{ 3 } + { a }^{ 2 }c + a{ c }^{ 2 } $ is<br>
Question 441 :
The rectangular fence is enclosed with an area $16$cm$^{2}$. The width of the field is $6$ cm longer than the length of the fields. What are the dimensions of the field?<br/>
Question 442 :
Number of positive integral values of $b$ for which both roots of the quadratic equation $\displaystyle x^2 + bx - 16 = 0$ are integers, is 
Question 444 :
If each pair of the following three equations $ { x }^{ 2 }+ax+b=0$, ${ x }^{ 2 }+cx+d=0$, ${ x }^{ 2 }+ex+f=0$ has exactly one root in common, then <br/>
Question 445 :
The coefficient of $x$ in the equation $x^2+px+q=0$ was wrongly written as $17$ in place of$13$ and the roots thus found was $-2$ and $-15$.<br>Then the roots of the correct equation are
Question 446 :
Hypotenuse length is$\displaystyle3\sqrt { 10 }$. Base length istripled and perpendicular doubles, new length of hypotenuse will be$\displaystyle 9\sqrt { 5 }$. Find the length of base.
Question 447 :
lf $\mathrm{a},\ \mathrm{b},\ \mathrm{c}$ are in G.P. then the equations $\mathrm{a}\mathrm{x}^{2}+2\mathrm{b}\mathrm{x}+\mathrm{c}=0$ and $\mathrm{d}\mathrm{x}^{2}+2\mathrm{e}\mathrm{x}+\mathrm{f}=0$ have a common root if $\dfrac { d }{ a } ,\dfrac { e }{ b } ,\dfrac { f }{ c } $ are in <br/>
Question 448 :
If a,b,c >0 and $a=2b+3c$, then the roots of the equation $ax^2+bx+c=0$ are real if
Question 451 :
All the values of '$a$' for which the quadratic expression $ax^2+(a-2)x-2$ is negative for exactly two integral values of $x$ may lie in
Question 452 :
$(a^{4}-1)x^{2}-(a^{2}+1)(sin^{-1}sin^{3} 2)x+(cos^{-1}cos2)(a^{2}-1) =0$.<br>.Find the set of values of a so that above equation have roots of opposite in sign.<br><br><br>
Question 453 :
If the probability of the occurrence of an event is P then what is the probability that the event doesn't occur.
Question 454 :
The probability of an event happening and the probability of the same event not happening (or the complement) must be a <br/>
Question 455 :
If $P(A) = \dfrac{5}{9}$, then the odds against the event $A$ is
Question 457 :
The probability expressed as a percentage of a particular occurrence can never be
Question 458 :
The probability of guessing the correct answer to a certain test is $\displaystyle\frac{x}{2}$. If the probability of not guessing the correct answer to this questions is $\displaystyle\frac{2}{3}$, then $x$ is equal to ______________.
Question 459 :
The probability of an event $A$ lies between $0$ and $1$, both inclusive. Which mathematical expression best describes this statement?<br/>
Question 461 :
Two dice are thrown. Find the odds in favour of getting the sum $4$.<br/>
Question 462 :
If the odd in favour of an event are $4$ to $7$, find the probability of its no occurence.
Question 464 :
A bag contains 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blueand 1 is black?
Question 465 :
A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is
Question 466 :
A die is thrown .The probability that the number comes up even is ______ .
Question 467 :
A bulb is taken out at random from a box of 600 electricbulbs that contains 12 defective bulbs. Then theprobability of a non-defective bulb is
Question 468 :
A pair of dice is thrown. Find the probability of getting a sum of $8$ or getting an even number on both the dices.
Question 469 :
If I calculate the probability of an event and it turns out to be $7$, then I surely know that<br/>
Question 470 :
What is the maximum value of the probability of an event?
Question 471 :
According to the property of probability, $P(\phi) = 0$ is used for <br>
Question 472 :
Out of the digits $1$ to $9$, two are selected at random and one is found to be $2$, the probability that their sum is odd is
Question 473 :
A biased coin with probability $p , 0 < p < 1 ,$ of heads is tossed until a head appears for thefirst time. If the probability that the number of tosses required is even, is $2 / 5 ,$ then $p$ equal to
Question 474 :
A fair dice has faces numbered $0, 1, 7, 3, 5$ and $9$. If it is thrown, the probability of getting an odd number is
Question 475 :
One hundred identical coins each with probability p as showing up heads are tossed. If $0 < p < 1$ and the probability of heads showing on 50 coins is equal to that of heads on 51 coins, then the value of p is
Question 476 : A coin is tossed $400$ times and the data of outcomes is below:<span class="wysiwyg-font-size-medium"> <span class="wysiwyg-font-size-medium"><br/><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Outcomes </p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$H$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$T$</p></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Frequency</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$280$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$120$</p></td></tr></tbody></table><p><br/></p><p>Find:</p><p>(i) $P(H)$, i.e., probability of getting head</p><p>(ii) $P (T)$, i.e., probability of getting tail. </p><p>(iii) The value of $P (H) + P (T)$.</p>
Question 477 :
If the events $A$ and $B$ mutually exclusive events such that $P(A)=\dfrac {1}{3}(3x+1)$ and $P(B)=\dfrac {1}{4}(1-x)$, then the aet of possible values of $x$ lies in the interval:
Question 479 :
Vineeta said that probability of impossible events is $1$. Dhanalakshmi said that probability of sure events is $0$ and Sireesha said that the probability of any event lies between $0$ and $1$.<br>in the above, with whom will you agree?
