Question 1 :
Choose the correct answer from the alternatives given.<br/>If x - $\dfrac{1}{x}$ = 3 then find the value of $x^3 + \dfrac{1}{x^3}$. 
Question 2 :
$f(x)=2x^3-5x^2+ax+a$Given that $(x+2)$ is a factor of $f(x)$, find the value of the constant $a$.
Question 5 :
What is $\dfrac {x^{2} - 3x + 2}{x^{2} - 5x + 6} \div \dfrac {x^{2} - 5x + 4}{x^{2} - 7x + 12}$ equal to
Question 6 :
If $kx^3 + 9x^2+4x -10 $ divided by $x+3$ leaves a remainder $5$, then the value of $k$ will be 
Question 7 :
The value of $m$, in order that ${ x }^{ 2 }-mx-2$ is the quotient when $3{ x }^{ 3 }+3{ x }^{ 2 }-4$ is divided by $x+2$, is
Question 9 :
If (x -1) is a factor of polynomial f(x) but not of g(x), then it must be a factor of
Question 10 :
By Remainder Theorem find the remainder, when $ p(x)$ is divided by $g(x)$, where$p(x) = x^3-  3x^2 + 4x + 50\ and\ g(x) = x-  3$.<br/>
Question 12 :
State whether the statement is True or False.Expand: $(2a+b)^3 $ is equal to $8a^3+12a^2b+6ab^2+b^3 $.<br/>
Question 13 :
If $x^{100} + 2x^{99} + k$; is divisible by (x + 1), then the value of k is
Question 14 :
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 15 :
If $\displaystyle a + \dfrac{1}{a} = m$ and $\displaystyle a \neq 0$; find in terms of $\displaystyle 'm'$ ; the value of: $\displaystyle a - \dfrac{1}{a}$
Question 17 :
Use the factor theorem and state whether $g(x)$ is a factor of $p(x)$ in the following case. State True Or False:$p(x)=x^3-4x^2+x+6; \ g(x)=x-3$<br/>
Question 20 :
If $(x + 2a)$ is a factor of $x^5 - 4a^2x^3 + 2x + 2a + 3,$ find $a$.<br/>
Question 21 :
If $\displaystyle  a^{2}+b^{2}=13 \ and \ ab=6 $ find :<br/>$\displaystyle  3\left ( a+b \right )^{2}-2\left ( a-b \right )^{2}$<br/>
Question 22 :
If both $x + 1$ and $x-  1$ are factors of $ax^3 + x^2+  2a + b = 0$, find the values of $a$ and $b$ respectively.
Question 23 :
If ${ x }^{ 3 }+ax-28$ is exactly divisible by $x-4$, then the value of $a$ is
Question 24 :
The value of $k$ for which $x - k$ is a factor of $x^{3} - kx^{2} + 2x + k + 4$ is<br/>
Question 25 :
If $p(x) = x^3-3x^2+6x-4$ and $p\left (\dfrac{\sqrt{3}}{2}\right) = 0$ then by factor theorem the corresponding factor of $p(x)$ is <br/>
Question 26 :
Find out whether or not the first polynomial is a factor of the second polynomial:$4a-1, 12a^2-7a-2$
Question 27 :
The value of$ \displaystyle \frac{(1.5)^{2}+(4.7)^{3}+(3.8)^{3}-3\times 1.5\times 4.7\times 3.8}{(1.5)^{2}+(4.7)^{2}+(3.8)^{2}-1.5\times 4.7-4.7\times 3.8-1.5\times 3.8} $
Question 29 :
If on division of a polynomial p (x) by a polynomial g (x), the quotient is zero, what is the relation between the degrees of p (x) and g (x) ?<br/>
Question 30 :
Factorise : $(a - b)^3 + (b - c)^3 + (c - a)^3$
Question 32 :
Given that $x = 2$ is a solution of $x^3 - 7x + 6 = 0$. The other solutions are
Question 33 :
The remainder when $x^{6} - 3x^{5} + 2x^{2} + 8$ is divided by $x - 3$ is<br>
Question 35 :
If $ a^2+b^2=10 $ and $ ab=3 $, then find $ a-b $. 
