Test Details

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Polynomials

Study point

Jan 29, 3:10 PM

60 minutes

Jan 30, 4:00 PM

30.0 marks

MCQ

25 questions

STUDY POINT CBSE ICSE

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Maths

Science

Class 9

Maths

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Question Text

Question 1 :
The value of p for which $(x-2)$ is a factor of polynomial $x^4 - x^3 + 2x^2 - px +4$ is:

Question 2 :
The product of $x^2y$ and $\cfrac{x}{y}$ is equal to the quotient obtained when $x^2$ is divided by ____.

Question 3 :
State whether the statement is True or False.Evaluate: $(2a+3)(2a-3)(4a^2+9)$ is equal to $16a^4-81$.

Question 5 :
State whether the statement is True or False.Evaluate: $(6-5xy)(6+5xy)$ is equal to $36-25x^2y^2$.

Question 6 :
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 7 :
If $ a^2+b^2=29 $ and $ ab=10 $, then find $ a-b $. 

Question 9 :
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 11 :
If $x+y -z = 4$ and $x^2+y^2+ z^2=50$, find the value of $xy -yz-zx$

Question 12 :
Use the identity $(x + a) (x + b) = x^2 + (a + b) x + ab$ to find the following products.$(xyz +4) (xyz +2)$

Question 13 :
If $kx^3 + 9x^2+4x -10 $ divided by $x+3$ leaves a remainder $5$, then the value of $k$ will be 

Question 14 :
If $\displaystyle  a^{2}+b^{2}=13 \ and \ ab=6 $ find : $\displaystyle  a^{2}-b^{2}$

Question 15 :
If $\displaystyle \dfrac{x^{2} + 1}{x} = 3\dfrac{1}{3}$ and $\displaystyle x > 1$; find the value of  $\displaystyle x - \dfrac{1}{x}$

Question 19 :
State whether the statement is True or False.Expand: $(2a+b)^2 $ is equal to $4a^2+4ab+b^2$.

Question 21 :
If ${ x }^{ 3 }-{ ax }^{ 2 }+bx-6\quad is\quad exactly\quad divisible\quad by\quad { x }^{ 2 }-5x+6.\quad then\quad \frac { a }{ b } \quad is$

Question 22 :
If $\displaystyle ax^{3}+4x^{2}+3x-4$ and $\displaystyle x^{3}-4x+a$ leave same remainder when divided by $( x - 3 )$, the value of $-a$ is 

Question 23 :
The product of two positive numbers is $120$ and the sum of their square is $289$. The difference between them is:

Question 24 :
The remainder obtained by dividing $x^{n} - \dfrac{a}{b}$ by $ax - b$ is

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