Test Details

Exponents and Powers

Exam

Feb 20, 12:10 PM

60 minutes

Feb 20, 2:00 PM

92.0 marks

MCQ

48 questions

chinmayee Panda

Collaborative professional with four years experience in teaching science to fourth and fifth standard students. A recent graduate from pragati degree College , seeking a position to teach high school students at sunshine public school. An encouraging educator with an ability to make maths and science interesting for adolescents. Provide analogies, group activities and prepare teaching plans that facilitate classroom participation.

Class Details

English

7th

English

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Question Text

Question 1 :
State True or False.Simplify and express as positive indices: $(x^ny^{-m})^4.\times (x^3y^{-2})^{-n}$, then answer is $\dfrac{x^ny^{2n}}{y^{4m}}= x^ny^{2n-4m} $.

Question 2 :
What is the smallest integer n for which $\displaystyle { 25 }^{ n }>{ 5 }^{ 12 }$?

Question 3 :
Which expression is not equivalent to $3\times 3\times 3\times 3\times 3\times 3$?

Question 8 :
If 15 m$^2$n$^3$ is divided by 5m$^2$n$^2$, then the index of quotient is

Question 9 :
$\displaystyle \left [ \left ( -2 \right )^{4}-\left ( 11-1 \right )\right ]\div 3$

Question 17 :
If $\sqrt { { 2 }^{ x } } =16$, then $x=$

Question 19 :
The value of $\left ( \displaystyle \frac {-1}{216} \right )^{-2/3}$ is

Question 24 :
If $\displaystyle x^{x\sqrt{x}}=\left ( x\sqrt{x} \right )^{x}$, then x is equal to

Question 25 :
Suppose ${ 4 }^{ a }=5,{ 5 }^{ b }=6,{ 6 }^{ c }=7,{ 7 }^{ d }=8$, then the value of $abcd$ is ?

Question 27 :
Fill in the blanks If $800 = 8\times 10^8 \times x^{-3/2}$, then x = ____.

Question 28 :
If $3^{n} = n^{6}$, find the value of $ n^{18} $

Question 29 :
If $z=\alpha\sin\theta+\beta\cos\theta$, where $\alpha$ and $\beta$ are positive constants. The maximum value of $z$ is

Question 33 :
If 9$^{x+2}$= 240 + 9$^{x}$ then the value of x is:

Question 34 :
If $a^{b} = 4  -ab$ and $b^{a} = 1$, where $a$ and $b$ are positive integers, find $a$.

Question 35 :
State whether the following statement is true (T) or false (F): $\dfrac{2^3}{7} < \bigg(\dfrac{2}{7}\bigg)^3$

Question 37 :
$\displaystyle \frac{1}{\left ( 216 \right )^{\frac{-2}{3}}}+\frac{1}{\left ( 256 \right )^{\frac{-3}{4}}}+\frac{1}{\left ( 243 \right )^{\frac{-1}{5}}}$ is equal to:

Question 38 :
What is the value of b in the equation ${4^{2b-3} = 4^{1-b}}$ ?

Question 40 :
Solve for x ${5^{x + 1}}\, - {5^{x - 2}} = 620$

Question 41 :
$\dfrac{2^{n + 4} - 2 \times 2^n}{2 \times 2^{n + 3}} + 2^{-3} = $ ?

Question 42 :
If $2^a = 3^b = 6^c$ then C cannot be equal to

Question 44 :
Let $f(x)=x^{100}$. If $f(x)$ is divided by $x^{2}+x,$ then the remainder is $r(x)$.Find the value of $r(5)$?

Question 45 :
If $a , b , c$ and $d$ are natural numbers such that $a ^ { 3 } = b ^ { 6 } , c ^ { 3 } = d ^ { 4 } ,$ and $d - a = 61 ,$ then thesmallest value of $c - b$ is:

Question 48 :
If $5^{k^2}(25^{2k})(625) = 25\sqrt{5}$ and $k < -1$, find the value of $k$.

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