Question 36 :
The value of $\displaystyle\left (5^{\cfrac {1}{2}} + 3^{\cfrac {1}{2}}\right ) \left (5^{\cfrac {1}{2}} - 3^{\cfrac {1}{2}}\right )$ is
Question 37 :
Simplify: $(x - 3y - 5z)(x^2 + 9y^2 + 25z^2 + 3xy - 15yz + 5zx)$
Question 38 :
If $a + b + c = 0$ then $a^3 + b^3 + c^3$ is
Question 43 :
If $\left (x + \dfrac {1}{x}\right ) = 2\sqrt {3}$, then the value of $\left (x^{3} + \dfrac {1}{x^{3}}\right )$ is
Question 44 :
Find the value of 'a' if (x-2) is factor of $2x^3-6x^2+5x+a$.
Question 46 :
Use the identity $(x + a) (x + b) = x^2 + (a + b) x + ab$ to find the following products.$(xyz +4) (xyz +2)$
Question 47 :
State whether the statement is True or False.Evaluate: $(6-5xy)(6+5xy)$ is equal to $36-25x^2y^2$.
Question 51 :
If $(x+1)$ and $(x-2)$ are the factors of the expression $(2x^3-px^2+x+q)$, then the values of $p$ and $q$ are given by:
Question 52 :
Find the values of $a$ and $b$ so that $x^4+x^3+8x^2+ax+b$ is divisible by $x^2+1$<br/>
Question 53 :
Using remainder theorem, find the reminder when $x^3-ax^2+2x-a$ is divided by $x-a$.
Question 56 :
Polynomials $p(x), g(x), q(x)$ and $r(x)$, which satisfy the division algorithm and deg $r(x)=0$, are<br/>
Question 57 :
If $a + b + c = 0$, then $a^3 + b^3 + c^3$ is equal to
Question 58 :
Given that $(x + 1)$ is a common factor of $x^2 +ax + b$ and $x^2 +cx-d$, then <br/>
Question 60 :
Which among $-2$ and $1$  satisfy the equation $32 = 4x + 40$.<br/>
Question 61 :
If $x - 3$ is a factor of $x^{2} - ax - 15$, then $a =$
Question 63 :
Determine which of the following polynomials has $x - 2$, a factor :<br/>(i) $3x^2+6x-24$<br/>(ii) $4x^2+x-2$<br/>
Question 64 :
State whether the following statement is true or not:If $\dfrac { a }{ b } +\dfrac { b }{ a } =-1$, then ${ a }^{ 3 }-{ b }^{ 3 }=0$.
Question 65 :
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.$t^2-3, 2t^4+3t^3-2t^2-9t-12$<br/>
Question 66 :
If $\displaystyle f\left ( x \right )=x^{4}-2x^{3}+3x^{2}-ax+b $ is a polynomial such that when it is divide by $(x - 1)$ and $(x + 1)$ the remainders are $5$ and $19$ respectively the remainder when $f(x)$ is divisible by $(x - 2)$ is 
Question 68 :
State whether the statement is True or False.Expand: $(2a-5b-4c)^2$ is equal to $4a^2+25b^2+16c^2-20ab+40bc-16ca $.
Question 69 :
A number when divided by $259$ leaves a remainder $139$. What will be the remainder when the same number is divided by $37$?
Question 70 :
$\root 3 \of a + \root 3 \of b + \root 3 \of c = 0\;{\text{then}}{\left( {a + b + c} \right)^3} $
Question 77 :
What is the value of $P$ for which $(a-2)$ is a factor of $a^2-5a+P$ ?
Question 78 :
Polynomials $p(x), g(x), q(x)$ and $r(x)$, which satisfy the division algorithm and "deg $p(x) = $ deg $q(x)$" are<br/>
Question 80 :
When $4g^3 - 3g^2 + g + k$ is divided by $g - 2$, the remainder is $27$. Find the value of $k$.