Question 480 :
Ticket numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?
Question 481 :
A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number between 1 to 15. What is the probability that it will point to an odd number.
Question 482 :
A card is drawn randomly from a well shuffled pack of 52 playing cards and following events are defined:<br>A : The drawn card is a face card.<br>Find odds in favor of A<br>
Question 483 :
Cards are drawn one-by-one without replacement from a well shuffled pack of 52 cards. Then the probability that aface card (Jack, Queen or King) will appear for the first time on the third turn is equal to
Question 484 :
The chance of an event happening is the square of the chance of a second event but the odds against the first are the cubes of the odds against the second. The chance of happening of each event are
Question 485 :
A die is thrown once.find the probability of getting a prime number less than $5.$
Question 486 :
The probability that a person will hit a target in shooting practice is $0.3$. If he shoots $10$ times, then the probability of his shooting the target is
Question 487 :
The probability of atleast one double six being thrown in $n$ thrown with two ordinary dice is greater than $99$%.<br>Then, the least numerical value of $n$ is
Question 488 :
A card is drawn from an ordinary pack of $52$ cards and a gambler bets that it is a spade or an ace. What are the odds against his winning the bet?<br/>
Question 489 :
One of the two events, A and B must occur. If $P\left ( A \right )=\dfrac{2}{3}P\left ( B \right ),$ the odds in favour of $B$ are
Question 490 :
A coin tossed $100$ times. The no. of times head comes up is $54$.What is the probability of head coming up?
Question 491 :
In a race, the odds in favour of horses $A, B, C, D$ are $1:3, 1:4, 1:5$ and $1:6$ respectively. Find probability that one of them wins the race.
Question 492 :
A problem in statistics is given to three students whose chance of solving it are $ \dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}$ respectively. The probability that the question is solved is
Question 493 :
If $10$% of the attacking a air crafts are expected to be shot down before reaching the target, the probability that out of $5$ aircrafts atleast four will be shot before they reach the target is
Question 494 :
If E and $\bar{E}$ denote the happening and not happeningof an event and$P\left ( \bar{E} \right )=\frac{1}{5}, P\left ( E \right )=$
Question 495 :
Three dice of colours red, blue and green are rolled together. Let $A$ be the event that red die shows the number $1$ and $B$ be the event that the sum.Find probability of the event A.
Question 496 :
A bag contains 2012 cards numbered as 1 , 2 , 3 , ....... upto 2012 , well mixed up . A person 'P' draw a card from the bag and puts it back in the bag , after that a person 'Q' draws a card from the bag . The odds in favour of "P draws larger number" is<br><br>
Question 497 :
A die is rolled. If the outcome is an odd number, what is the probability that it is prime?
Question 498 :
Let $A$ and $B$ be two events with $P(A) = \dfrac {1}{3}, P(B) = \dfrac {1}{6}$ and $P(A\cap B) = \dfrac {1}{12}$. What is $P(B|\overline {A})$ equal to?
Question 499 :
Odds $8$ to $5$ against a person who is $40$yr old living till he is $70$ and $4$ to $3$ against another person now $50$ till he will be living $80$. Probability that one of them will be alive next $30$yr.
Question 500 :
Two dices are thrown simultaneously. What is the probability of getting two numbers whose product is even?
Question 501 :
The odds in favour of getting atleast one time an even prime when a fair die is tossed three times is
Question 502 :
For a biased die the probabilities for the different faces to turn up are given below :<br/>$\begin{array} { l l l l l } {Face} \quad \quad\quad \quad  { 1} & { 2 } & { 3 } & { 4 } & { 5 } & { 6 } \\ {Probabilities} { 0.10 } & { 0.32 } & { 0.21 } & { 0.15 } & { 0.05 } & { 0.17 } \end{array}$<br/>The die is tossed & you are told that either face one or face two has turned up. Then the probability that it is face one is : 
Question 503 :
Two cards are drawn at random from a pack of $52$ cards. The probability of these two being "Aces" is
Question 504 :
There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelope, is.
