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MATHS MCQ

Exponents and Powers · ICSE STD 7 (ICSE - English Medium). 16 questions.

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16 questions · timed · auto-graded

MCQ 11 Mark
Which of the following numbers is in the standard form ?
  • A
    $26.57 \times 10^4$
  • B
    $2.657 \times 10^4$
  • C
    $265.7 \times 10^3$
  • D
    $0.2657 \times 10^6$
Answer
$2.657 \times 10^5$ is in standard form. (b)
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MCQ 21 Mark
The usual form of $5.658 \times 10^5$ is
  • A
    5658
  • B
    56580
  • C
    565800
  • D
    5658000
Answer
$5.658 \times 10^5=565800 \text { (c) }$
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MCQ 31 Mark
The standard form of 751.65 is
  • A
    $7.5165 \times 10^2$
  • B
    $75.165 \times 10^1$
  • C
    $7.5165 \times 10^4$
  • D
    $7.51 \times 10^2$
Answer
Standard form of $751.65=7.5165 \times 10^2( a )$
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MCQ 41 Mark
If $2^3+1^3=3^x$, then the value of $x$ is
  • A
    $0$
  • B
    $1$
  • ✓
    $2$
  • D
    $3$
Answer
Correct option: C.
$2$
$2^3+1^3=3^x$
$\Rightarrow 8+1=3^x$
$\Rightarrow 9=3 x$
$\Rightarrow 3^2=3^x$
$\Rightarrow x=2$
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MCQ 51 Mark
The value of $\left[\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2}\right] \div\left(\frac{1}{5}\right)^{-2}$ is
  • A
    $0$
  • B
    $-1$
  • ✓
    $1$
  • D
    $\frac{7}{5}$
Answer
Correct option: C.
$1$
${\left[\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2}\right] \div\left(\frac{1}{5}\right)^{-2}}$
$=\left(3^2+4^2 \div 5^2\right.$
$=(9+16) \div 25$
$=25 \div 25$
$=1$
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MCQ 61 Mark
The value of $\left(6^{-1}-8^{-1}\right)^{-1}$ is
  • A
    $\frac{-1}{2}$
  • B
    $-2$
  • C
    $\frac{1}{24}$
  • ✓
    $24$
Answer
Correct option: D.
$24$
$\left(6^{-1}-8^{-1}\right)^{-1}$
$=\left(\frac{1}{6}-\frac{1}{8}\right)^{-1}$
$=\left(\frac{4-3}{24}\right)^{-1}$
$=\left(\frac{1}{24}\right)^{-1}$
$=24$
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MCQ 71 Mark
The value of $5^{-1}-6^{-1}$ is
  • A
    $\frac{1}{30}$
  • B
    $\frac{-1}{30}$
  • C
    30
  • D
    (-30)
Answer
$\begin{array}{c}
5^{-1}-6^{-1}=\frac{1}{5}-\frac{1}{6} \\
=\frac{6-5}{30}=\frac{1}{30}
\end{array}$
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MCQ 81 Mark
The value of $\frac{10^{22}+10^{20}}{10^{20}}$ is
  • A
    $10$
  • ✓
    $101$
  • C
    $10^{22}$
  • D
    $10^{42}$
Answer
Correct option: B.
$101$
$\frac{10^{22}+10^{20}}{10^{20}}=\frac{10^{20} \times 10^2+10^{20}}{10^{20}}$
$=\frac{10^{20}\left(10^2+1\right)}{10^{20}}$
$=10^2+1$
$=100+1$
$=101$
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MCQ 91 Mark
The value of the expression $\frac{(-1)^{101} \times(8)^5}{(4)^7}$ is equal to
  • A
    $2$
  • ✓
    $-2$
  • C
    $\frac{1}{16}$
  • D
    $-\frac{1}{16}$
Answer
Correct option: B.
$-2$
$\frac{(-1)^{101} \times(8)^5}{(4)^7}$
$=\frac{(-1)^{101} \times\left(2^3\right)^5}{\left(2^2\right)^7}$
$=\frac{-1 \times 2^{3 \times 5}}{2^{2 \times 7}}$
$=\frac{-1 \times 2^{15}}{2^{14}}$
$=-1 \times 2^{15-14}$
$=-1 \times 2$
$=-2$
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MCQ 101 Mark
The law $\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$ does not hold when
  • A
    $a =3, b =2$
  • B
    $a=-2, b=3$
  • C
    $n =0$
  • ✓
    $b=0$
Answer
Correct option: D.
$b=0$
$\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$
$b=0,$ as $\left(\frac{a}{0}\right)^n=\frac{a^n}{0^n}$
Division by 0 is not admissible. $(d)$
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MCQ 111 Mark
The value of $\left(5^{30} \times 5^{20}\right) \div\left(5^5\right)^9$ in the exponential form is
  • A
    $5^{-5}$
  • ✓
    $5^5$
  • C
    $5^{50}$
  • D
    $5^{95}$
Answer
Correct option: B.
$5^5$
$\left(5^{30} \times 5^{20}\right) \div\left(5^5\right)^9$
$=5^{30+20} \div 5^{5 \times 9}$
$={ }^{250} \div 5^{45}$
$=5^{50-45}$
$=5^5$
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MCQ 121 Mark
$\left(-\frac{3}{4}\right)^5$ is equal to
  • A
    $\frac{81}{256}$
  • B
    $-\frac{81}{256}$
  • ✓
    $-\frac{243}{1024}$
  • D
    $\frac{243}{1024}$
Answer
Correct option: C.
$-\frac{243}{1024}$
$\left(-\frac{3}{4}\right)^5=\frac{(-3) \times(-3) \times(-3) \times(-3) \times(-3)}{4 \times 4 \times 4 \times 4 \times 4}$
$=-\frac{243}{1024}$
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MCQ 131 Mark
$\left(-\frac{3}{2}\right)^{-1}$ is equal to
  • A
    $\frac{2}{3}$
  • B
    $-\frac{2}{3}$
  • C
    $\frac{3}{2}$
  • D
    $\frac{4}{9}$
Answer
$\left(-\frac{3}{2}\right)^{-1}=-\frac{2}{3}$
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MCQ 141 Mark
The expression $(p q r))^3$ is equal to
  • A
    $p^3 q r$
  • B
    $p q^3 r$
  • C
    $pqr ^3$
  • D
    $p^3 q^3 r^3$
Answer
$(p q r)^3=p^3 q^3 r^3(d)$
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MCQ 161 Mark
$a \times a \times a \times b \times b \times b$ is equal to
  • A
    $a^3 b^2$
  • B
    $a^2 b^3$
  • C
    $(a b)^3$
  • D
    $a^6 b 6$
Answer
$a \times a \times a \times b \times b \times b=a^3 b^3=(a b)^3(c)$
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