Question 81 :
If $\displaystyle \sum _{ a,b,c }^{  }{ a=0 } $ then the value of $\displaystyle \sum _{ a,b,c }^{  }{ { a }^{ 3 }-abc } $ is
Question 82 :
Give an example of polynomials f(x), g(x), q(x) and r(x) satisfying f(x) = g(x) q(x) + r(x) where deg r(x) = 0<br>
Question 85 :
Divide the polynomial $p(x)$ by the polynomial $g(x)$ and find the quotient and remainder. <br/>$p(x)=x^3-3x^2+5x-3$<br/>$ g(x)=x^2-2$<br/>
Question 87 :
If $2x^3 + 4x^2 + 2ax + b$ is exactly divisible by $x^2 - 1$, then the value of a and b respectively will be
Question 88 :
<i><b>Find the value of pq if$\displaystyle p^{3}-q^{3}=68$and p - q = -4</b></i>
Question 89 :
On dividing $f(x)$ by a polynomial $x-1-x^2$, the quotient $q(x)$ and remainder $r(x)$ are $(x-2)$ and $3$ respectively. Then $f(x)$ is<br/>
Question 90 :
If $\displaystyle \left ( x^{2}+4x-21 \right )$ is divided by  $x + 7$  then the quotient is
Question 91 :
Find the value of 'a' in $4x^{2}\, +\, ax\, +\, 9\, =\, (2x\, -\, 3)^{2}$
Question 93 :
The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their squares.
Question 94 :
State True or False.$24\sqrt 3x^3-125y^3 \ = \ $ <br> $(2\sqrt 3x-5y)(12x^2+10\sqrt 3xy+25y^2)$<br/>
Question 95 :
The remainder obtained when the polynomial $x^{4}-3 x^3+9x^{2}-27x+81$ is divided by $(x-3)$ is:<br/>
Question 96 :
If $a = \dfrac{1}{3 - 2\sqrt{2}}, b = \dfrac{1}{3 + 2\sqrt{2}}$, then the value of $a^{3} + b^{3}$ is<br/>
Question 97 :
Let $p(x)=ax^2+bx+c, q(x)=lx^2+mx+n. $ If $p(1)-q(1)= 0$, $p(2)-q(2)=1 $ and $p(3)-q(3)=4$, then $p(4)-q(4)$ equals 
Question 98 : <p>If $x^{51} + 51$ is divided by $x + 1$, then theremainder is</p>
Question 99 :
If the sum and difference of two numbers are 20 and 8 respectively then the difference of their squares is :
Question 101 :
Let P be a non zero polynomial such that $P(1 + x) = P(1 - x)$ for all real x, and $P(1) = 0$. Let m be the largest integer such that $(x - 1)^m$ divides $P(x)$ for all such $P(x)$. Then m equals
Question 103 :
When a positive integer $y$ is divided by $47,$ the remainder is $11$. Therefore, when $\displaystyle y^{2}$ is divided by $47$, the remainder will be 
Question 104 :
If $(x - 2)$ and $(x - 3)$ are two factors of $\displaystyle x^{3}+ax+b$, then find the remainder when $\displaystyle x^{3}+ax+b$ is divided by $x - 5$.
Question 105 :
Which of the following should be added to $\displaystyle 9x^{3}+6x^{2}+x+2$ so that the sum is divisible by $(3x + 1)$?
Question 107 :
If $ax^{3}+ bx^{2}+ c x + d$ is divided by $x - 2$, then the remainder is equal<br>
Question 108 :
Number of real solutions of $\sqrt { 2 x - 4 } - \sqrt { x + 5 } = 1$...
Question 109 :
Find the value of the reminder obtained when $6x^4 + 5x^3 - 2x + 8$ is divided by $x-\dfrac{1}{2}$.
Question 110 :
Total number of polynomials of the form ${ x }^{ 3 }+a{ x }^{ 2 }+bx+c$ that are divisible by ${ x }^{ 2 }+1$, where $a,b,c\in \left\{ 1,2,3,......10 \right\} $ is equal to
Question 111 :
If $\displaystyle { n }^{ 3 }-{ n }^{ 2 }=n-1$, then which of the following can be the value of $ n$?
Question 112 :
Which of the following is a factor of the polynomial $-2{x}^{2}+7x-6$?