Question 505 :
Two persons $A$ and $B$ have respectively $n + 1$ and $n$ coins, which they toss simultaneously. Then probability $P$ that $A$ will have more heads than $B$ is:
Question 506 :
If $a$ and $b$ are chosen randomly from the set consisting of numbers $1,\ 2,\ 3,\ 4,\ 5,\ 6$ with replacement. Then the probability that $\displaystyle \lim _{ x\rightarrow 0 }{ { \left[ \left( { a }^{ x }+{ b }^{ x } \right) /2 \right] }^{ 2/x }=6 }$ is
Question 507 :
The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second.The chances of the events are
Question 508 :
If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels?<br/>
Question 509 :
If two fair dice are rolled, what is the probability that the sum of the dice is at most $5$?
Question 510 :
$P(A\cap B) = \dfrac{1}{2}, P(\overline{A} \cap \overline{B})=\dfrac{1}{2}$ and $2P(A)=P(B)=p$, then the value of $p$ is equal to
Question 511 :
The odds is favour of winning a race for three horses $A, B$ and $C$ respectively $1:2, 1:3$ and $1:4$. Find the probability for winning of any one of them.
Question 512 :
In a given race, the odds in favour of four horses $A, B, C$ & $D$ are $1 : 3, 1 : 4, 1 : 5$ and $1 : 6$ respectively. Assuming that a dead heat is impossible, find the chance that one of them wins the race<br/>
Question 513 :
If $A$ and $B$ are independent events such that $P\left( A \right) =\dfrac { 1 }{ 5 }$, $P\left( A\cup B \right) =\dfrac { 7 }{ 10 }$, then what is $P\left( \bar { B } \right) $ equal to?
Question 514 :
The odds against a certain events are $5:2$ and the odds in favour of another events are $6:5$. The probability that at least one of the events will happens is:
Question 515 :
$A$ and $B$ each throw a dice. The probability that "$B$" throw is not smaller than "$A$" throw, is
Question 516 :
$(a)$ The probability that it will rain tomorrow is $0.85$. What is the probability that it will not rain tomorrow?<br><br>$(b)$ If the probability of winning a game is $0.6$, what is the probability of losing it?
Question 517 :
A family is going to choose two pets at random from among a group of four animals: a cat, a dog, a bird, and a lizard. Find the probability that the pets that the family chooses will include the lizard.
Question 518 :
If x is chosen at random from the set $\left \{2, 3, 4, 5, 6\right \}$, and y is chosen at random from the set $\left \{11, 13, 15\right \}$, find the probability that $xy$ is even.
Question 519 :
A bag contains yellow and black balls. The probability of getting a yellow ball from the bag of balls is $\dfrac23$. What is the probability of not getting a yellow ball?<br/>
Question 520 :
$A$ speaks truth in $70\%$ cases and $B$ in $80\%$ cases. In what percentage of cases they are likely to contradict each other in giving the same statement.
Question 521 :
The probability of getting head or tail in a throw ofa coin is ______.
Question 522 :
Three different numbers are selected at random from the set $A = \{1,2,3, ...... 10 \}$. The probability that the product of two of the numbers is equal to third is :<br/>
Question 523 : <p>From a batch of $100$ items of which $20$ are defective, exactly two items are chosen, one at a time, without replacement. Calculate the probability that the first item chosen is defective.</p>
Question 524 :
An ordinary die is rolled. From the following choices, the number thrown is most likely to be<br>
Question 525 :
A determinant is chosen at random from the set of all departments of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is :
Question 526 :
A bag contains $15$ cabbages, $20$ carrots, and $25$ turnips. If a single vegetable is picked at random from the bag, what is the probability that it will not be a carrot?
Question 527 :
If a person throw $3$ dice the probability of getting sum of digit exactly $15$ is
Question 528 :
The odds in favor of standing first of three students appearing in an examination are $1:2,2:5$ and $1:7$ respectively. The probability that either of them will stand first, is
Question 529 :
Four positive integers are taken at random and are multiplied together. Then the probability that the product ends in an odd digit other than 5 is
Question 530 :
Two dice are thrown. Find the odds in favour of getting the sum $6.$
Question 531 :
The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chance of each event is
Question 532 :
If $2$ cards are drawn from a pack of $52$, then the probability that they are from the same suit is___
Question 533 :
A party of $23$ persons take their seats at a round table. The odds against two specified persons sitting together is
Question 534 :
The probability that an electronic device produced by a company does not function properly is equal to $0.1$. If $10$ devices are bought, then the probability, to the nearest thousandth, than $7$ devices function properly is
Question 535 :
For two events $A$ and $B , P ( B ) = P ( B / A ) = 1 / 3$ and $P ( A / B ) = 4 / 7 ,$ then <br>Option a : $P \left( B ^ { \prime } / A \right) = 2 / 3$<br>Option b : $P \left( A / B ^ { \prime } \right) = 3 / 7$<br>Option c : $A$ and $B$ are mutually exclusive<br>Option d: $A$ and $B$ are independent
Question 536 :
A coin whose faces are marked 3 and 5 is tossed 4 times; what are the odds against the sum of the numbers thrown being less than 15?<br>
Question 537 :
Each of a and b can take values 1 or 2 with equal probability. The probability that the equation $ax^2 + bx + 1 = 0$ hasreal roots, is equal to
Question 538 :
A number is randomly selected from the set $\left \{6, 7, 8, 8, 8, 10, 10, 11\right \}$. Find the probability the number will be less than the mean.
