Test Details

Polynomials 2

Dec 15, 9:00 PM

120 minutes

Dec 16, 9:00 PM

100.0 marks

MCQ

50 questions

Kanu Da

Abhijit Mondal, BSC In Chemistry Honors From Ramakrishna Mission Residential College, Narendrapur. BE In Mechanical Engineering From Indian Institute Of Engineering Science And Technology, Shibpur. Expert in Mathematics, Mechanical Engineering and SCIENCE

Class Details

MATHEMATICS

Science

Basic Engineering

RRB JE, ALP, Technician

MATHEMATICS

Science

Basic Engineering

Eligible criteria for ALP and Technician - 12th pass with ITI, or Diploma /Btech in Mechanical or in Electrical. For ALP should be physically fit and eye 6/6. RRB JE - Diploma or Btech in Mechanical Engineering.

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Question Text

Question 1 :
When ${ x }^{ 2 }-2x+k$ divided the polynomial ${ x }^{ 2 }-{ 6x }^{ 3 }+16{ x }^{ 2 }-25x+10$ the reminder is (x+a), the value of is

Question 2 :
Calculate $\left( 6{ p }^{ 2 }+p-12 \right) \div \left( 2p+3 \right) $.

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

Question 6 :
One of the factors of $(-25x^2 -1) + (1 + 5x)^2$ is

Question 8 :
If $ax^2+2a^2x+b^3$ is divisible by $x+a$, then what is the relation between $'a'$ and $'b'$ is possible?

Question 9 :
Let $r(x)$ be the remainder when the polynomial $x^{135} + x^{125} - x^{115} + x^{5} + 1$ is divided by $x^{3} - x$. Then

Question 11 :
Evaluate :$\displaystyle \frac { 50xyz\left( x+y \right) \left( y+z \right) \left( z+x \right) }{ 100xy\left( x+y \right) \left( y+z \right) }$

Question 12 :
When $p (x)$ is divided by $ax - b$ then the remainder is :

Question 13 :
$\displaystyle \left ( 1-a \right )\left ( 1+a+a^{2} \right )+\left ( 1+a \right )\left ( 1-a+a^{2} \right )$ is equal to

Question 15 :
If $p(x)$ and $g(x)$ are any two polynomials with $g(x)\neq 0$, then we can find polynomial $q(x)$ and $r(x)$ such that $p(x) = q(x) g(x) + r(x)$ where

Question 17 :
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 18 :
Determine all the zeros of $x^3+5x^2-2x-10$ if two of its zeros are $\sqrt 2$ and $-\sqrt 2$

Question 20 :
The simplified value of the experession$\displaystyle \left ( a+b-c \right )^{2}+2\left ( a+b-c \right )\left ( a-b+c \right )+\left ( a-b+c \right )^{2}$ is

Question 21 :
The value of $k$ for which $x+k$ is a factor of $x^3 + kx^2 - 2x = k = 4$ is

Question 22 :
In the real number system, the equation $\sqrt { x+3-4\sqrt { x-1 } } +\sqrt { x+8-6\sqrt { x-1 } } =1$

Question 23 :
When N is divided by 4, the remainder is 3. What is the remainder when 2N is divided by 4?

Question 24 :
Factorise : ${ (ax+by) }^{ 2 }+{ (2bx-2ay) }^{ 2 }-6abxy$

Question 25 :
If $\displaystyle 2 \left ( x^{2} + 1 \right ) = 5x$, find $\displaystyle x - \dfrac{1}{x}$

Question 26 :
State whether the following statement is true or not:If $\dfrac { a }{ b } +\dfrac { b }{ a } =-1$, then ${ a }^{ 3 }-{ b }^{ 3 }=0$.

Question 29 :
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial.$t^2-3, 2t^4+3t^3-2t^2-9t-12$

Question 30 :
The value of $m$ for which $x^3 - 2mx^2 + 16$ is divisible by $(x + 2)$, is

Question 31 :
The value of $\displaystyle \left ( 5x-3y \right )^{2}-\left ( 5x+3y \right )^{2}$, when $\displaystyle x=-1$ and $y=\sqrt{\cfrac{1}{25}}$ is

Question 34 :
If $a = \dfrac{1}{3 - 2\sqrt{2}}, b = \dfrac{1}{3 + 2\sqrt{2}}$, then the value of $a^{3} + b^{3}$ is

Question 35 :
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 36 :
When $3x^{3} + 2x^{2} + 2x + k$ is divided by $x + 2$, the remainder is $4$. Calculate the value of $k$.

Question 38 :
If $x^4 \, + \, 2x^3 \, - \, 3x^2 \, + \, x \, - \, 1$ is divided by $x - 2$. then the remainder is

Question 39 :
Find the number of zeros in the end in product $5 ^ { 6 } \cdot 6 ^ { 7 } .7 ^ { 8 } \cdot 8 ^ { 9 } \dots 30 ^ { 31 }.$

Question 40 :
If $\displaystyle \left ( x+2 \right )$ is a factor of the polynomial $\displaystyle f\left ( x \right )= x^{2}+ax+2b$ and $\displaystyle a+b=4$, then the value of $a$ and $b$ are-

Question 41 :
(64x$^3$ + y$^3$) $\div$ (16x$^2$ - 4xy + y$^2$) is equal to

Question 42 :
Divide $\displaystyle 8\left( 3x+4 \right) \left( 8x+9 \right) $ by $\displaystyle \left( 3x+4 \right) $

Question 43 :
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 44 :
Workout the following divisions $a(a + 1) (a + 2) (a + 3) \div a(a + 3)$

Question 49 :
If $2x+ky+z$ is a factor of $\displaystyle 9y^{2}-z^{2}-2xz+6xy $, then the value of k is equal to

Question 50 :
The value of $k$ for which $(x - 1)$ is a factor of $x^{3} - kx^{2} + 11x - 6$ is

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