Test Details

Indices and Cube Root

Feb 16, 7:30 PM

90 minutes

Feb 16, 10:00 PM

80.0 marks

MCQ

45 questions

vinayak sir

Hi good morning students सर्व विद्यार्थी सकाळी आठ ते अकरा या वेळेत येथे उपस्थित राहतील काही अडचणी असल्यास आपण विचारू शकता सर्व विषयाचे तास सुरू आहेत

Class Details

Mathematics

Class 8th Scolership Exam

Mathematics

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Question Text

Question 1 :
If $27^{x + 1} = 9^{x + 3} = 3^{y}$, find the respective values of $x$ and $y$.

Question 5 :
State true or false: $\displaystyle \left ( \frac{-7}{9} \right )^{2} \div \frac{49}{81} = - 1$

Question 7 :
If $\displaystyle a={ b }^{ 6 }$, then $\displaystyle { a }^{ 3 }=$

Question 8 :
State true or false: <span>$\displaystyle \left [ \left ( \frac{3}{7} \right )^{2}\right ]^3 = \left ( \frac{3}{7} \right )^{5}$</span>

Question 10 :
<div>State true or false.</div>$\displaystyle \left(\frac {27}{125}\right)^{\tfrac {2}{3}} \times \left(\dfrac {9}{25}\right)^{-\tfrac {3}{2}}$ is equal to $\displaystyle 1 \dfrac {2}{3}$.<br/>

Question 11 :
If $a\downarrow b = \sqrt [b]{a}$, then find the approximate value of $10\downarrow 3$.

Question 14 :
Find the positive natural number for which $\displaystyle { n }^{ 2 }={ n }^{ 3 }=n$.

Question 15 :
The cubes of all even number between 1 and 5 are .........

Question 17 :
The cube of a single digit number may be a ________ digit number.

Question 18 :
<span>Solve:</span><div><br/></div><div>$\displaystyle \dfrac {x^{a(b - c)}}{x^{b(a - c)}} \div (\dfrac {x^b}{x^a})^c = $.</div>

Question 20 :
If $2 \times (\sqrt{2})^5 \times (\sqrt{2})^{-2/3} = (\sqrt{2})^{x+1}$ , then the valueof $x$ is:

Question 21 :
The product of $\displaystyle 20^{50}$ and $\displaystyle 50^{20}$ is written as an integer in expanded form. The number of zeroes at the end of the resulting integer is

Question 22 :
State whether the folloiwng statement is true (T) or false (F):<br>$x^m + x^m = x^{2m}$ where $x$ is a non-zero rational number and $m$ is a positive integer. <br><br>

Question 24 :
If $x=a+b$, $y=a\omega+b{\omega}^{2}$, $z=a{\omega}^{2}+b\omega$, $\omega$ is cube root of unity then value of ${x}^{3}+{y}^{3}+{z}^{3}$

Question 28 :
Which of the following values are equal?<br>(P) $1^{4}$ (Q) $4^{\circ}$ (R) $0^{4}$ (S) $4^{1}$.

Question 29 :
The value of $\left (\dfrac {x^{a}}{x^{b}}\right )^{a^{2} + ab + b^{2}} \cdot \left (\dfrac {x^{b}}{x^{c}}\right )^{b^{2} + bc + c^{2}} \cdot \left (\dfrac {x^{c}}{x^{a}}\right )^{c^{2} + ca + b^{2}}$.

Question 30 :
The value of $x - y^{(x-y)}$ when $x = 2$ and $y = -2$ is

Question 32 :
<div>Given: $x, y$ and $z$ are integers and <span>$3^{x + 5} = 27^{y + 1}$, then </span><span>$x$ is even.</span></div>

Question 34 :
If $\displaystyle c={ a }^{ 3 }-{ b }^{ 3 },$ then is $c$ a perfect cube?

Question 36 :
The number 12304 (two) is equal to the numerical in base ten

Question 38 :
Evaluate the given expressions:<br/>${ 125 }^{ \frac { 2 }{ 3 } }$

Question 40 :
Cube of any positive integer is of the form $9m$, $9m +1$ or $9m +8$, where $m$ is a non-negative integer.

Question 41 :
<div>State true or false:</div><div><span>Cube of a number ending with zero has three zeros at its right.</span><br/></div>

Question 42 :
<div><div>State true or false:</div></div><div><span>If a number ends with $5$, then its cube ends with $5$.</span><br/></div>

Question 43 :
State true or false:<div>There is no perfect cube which ends with $8$.</div>

Question 45 :
<div>State true or false:</div>A perfect cube may end with two zeros.

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