Question 2 :
If $a=\sqrt{11}+\sqrt{3}, b =\sqrt{12}+\sqrt{2}, c=\sqrt{6}+\sqrt{4}$, then which of the following holds true ?<br/>
Question 4 :
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 5 :
If $a=107,b=13$ using Euclid's division algorithm find the values of $q$ and $r$ such that $a=bq+r$
Question 6 :
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 8 :
If the quotient of $\displaystyle x^4 - 11x^3 + 44x^2 - 76x +48$. When divided by $(x^2 - 7x +12)$ is $Ax^2 + Bx + C$, then the descending order of A, B, C is
Question 10 :
Factorise the expressions and divide them as directed.$12xy(9x^2-  16y^2)\div  4xy(3x + 4y)$
Question 11 :
The values of x and y satisfying the two equation 32x+33y=31, 33x+32y=34 respectively will be
Question 13 :
The graph of the lines $x + y = 7$ and $x - y = 3$ meet at the point
Question 14 :
The value of $k$ for which the system of equations $3x + 5y= 0$ and $kx + 10y = 0$ has a non-zero solution, is ________.
Question 15 :
A member of these family with positive gradient making an angle of$\frac{\pi }{4}$ with the line3x-4y=2, is
Question 16 :
The sides of a triangle are given below. Check whether or not the sides form a right-angled triangle.$13cm, 12cm, 5cm$
Question 17 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $b$ when $c=13 \ cm$ and $a=5 \ cm$.
Question 18 :
In $\triangle ABC$, $\angle C={90}^{o}$. If $BC=a, AC=b$ and $AB=c$, find $a$ when $c=25 \ cm$ and $b=7 \ cm$.
Question 19 :
The sides of a triangle are given below. Check whether or not the sides form a right angled triangle.$50cm, 80cm, 100cm$
Question 20 :
$4\, RN^{2}\, =\, PQ^{2}\, +\, 4\, PR^{2}$<br/><b>State whether the above statement is true or false.</b><br/>
Question 21 :
If the points (1,1) (2,3) and (5,-1) form a right triangle, then the hypotenuse is of length
Question 22 :
A pair of numerical coordinates is required to specify each point in a ......... plane.
Question 23 :
Find the distance from the point (5, -3) to the line 7x - 4y - 28 = 0
Question 24 :
A rectangular hyperbola whose cente is C is cut by any circle of radius r in four point P, Q, R, S. The value of$CP^{2}+CQ^{2}+CR^{2}+CS^{2}$ is equal to :
Question 25 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?
Question 26 :
Solve:$\displaystyle \sin ^{4}\theta +2\cos ^{2}\theta \left ( 1-\frac{1}{\sec ^{2}\theta } \right )+\cos ^{4}\theta $
Question 28 :
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 29 :
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 30 :
If $\sec{2A}=\csc{(A-42^\circ)}$ where $2A$ is acute angle then value of $A$ is
Question 31 :
What is the minimum radius $(>1)$ of a circle whose circumference is an integer?
Question 32 :
A wire of length $36$ cm is bent in the form of a semicircle. What is the radius of the semicircle?
Question 33 :
If the circumference of a circle is reduced by 50 % then the area will be reduced by
Question 34 :
What is the area of the sector of a circle, whose radius is $6\ m$ when the angle at the centre is $42^{\circ}$?
Question 35 :
A horse is tied to a pole fixed at one corner of a $50 m \times 50 m$ square field of grass by means of a $20 m$ long rope. What is the area to the nearest whole number of that part of the field which the horse can graze?
Question 36 :
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 37 :
Two dice are thrown. Find the odds in favour of getting the sum $4$.<br/>
Question 38 :
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 39 :
A die is thrown .The probability that the number comes up even is ______ .
Question 40 :
What is the maximum value of the probability of an event?
