Test Details

Exponents and Powers,Factorisation

12:30 batch

Feb 04, 12:45 PM

40 minutes

Feb 05, 1:55 PM

76.0 marks

MCQ

28 questions

Mr. Vishal Gupta

EX - RIMC TEACHER, Teach Mathematics for Competitive Exams. Running an Academy for Defence Aspirants by the VISHAL ACADEMY. OUR TEAM IS THE EX - RIMC TEACHERS TEAM PREPARING STUDENTS FOR COMPETITIVE EXAMS.

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Question Text

Question 1 :
If $2^x - {2^{x - 1}} = 4$ then $x^x$ is equals to 

Question 2 :
If $a^{b} = 4  -ab$ and $b^{a} = 1$, where $a$ and $b$ are positive integers, find $a$.

Question 5 :
If $2^{3x - 2} = 16$, then calculate the value of $x $.

Question 6 :
If ${ 9 }^{ x-1 }={ 3 }^{ 2x-1 }-486 $,then the value of x is:

Question 8 :
Compare the size of a pen tip which is $0.000005$ m to that of the width of pen which is $ 0.0000249$ m.

Question 9 :
If $4x^{4} -12x^{3}+x^{^{2}}+3ax-b$ is divided by $x^{2}-1$ then a = _______, and b=______<br/>

Question 12 :
On dividing $x^3-3x^2+x+2$ by polynomial $g(x)$, the quotient and remainder were $x -2$ and $4 - 2x$ respectively, then $g(x)$ is<br/>

Question 14 :
Simplify: $\displaystyle \frac { 20xyz\left( 4x+5y+6z \right)  }{ xz\left( 40x+50y+60z \right)}$

Question 15 :
Find the product of $\displaystyle\frac { { k }^{ 2 }+13k+42 }{ { k }^{ 2 }+15k+56 } $ and $\displaystyle\frac { { k }^{ 2 }+8k }{ { k }^{ 2 }+11k+30 } $:

Question 16 :
State whether True or False.Factorization of $12 (a + b)^2 - (a + b) - 35$ is $(4a + 4b - 7) (3a + 3b + 5)$.<br/>

Question 17 :
Find the polynomial which when divided by $3x + 4$, equals $2x^{2} + 5x - 3$ with a remainder of $3$

Question 19 :
If $ab + bc + ca = 0$, then the value of $\displaystyle \frac{1}{a^{2}-bc}+\frac{1}{b^{2}-ca}+\frac{1}{c^{2}-ab}$ will be

Question 21 :
Simplify: $\displaystyle \frac { 49\left( { x }^{ 4 }-2{ x }^{ 3 }-15{ x }^{ 2 } \right)  }{ 14x\left( x-5 \right)  } $

Question 22 :
Find the value of K if (x + 1) is a factor of $x^8+ Kx^3 - 2x + 1$.

Question 23 :
Divide $\displaystyle 10{ a }^{ 2 }{ b }^{ 2 }\left( 5x-25 \right)$ by $15ab\left( x-5 \right) $

Question 24 :
$\displaystyle \frac{x^{-1}}{x^{-1} + y^{-1}} + \frac{x^{-1}}{x^{-1} - y^{-1}}$ is equal to

Question 25 :
Divide $\displaystyle \left( 9{ x }^{ 2 }-24x+16 \right) $ by $\displaystyle \left( 3x-4 \right) $

Question 26 :
Which of the following does not have $\displaystyle (x-3)$ as a factor?

Question 28 :
Simplify: $\displaystyle \left( { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }-{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }+{ a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 } \right) \div { a }^{ 2 }{ b }^{ 2 }{ c }^{ 3 }$

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