Question 114 :
The value of $x+y+z$ if ${x}^{2}+{y}^{2}+{z}^{2} = 18$ and $xy + yz + zx = 9$ is
Question 115 :
When $2f^3 + 3f^2 - 1$ is divided by $f+2$, find the remainder.<br/>
Question 116 :
Find the factor of the polynomial $P(x)= \left (12x^4+13x^3-35x^2-16x+20 \right )$ .<br/>
Question 118 :
The polynomials $p\left( x \right) = k{x^3} + 3{x^2} - 3$ and $Q\left( x \right) = 2{x^3} - 5x + k$, when divided by (x - 4) leave the same remainder. The value of K is
Question 119 :
If ${x^2} - 3x + 2$ is a factor of $f(x) = {x^4} - p{x^2} + q$ ,then $(p,q) = $
Question 120 :
Simplify: $\displaystyle \frac { 49\left( { x }^{ 4 }-2{ x }^{ 3 }-15{ x }^{ 2 } \right)  }{ 14x\left( x-5 \right)  } $
Question 121 :
If n is an integer, what is the remainder when $5x^{2n + 1}- 10x^{2n} + 3x^{2n-1} + 5$ is divided by x + 1?
Question 122 :
Divide $\displaystyle 10{ a }^{ 2 }{ b }^{ 2 }\left( 5x-25 \right)$ by $15ab\left( x-5 \right) $
Question 123 :
If $8a-64b-c=24\sqrt [ 3 ]{ abc } $, where a, b, $c\neq 0$, then which of the following can be true ?
Question 125 :
If $\displaystyle { \left( n+1 \right)  }^{ 3 }-{ \left( n-1 \right)  }^{ 3 }=n+2$, then which of the following can be the value of $n$ ?<br/>
Question 126 :
If $\displaystyle { \left( n+1 \right)  }^{ 3 }-{ n }^{ 3 }=-n$ , then which of the following can be the value of $n$ ?
Question 127 :
If$\displaystyle x=a\left ( b-c \right );y=b\left ( c-a \right );z=c\left ( a-b \right )$ then$\displaystyle \left ( \frac{x}{a} \right )^{3}+\left ( \frac{y}{b} \right )^{3}+\left ( \frac{z}{c} \right )^{3}$ is equal to
Question 129 :
The equationd $x^{x^{x^{+}}} = 2$ is satisfied when $x$ is equal to
Question 130 :
When a number P is divided by 4 it leaves remainder 3. If twice of the number P is divided by the same divisor 4, then what will be the remainder?
Question 133 :
If a remainder of $4$ is obtained when $x^{3} + 2x^{2} - x - k$ is divided by $x - 2$, find the value of $k$.
Question 134 :
Assertion: Let $\displaystyle f\left ( x \right )=6x^{4}+5x^{3}-38x^{2}+5x+6 $ then all four roots of $\displaystyle f\left ( x \right )=0 $ are real & distinct out of which two are positive & two are negative.
Reason: $\displaystyle f\left ( x \right ) $ has two changes in sign in given order as well as when $x$ is replaced by $-x$.
Question 135 :
Square root of $\dfrac {x^{2}}{y^{2}} + \dfrac {y^{2}}{4x^{2}} - \dfrac {x}{y} + \dfrac {y}{2x} - \dfrac {3}{4}$ is $\dfrac {x}{y} - \dfrac {1}{2} - \dfrac {y}{2x}$
Question 137 :
Let p(x) be a quadratic polynomial such that $p(0)=1$. If p(x) leaves remainder $4$ when divided by $x-1$ and it leaves remainder $6$ when divided by $x+1$; then which one is correct?
Question 138 :
Which of the following is the remainder when $z\left({5z}^{2}-80\right)$ is divided by $5z\left(z-4\right)$:
Question 139 :
Let $f(x)=x^6-2x^5+x^3+x^2-x-1$ and $g(x)=x^4-x^3-x^2-1$ be two polynomials. Let $a,b,c$ and $d$ be the roots of $g(x)=0$. Then the value of $f(a)+f(b)+f(c)+f(d)$ is
Question 140 :
If the roots of ${x^4} + q{x^2} + kx + 225 = 0$ are in arithmetic progression, then the value of q is
Question 141 :
$\displaystyle \frac{x^{-1}}{x^{-1} + y^{-1}} + \frac{x^{-1}}{x^{-1} - y^{-1}}$ is equal to