Question 539 :
If odds against solving a question by three students are $2:1, 5:2$ and $5:3$ respectively, then probability that the question is solved only by one students is
Question 540 :
A fair coin is tossed five times. Calculate the probability that it lands head-up at least twice.
Question 541 :
A man and his wife appear for an interview for two posts. The probability of the man's selection is $\dfrac{1}{5}$ and that of his wife selection is $\dfrac{1}{7}$. The probability that at least one of them is selected, is:
Question 542 :
The odds that a book will be favorably reviewed by three independent critics are $5$ to $2,$ $4$ to $3$ and $3$ to $4$ respectively. What is the probability that of the three reviews a majority will be favorable?<br/>
Question 543 :
The chance of an event happening is the square of the chance, of a second event but the odds against the first are the cubes of the odds against thefirst are the cubes of the odds against the second. Find the chance of each.
Question 544 :
There are only three events $A,B,C$ one of which must and only one can happen; the odds are $8$ to $3$ against $A,5$ to $2$ against $B$; find the odds against $C$
Question 545 :
In throwing $3$ dice, the probability that atleast $2$ of the three numbers obtained are same is
Question 546 :
In a set of games it is $3$ to $5$ in favour of the winner of the previous game.. Then the probability that a person who has won the first game shall win at least $2$ out of the next $5$ games is ?
Question 547 :
A fair coin is flipped $5$ times.<br/> The probability of getting more heads than tails is $\dfrac{1}{2}$<br/><br/>
Question 548 :
There are four letters and four addressed envelopes. The probability that all letters are not dispatched in the right envelope is:<br/>
Question 549 :
In a group of $13$ cricket players, four are bowlers. Find out in how many ways can they form a cricket team of $11$ players in which atleast $2$ bowlers are included.
Question 550 :
X and Y plays a game in which they are asked to select a number from $21-50$. If the two number match both of them wins a prize. Find the probability that they will not win a prize in the single trial.
Question 551 :
There are two bags $A$ and $B$. Bag A contains $3$ white and $4$ red balls whereas bag $B$ contains $4$ white and $3$ red balls. Three balls are drawn at random (without replacement) from one of the bags and are found to be two white and one red. Find the probability that these were drawn from bag $B$.
Question 552 :
There are two events $A$ and $B$. If odds against $A$ are as $2:1$ and those in favour of $ A \cup B$ are $3:1$ , then
Question 553 :
Solve:$\displaystyle \sin ^{4}\theta +2\cos ^{2}\theta \left ( 1-\frac{1}{\sec ^{2}\theta } \right )+\cos ^{4}\theta $
Question 554 :
$\left( \dfrac { cosA+cosB }{ sinA-sinB }  \right) ^{ 2014 }+\left( \cfrac { sinA+sinB }{ cosA-cosB }  \right) ^{ 2014 }=...........$
Question 555 :
If $\displaystyle x=y\sin \theta \cos \phi ,y=\gamma \sin \theta \sin \phi ,z=\gamma \cos \theta $. Eliminate  $\displaystyle \theta $ and  $\displaystyle \phi $
Question 557 :
find whether ${ \left( \sin { \theta  } +co\sec { \theta  }  \right)  }^{ 2 }+{ \left( \cos { \theta  } +\sec { \theta  }  \right)  }^{ 2 }=7+\tan ^{ 2 }{ \theta  } +\cos ^{ 2 }{ \theta  } $ is true or false.
