Test Details

Polynomials

Chapter 2

Nov 23, 8:00 PM

120 minutes

Nov 23, 10:00 PM

61.0 marks

MCQ

46 questions

manish sahu

MTECH (IIT DELHI)

Class Details

Maths

10th

Maths

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Question Text

Question 2 :
$\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 6 :
Work out the following divisions.$10y(6y + 21) \div 5(2y + 7)$

Question 7 :
If $\alpha , \beta $ are the roots of the equation $ax^{2}+bx+c=0$, find the value of $\alpha ^{2}+\beta ^{2}$.

Question 12 :
The common quantity that must be added to each term of $a^{2}:b^{2}$ to make itequal to $a:b$ is:

Question 13 :
Divide the first expression by the second. Write the quotient and the remainder. $\displaystyle x^2-\frac{1}{4x^2}; x-\frac{1}{2x}$

Question 14 :
What is the remainder, when $(4{x^3} - 3{x^2} + 2x - 1)$ is divided by (x+2)?

Question 15 :
Factorise the expressions and divide them as directed.$12xy(9x^2-  16y^2)\div  4xy(3x + 4y)$

Question 18 :
Factorise the expressions and divide them as directed.$4yz(z^2 + 6z-  16)\div  2y(z + 8)$

Question 19 :
State whether True or False.Divide : $a^2 +7a + 12 $ by $  a + 4 $, then the answer is $a+3$.

Question 20 :
Simplify:Find$\ x(x + 1) (x + 2) (x + 3) \div  x(x + 1)$

Question 21 :
What must be added to $x^3-3x^2-12x + 19$, so that the result is exactly divisible by $x^2 + x-6$?

Question 23 :
The product of the roots of the quadratic equation $2x^{2}-8x+3=0$ is

Question 25 :
The degree of the remainder is always less than the degree of the divisor.

Question 26 :
If $x\ne -5$ , then the expression $\cfrac{3x}{x+5}\div \cfrac {6}{4x+20}$ can be simplified to

Question 27 :
Work out the following divisions. $96abc(3a -12) (5b +30)\div  144(a-  4) (b+  6)$

Question 28 :
If a polynomial $p(x)$ is divided by $x - a$ then remainder is

Question 33 :
Workout the following divisions $11a^3b^3(7c - 35) \div 3a^2b^2 (c - 5)$

Question 35 :
If the equation$\displaystyle{ px }^{ 2 }+2x+p=0$ hastwo distinct roots if.

Question 37 :
Find the Quotient and the Remainder when the first polynomial is divided by the second. $(x^3+1) $ by $(x+1)$

Question 38 :
Using long division method, divide the polynomial$4p^3-4p^2+6p -\displaystyle \frac{5}{2}$ by $2p-1$

Question 39 :
If one of the zeros of the quadratic polynomial $2x^2 + px + 4$ is 2, find the other zero. Also find the value of p

Question 40 :
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 41 :
If $ \alpha, \beta $ be the roots of the equation $ a x^{2}+b x+c=0, $ then value of $\dfrac{ \left(a \alpha^{2}+c\right) }{(a \alpha+b)}+\dfrac{\left(a \beta^{2}+c\right)}{ (a \beta+b)} $ is

Question 42 :
What must be added to $f(x)=4x^4+2x^3+2x^2+x-1$ so that the resulting polynomial is divisible by $g(x)=x^2+2x-3$

Question 43 :
If the sum of two numbers is $9$ and the sum of their squares is $41$, then the numbers are

Question 44 :
If the roots of the equation, $ax^2+bx+c=0$, are of the form $\alpha / (\alpha -1)$ and $(\alpha +1)/\alpha$, then the value of $(a+b+c)^2$ is

Question 45 :
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 46 :
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 ${p}^{2}c-{b}^{2}q=$

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