Question 2 :
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 4 :
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 7 :
Find the Quotient and the Remainder when the first polynomial is divided by the second.$$-6x^4 + 5x^2 + 111$$ by $$2x^2+1$$
Question 8 :
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 10 :
If the roots of $${ x }^{ 2 }-2mx+{ m }^{ 2 }-1=0$$ lie between $$-2$$ and $$4$$, then
Question 11 :
If 2 and $$-\dfrac {1}{2}$$ as the sum and product of its zeros respectively then the quadratic polynomial f(x) is<br/>
Question 14 :
Simplify: $$\displaystyle \frac { 36ab\left( a+2 \right) \left( a+3 \right)  }{ 12a\left( a+3 \right)  } $$
Question 16 :
If $$x^4 \, + \, 2x^3 \, - \, 3x^2 \, + \, x \, - \, 1$$ is divided by $$x - 2$$. then the remainder is
Question 17 :
The area of a rectangle is $$\displaystyle 12y^{4}+28y^{3}-5y^{2}$$. If its length is $$\displaystyle 6y^{3}-y^{2}$$, then its width is
Question 21 :
Divide $$\displaystyle 10{ a }^{ 2 }{ b }^{ 2 }\left( 5x-25 \right)$$ by $$15ab\left( x-5 \right) $$
Question 22 :
Evaluate: $$\displaystyle \frac { 35\left( x-3 \right) \left( { x }^{ 2 }+2x+4 \right)  }{ 7\left( x-3 \right)  } $$
Question 23 :
If $$\alpha, \beta$$ be the roots $$x^2+px-q=0$$ and $$\gamma, \delta$$ be the roots of $$x^2+px+r=0$$, then $$\dfrac{(\alpha -\gamma)(\alpha -\delta)}{(\beta -\gamma )(\beta -\delta)}=$$
Question 24 :
If $$\alpha$$ and $$\beta$$ are the roots of the equation $$ \displaystyle 5x^{2}-x-2=0, $$  then the equation for which roots are $$ \displaystyle \dfrac{2}{\alpha }$$ and $$\dfrac{2}{\beta } $$ is
Question 25 :
Suppose $$\alpha ,\beta .\gamma $$ are roots of $${ x }^{ 3 }+{ x }^{ 2 }+2x+3=0$$. If $$f(x)=0$$ is a cubic polynomial equation whose roots are $$\alpha +\beta ,\beta +\gamma ,\gamma +\alpha $$ then $$f(x)=$$
Question 26 :
The number of integers $$n$$ for which $$3x^3-25x+n=0$$ has three real roots is$$?$$<br/>
Question 27 :
Divide $$\displaystyle x\left( x+1 \right) \left( x+2 \right) \left( x+3 \right)$$ by $$\left( x+3 \right) \left( x+2 \right) $$
Question 28 :
Find the value of p for which the given equation has real roots.<br>$$\displaystyle8p{ x }^{ 2 }-9x+3=0$$<br>
Question 29 :
Let $$f(x)=2{ x }^{ 2 }+5x+1$$. If we write $$f(x)$$ as<br>$$f(x)=a(x+1)(x-2)+b(x-2)(x-1)+c(x-1)(x+1)$$ for real numbers $$a,b,c$$ then
Question 31 :
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 33 :
$$2\times 2\times 2\times 3\times 3\times 13 = 2^{3} \times 3^{2} \times 13$$ is equal to
Question 35 :
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 38 :
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 39 :
State the following statement is True or False<br>35.251252253...is an irrational number<br>
Question 42 :
If $$a=107,b=13$$ using Euclid's division algorithm find the values of $$q$$ and $$r$$ such that $$a=bq+r$$
Question 43 :
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 44 :
State whether the given statement is True or False :<br/>$$2\sqrt { 3 }-1 $$ is an irrational number.
Question 45 :
The LCM of 54 90 and a third number is 1890 and their HCF is 18 The third number is
Question 46 :
Euclids division lemma can be used to find the $$...........$$ of any two positive integers and to show the common properties of numbers.
Question 48 :
The greatest number that will divided $$398, 436$$ and $$542$$ leaving $$7,11$$ and $$14$$ remainders, respectively, is
Question 50 :
State whether the given statement is True or False :<br/>$$3+\sqrt { 2 } $$ is an irrational number.
Question 52 :
Use Euclid's division lemma to find the HCF of the following<br/>8068 and 12464
Question 53 :
If $$a$$ is an irrational number then which of the following describe the additive inverse of $$a$$.
Question 54 :
The number of times $$79$$ must be subtracted from $$50,000,$$ so that the remainder is $$43759$$ is 
Question 57 :
State whether the given statement is True or False :<br/>$$\sqrt { 3 } +\sqrt { 4 } $$ is an irrational number.
Question 58 :
State whether the following statement is true or not:$$7-\sqrt { 2 } $$ is irrational.
Question 59 :
$$n$$  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 60 :
Write whether every positive integer can be of the form $$4q + 2$$, where $$q$$ is an integer.<br/>
Question 62 :
If these numbers form positive odd integer 6q+1, or 6q+3 or 6q+5 for some q then q belongs to:<br/>
Question 63 :
Say true or false:A positive integer is of the form $$3q + 1,$$ $$q$$  being a natural number, then you write its square in any form other than  $$3m + 1$$, i.e.,$$ 3m $$ or $$3m + 2$$  for some integer $$m$$.<br/>
Question 64 :
Three ropes are $$7\ m, 12\ m\ 95\ cm$$ and $$3\ m\ 85\ cm$$ long. What is the greatest possible length that can be used to measure these ropes?
Question 65 :
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