Question 558 :
The expression$ \displaystyle \left (\tan \Theta +sec\Theta \right )^{2} $ is equal to
Question 559 :
$\tan \theta$ increases as $\theta$ increases.<br/>If true then enter $1$ and if false then enter $0$.<br/>
Question 560 :
If $sec\theta -tan\theta =\dfrac{a}{b},$ then the value of $tan\theta $ is
Question 563 :
Find the value of $ \displaystyle  \theta , cos\theta  \sqrt{\sec ^{2}\theta -1}     = 0$
Question 564 :
Find the value of $\sin^3\left( 1099\pi -\dfrac { \pi  }{ 6 }  \right) +\cos^3\left( 50\pi -\dfrac { \pi  }{ 3 }  \right) $
Question 566 :
Which of the following is equal to $\sin x \sec x$?
Question 568 :
Value of ${ cos }^{ 2 }{ 135 }^{ \circ  }$
Question 570 :
Given $tan \theta = 1$, which of the following is not equal to tan $\theta$?
Question 572 :
Simplest form of $\displaystyle \dfrac{1}{\sqrt{2 + \sqrt{2 + \sqrt{2 + 2 cos 4x}}}}$ is
Question 573 :
The solution of $(2 cosx-1)(3+2 cosx)=0$ in the interval $0 \leq \theta \leq 2\pi$ is-
Question 576 :
The given relation is $(1 + \tan a + \cos a)(\sin a - \cos a )= 2\sin a\tan a - cat\,a\cos a$
Question 577 :
Select and wire the correct answer from the given alternatives. <br/>$\cos \left(\dfrac {3\pi}{2}+\theta \right)=$ ____
Question 578 :
The value of $[\dfrac{\tan 30^{o}.\sin 60^{o}.\csc 30^{o}}{\sec 0^{o}.\cot 60^{o}.\cos 30^{o}}]^{4}$ is equal to
Question 579 :
The given expression is $\displaystyle \sin { \theta  } \cos { \left( { 90 }^{ o }-\theta  \right)  } +\cos { \theta  } \sin { \left( { 90 }^{ o }-\theta  \right)  } +4 $ equal to :<br/>
Question 580 :
The value of $\sqrt { 3 } \sin { x } +\cos { x } $ is max. when $x$ is equal to
Question 583 :
Eliminate $\theta$ and find a relation in x, y, a and b for the following question.<br/>If $x = a sec \theta$ and $y = a tan \theta$, find the value of $x^2 - y^2$.
Question 585 :
Express$\displaystyle \cos { { 79 }^{ o } } +\sec { { 79 }^{ o } }$ in terms of angles between$\displaystyle { 0 }^{ o }$ and$\displaystyle { 45 }^{ o }$
Question 586 :
Choose and write the correct alternative.<br>If $3 \sin \theta = 4 \cos \theta$ then $\cot \theta = ?$<br>
Question 587 :
If $\displaystyle  \cos A+\cos ^2A=1$ then the value of $\displaystyle  \sin ^{2}A+\sin ^{4}A$ is
Question 588 :
IF A+B+C=$ \displaystyle 180^{\circ}  $ ,then $  tan A+tanB+tanC $ is equal to
Question 590 :
If$\displaystyle \cot A=\frac{12}{5}$ then the value of$\displaystyle \left ( \sin A+\cos A \right )$ $\displaystyle \times cosec$ $\displaystyle A$ is
Question 592 :
If $\sin \theta + \cos\theta = 1$, then what is the value of $\sin\theta \cos\theta$?
Question 596 :
If $sin({ 90 }^{ 0 }-\theta )=\dfrac { 3 }{ 7 } $, then $cos\theta $
Question 598 :
If $3\sin\theta + 5 \cos\theta =5$, then the value of $5\sin\theta -3 \cos\theta $ are 
Question 599 :
The angle of elevation and angle of depression both are measured with
Question 600 :
If $\theta$ increases from $0^0$ to $90^o$, then the value of $\cos\theta$: <br/>
Question 601 :
Given $\cos \theta = \dfrac{\sqrt3}{2}$, which of the following are the possible values of  $\sin 2 \theta$?
Question 602 :
If $\sec{2A}=\csc{(A-42^\circ)}$ where $2A$ is acute angle then value of $A$ is
Question 605 :
If $\displaystyle \frac { x\text{ cosec }^{ 2 }{ 30 }^{ o }{ \sec }^{ 2 }{ 45 }^{ o } }{ 8{ \cos }^{ 2 }{ 45 }^{ o }{ \sin }^{ 2 }{ 90 }^{ o } } ={ \tan }^{ 2 }{ 60 }^{ o }-{ \tan }^{ 2 }{ 45 }^{ o }$, then $x$ is :
Question 606 :
If $\displaystyle \sec 2A=\text{cosec } \left ( A-42^{\circ} \right )$ where $2A$ is acute angle, then value of $A$ is
Question 607 :
Let $f\displaystyle \left ( \theta \right )=\dfrac{\cot \theta }{1+\cot \theta }$ and $\alpha +\beta =\dfrac{5\pi }{4},$ then the value $f\left ( \alpha \right )f\left ( \beta \right )$ is
Question 608 :
The domain of $\displaystyle \frac{\cos ^{-1}x}{\left [ x \right ]}$ where $\left [.\right ]$ represent greatest integer function is given by
Question 609 :
Find the value of $\cos^2 \theta (1 + \tan^2 \theta) + \sin^2 \theta (1 + \cot^2 \theta)$.
