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Polynomial

Ntse

Dec 13, 8:00 PM

45 minutes

Dec 13, 9:00 PM

50.0 marks

MCQ

50 questions

satyanarayan sir

I am maths faculty (NITian)

Class Details

Maths

Class 9th NTSE

Maths

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Question Text

Question 5 :
If x+2 is a factor of $ \displaystyle \left \{ \left ( x+1 \right )^{5}+(2x+k)^{3} \right \} $, then the value of 'k' is 

Question 6 :
Find the value of $k$, if $x-1$ is a factor of $p(x)$ in each of the following cases:$p(x)=2x^2+kx+\sqrt 2$

Question 8 :
If 1 is zero of the polynomial p(x) = $\displaystyle ax^{2}-3\left ( a-1 \right )x-1$ then the value of 'a' is

Question 11 :
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 13 :
$f(x)=2x^3-5x^2+ax+a$Given that $(x+2)$ is a factor of $f(x)$, find the value of the constant $a$.

Question 15 :
If $ a^2+b^2=29 $ and $ ab=10 $, then find $ a-b $. 

Question 16 :
The remainder when $x^{2}+ 2x + 1$ is divided by $(x+1)$ is

Question 18 :
State True or False.If $x^2-1$ is a factor of $ax^4+bx^3+cx^2+dx+e$, then $a+c+e=b+d=0$

Question 20 :
Choose the correct answer from the alternatives given. If x - $\dfrac{1}{x}$ = 3 then find the value of $x^3 + \dfrac{1}{x^3}$.

Question 24 :
Find out whether or not the first polynomial is a factor of the second polynomial:$4a-1, 12a^2-7a-2$

Question 25 :
If $\alpha$ and $\beta$ are zeroes of the polynomial $p(x) = 2x^{2} -7x +3$, find the value $\alpha^{2} + \beta^{2}$.

Question 27 :
State whether the statement is True or False.Evaluate: $(6-xy)(6+xy)$ is equal to $36-x^2y^2$.

Question 30 :
Let $r(x)$ be the remainder when the polynomial $x^{135}+x^{126}-x^{115}+x^{5}+1$ is divided by $x^{3}-x$. Then:

Question 32 :
State True or False, if the following are zeros of the polynomial, indicated against them: $p(x)=3x+1, \ x=-\dfrac {1}{3}$

Question 33 :
If 2 is a zero of the polynomial $2x^2+kx-14$, then the value of k is :

Question 34 :
If $(x + 2a)$ is a factor of $x^5 - 4a^2x^3 + 2x + 2a + 3,$ find $a$.

Question 35 :
The remainder when $x^{3} - 6x^{2} + 11x - 6$ is divided by $x + 2$ is

Question 36 :
Factorise : $(a - b)^3 + (b - c)^3 + (c - a)^3$

Question 37 :
If quotient = $3x^2\, -\, 2x\, +\, 1$, remainder = $2x - 5$ and divisor  = $x + 2$, then the dividend is:

Question 38 :
If one zero of $2x^2-3x + k$ is reciprocal to the other, then the value of k is

Question 40 :
If (x -1) is a factor of polynomial f(x) but not of g(x), then it must be a factor of

Question 41 :
Without actually calculating the cubes, find the value of :$\left ( \dfrac{1}{2} \right )^{3}+\left ( \dfrac{1}{3} \right )^{3}-\left ( \dfrac{5}{6} \right )^{3}$

Question 42 :
Verify whether the following are zeros of the polynomial indicated against them:$g(x)=5x^2+7x, \ x=0, -\dfrac {7}{5}$

Question 44 :
Without actually calculating the cubes, find the value of each of the following:$(28)^3+(-15)^3+(-13)^3$

Question 47 :
Simplify: $(x - 3y - 5z)(x^2 + 9y^2 + 25z^2 + 3xy - 15yz + 5zx)$

Question 48 :
By Remainder Theorem find the remainder, when $ p(x)$ is divided by $g(x)$, where$p(x) = x^3-  3x^2 + 4x + 50\ and\ g(x) = x-  3$.

Question 49 :
If $(y - 3)$ is a factor of $y^{3} + 2y^{2} - 9y - 18$, then find the other two factors

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