Question 612 :
Which of the following is equivalent to $\dfrac {\tan n\,\, \text{cosec}\, n}{\sin n \,\,\sec n}$?
Question 615 :
The value of $\cos { { 10 }^{ 0 } } -\sin { { 10 }^{ 0 } } $ is?<br/>
Question 616 :
The value of $\displaystyle \frac{\sin ^{3}\theta +\cos ^{3}\theta }{\sin \theta +\cos \theta }+\frac{\left ( \cos ^{3}\theta -\sin ^{3}\theta  \right )}{\cos \theta -\sin \theta }$
Question 617 :
Choose correct option for following statement.$\cos \theta$ decreases as $\theta$ increases in the interval $(0,\pi)$.<br/>
Question 620 :
If A and B are acute angles such that $sin  A=\sin^{2}B,  2 \cos^{2}A=3  \cos^{2}B;$ then
Question 621 :
If $\sin A + \sin^{2}A + \sin^{3}A = 1$, then find the value of $\cos^{6}A-4\cos^{4}A + 8\cos^{2}A$ is:
Question 623 :
<br/> lf $0< x, y <\displaystyle \frac{\pi}{2}$ then the system of equations<br/>$\sin x.\sin y =\dfrac 34$ and $\tan x.\tan y =3$ has a solution at<br/>
Question 626 :
The value of $\displaystyle \frac { 2\cos { { 67 }^{ o } }  }{ \sin { { 23 }^{ o } }  } -\frac { \tan { { 40 }^{ o } }  }{ \cot { { 50 }^{ o } }  } -\sin { { 90 }^{ o } } $ is :
Question 627 :
If $\sin { \left( \theta +\phi \right) } =n\sin { \left( \theta -\phi \right) } , n\neq 1$, then the value of $\dfrac { \tan { \theta } }{ \tan { \phi } } $ is
Question 628 :
If $\displaystyle \sin \left ( A+B \right ) =\frac{\sqrt{3}}{2}$ and $\displaystyle \cot \left ( A-B \right )=1$, then find $A$
Question 629 :
The value of the expression$\displaystyle \frac {tan^2 20^0 - sin^2 20^0}{tan^2 20^0 . sin^2 20^0}$ is
Question 631 :
Solve : $4\sin x \cos x + 2 \sin x + 2 \cos x + 1 = 0$
Question 632 :
If a.cot $\theta+$b.cosec $\theta = $ p and b.cot $\theta\ +\ $a.cosec $\theta =q$, then the value of $p^{2}-q^{2}$ is equal to:<br/>
Question 633 :
The value of $\cos \dfrac {2\pi}{7} + \cos \dfrac {4\pi}{7} + \cos \dfrac {6\pi}{7}$ is
Question 634 :
The value of $\sec$ $(90^0 - \theta) \sin \theta$ is <br/><br/><br/>
Question 635 :
If $\sin \theta = \dfrac {3}{5}$, then the value of $\text{cosec}\, \theta$ is
Question 636 :
The value of cos{ $ {cos^{-1} \left ( \dfrac {\sqrt 3}{2}\right )+ \dfrac{ \pi }{6}} $} is
Question 637 :
Find $\theta$, if $\displaystyle\frac{2\tan\displaystyle\frac{\theta}{2}}{1 + \tan^2\displaystyle\frac{\theta}{2}} = 1,\quad 0^{\small\circ} < \theta \le 90^{\small\circ}$<br/>
Question 638 :
If $b\tan \theta =a$, then the value of $\dfrac{a\sin \theta -b\cos \theta }{a\sin \theta +b\cos \theta}$<br/>
Question 640 :
Find the value of:$\sin ^{ 2 }{ 30 } \cos ^{ 2 }{ 45 } +4\tan ^{ 2 }{ 30 } +\cfrac { 1 }{ 2 } \sin ^{ 2 }{ 90 } +\cfrac { 1 }{ 2 } \cot ^{ 2 }{ 60 } $
Question 643 :
If $\displaystyle x= \frac{2\sin \alpha}{1+\cos \alpha+\sin \alpha}$ then $\displaystyle \frac{1-\cos \alpha+\sin \alpha}{1+\sin \alpha}$ is equal to<br/><br/><br/>
Question 644 :
$\cos 75^{\circ} + \cot 75^{\circ}$, when expressed in terms of angles between $0^{\circ}$ and $30^{\circ}$, becomes
Question 646 :
If $\theta =\dfrac{\pi}{2^n+1}$, then the value of $\cos\theta \cos 2\theta \cos 2^2\theta$------$\cos 2^{n-1}\theta$ is?
Question 648 :
The value of $\displaystyle \frac { \cot { { 40 }^{ o } }  }{ \tan { { 50 }^{ o } }  } -\frac { 1 }{ 2 } \left( \frac { \cos { { 35 }^{ o } }  }{ \sin { { 55 }^{ o } }  }  \right) $ is 
Question 650 :
Given that $\cos {(A-B)}=\cos {A}\cos {B}+\sin {A}\sin {B}$, find the value of $\cos{15}^{o}$.
Question 651 :
If $\cos 9 \alpha = \sin  \alpha$ and $9 \alpha < 90^o$, what is the value of $\tan  5 \alpha$?
Question 652 :
The values of ${x}$ in $(-\pi,\pi)$ which satisfy the equation $8^{1+|cosx|+|cos^{2}x|+|cos^{3}x|+.......\infty }=4^{3}$ are<br/>
Question 656 :
Let $\displaystyle -\frac { \pi }{ 6 } <\theta <-\frac { \pi }{ 12 }$, Suppose$\displaystyle { \alpha }_{ 1 }$ and$\displaystyle { \beta }_{ 1 }$ are the roots of the equation$\displaystyle { x }^{ 2 }-2x\sec { \theta } +1=0$ and$\displaystyle { \alpha }_{ 2 }$ and $\displaystyle { \beta }_{ 2 }$ are the roots of the equation$\displaystyle { x }^{ 2 }+2x\tan { \theta } -1=0$. If$\displaystyle { \alpha }_{ 1 }>{ \beta }_{ 1 }$ and$\displaystyle { \alpha }_{ 2 }>{ \beta }_{ 2 }$, then$\displaystyle { \alpha }_{ 1 }+{ \beta }_{ 2 }$ equals to
Question 657 :
In $\triangle ABC, \angle B = 90^{\circ}, BC = 7$ and $AC - AB = 1$, then $\cos C = .....$
Question 659 :
If $\cos x + \sec x = - 2$ for a positive odd integer $n$ then $\cos^nx + \sec^nx$ is
Question 660 :
If $\displaystyle \sin \theta+\sin ^{2} \theta +\sin ^{3}\theta= 1$ then the value of $\displaystyle \cos ^{6}\theta-4\cos ^{4}\theta+8\cos ^{2}\theta$ equals<br/>
Question 662 :
If $\displaystyle \frac{\sin x}{a}= \frac{\cos x}{b}= \frac{\tan x}{c}= k,$ then $\displaystyle bc+\frac{1}{ck}+\frac{ak}{1+bk} $ is equal to<br><br><br>
Question 663 :
If $0\leq x, y\leq 180^o$ and $\sin (x-y)=\cos(x+y)=\dfrac 12$, then the values of $x$ and $y$ are given by
Question 664 :
In $\triangle ABC$, the measure of $\angle B$ is $90^{\circ}, BC = 16$, and $AC = 20$. $\triangle DEF$ is similar to $\triangle ABC$, where vertices $D, E,$ and $F$ correspond to vertices. $A, B$, and $C$, respectively, and each side of $\triangle DEF$ is $\dfrac {1}{3}$ the length of the corresponding side of $\triangle ABC$. What is the value of $\sin F$?
Question 665 :
If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then
Question 666 :
${\cos ^2}{48^ \circ } - {\sin ^2}{12^ \circ }$ is equal to -
Question 667 :
If $\sin x + \sin^{2}x=1,$ then the value of $\cos^{12} x + 3 \cos^{10} x + 3 cos^{8} x + cos ^{6} x -1$ is equal to :
Question 668 :
If $\displaystyle \frac { \sin ^{ 4 }{ x }  }{ 2 } +\frac { \cos ^{ 4 }{ x }  }{ 3 } =\frac { 1 }{ 5 } ,$ then:
Question 670 :
Which one of the following when simplified is not equal to one?
Question 671 :
In a $\Delta ABC$, if $\cos A \cos B \cos C=\displaystyle\dfrac {\sqrt 3-1}{8}$ and $\sin A. \sin B. \sin C=\displaystyle \dfrac {3+\sqrt 3}{8}$, <br/><br/>then- On the basis of above information, answer the following questions:The value of $ \tan A \tan B + \tan B \tan C + \tan C \tan A$ is:
Question 672 :
If $\tan { \theta  } +\sin { \theta  } =m, \tan { \theta - \sin { \theta =n }  } $, then $(m^{2}-n^{2})^{2}=$.<br/>
Question 674 :
If $\displaystyle X=\tan 1^{0}+\tan 2^{0}+........+\tan 45^{0}$ and $\displaystyle y= -(\cot 46^{0}+\cot 47^{0}+.......+\cot 89^{0})$ then find the value of $(x + y)$.
Question 677 :
If $ \cos^{-1}\left ( 4x^{3}-3x \right )= 2\pi -3\cos^{-1}x $, then $ x $ lies in interval
Question 678 :
The value of the expression $(\tan1^{0} \tan2^{0} \tan 3^{0}...\tan89^{0})$ is equal to<br/>
Question 679 :
If $x_{1}=1$ and $x_{n+1}=\frac{1}{x_{n}}\left ( \sqrt{1+x_{n}^{2}}-1 \right ),n\geq 1,n \in N$, then $x_{n}$ is equal to :<br>
Question 680 :
For all real values of $\theta$ , $\cot\theta-2 \cot 2\theta$ is equal to
Question 681 :
If $\sin (\alpha+\beta)=1$ and $\sin(\alpha -\beta)=1/2$ where $\alpha, \beta \epsilon [0, \pi /2]$ then
Question 683 :
In $\displaystyle A_{n}=\cos^{n}\theta+\sin^{n}\theta, n\in N$ and $\displaystyle \theta \in R$<br/><br/>If $\displaystyle A_{n-4}-A_{n-2}=\sin^{2}\theta\cos^{2}\theta A_{\lambda} $ , then $\displaystyle \lambda $ equals<br/>
Question 685 :
In a right angle triangle $\triangle ABC,\,\sin ^{ 2 }{ A } +\sin ^{ 2 }{ B } +\sin ^{ 2 }{ C } $ is
Question 686 :
If $x \cos \alpha +y \sin \alpha=x \cos\beta+y \sin\beta=2a(0 < \alpha, \beta < \pi /2)$, then
Question 687 :
If $\displaystyle \frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1,\frac{x}{a}\sin \theta-\frac{y}{b}\cos \theta=1,$ then eliminate $\theta $<br>
Question 689 :
If $2 \sec 2\alpha = \tan\beta + \cot \beta$, then one of the value of $\alpha+\beta$ is-
Question 691 :
The value of $\displaystyle \sum _{ r=0 }^{ 10 }{ \cos ^{ 3 }{ \dfrac { \pi r }{ 3 } } }$ is equal to:
Question 692 :
If$\displaystyle \cos \theta =\frac{3}{5},$ then the value of$\displaystyle \frac{\sin \theta -\tan \theta +1}{2\tan ^{2}\theta }$
Question 693 :
If the quadratic equation $ax^2+bx+c=0$ ($a > 0$) has $\sec^2\theta$ and $\text{cosec}^2\theta$ as its roots, then which of the following must hold good?<br>
Question 694 :
$A$ tower of height $h$' standing at the centre of a square with sides of length $a$' makes the same angle $\alpha$ at each of the four corners then $a^{2}=$
Question 695 :
If $16\cot \theta = 12$, then $\dfrac {\sin \theta - \cos \theta}{\sin \theta + \cos \theta} = $ _____
Question 696 :
Assertion: In a triangle ABC if a, b, c are in A.P., then $\displaystyle \cot \frac{A}{2}\cot \frac{C}{2}=2$
Reason: Three numbers a, b, c are in A.P. if $ a+ c = 2b$.
Question 698 :
The value of $ \cos y \cos\left(\dfrac{\pi}{2} -x\right) - \cos \left(\dfrac{\pi}{2}-y \right)\cos x + \sin y \cos\left(\dfrac{\pi}{2}-x\right)+ \cos x \sin\left(\dfrac{\pi}{2} -y\right)$ is zero if
Question 699 :
If $\sin x+\sin ^{2}x=1$,thenthe value of $\cos ^{12}x+3\cos ^{10}x+3\cos ^{8}x+\cos ^{6}x-2$ is equal to
Question 700 :
What is $\left(\dfrac{sec 18^{\circ}}{sec 144^{\circ}} + \dfrac{cosec 18^{\circ}}{cosec 144^{\circ}}\right)$ equals to?
Question 701 :
Let $x=(1+\sin A)(1-\sin B)(1+\sin C), y=(1-\sin A)(1-\sin B)(1-\sin C)$ and if $x=y$, then
Question 702 :
If $\sin x= \cos y,\sqrt{6}\sin y= \tan z$ and $2\sin z= \sqrt{3}\cos x$; $u,v,w$ denotes respectively $\sin ^{2}x, \sin ^{2}y, \sin ^{2}z$ then the value of the triplet $\left ( u,v,w \right )$ is
