Tag: maths

Questions Related to maths

Express $2.53\times 10^{-4}$ in standard notation

maths square and square root scientific notation use of exponents power of 10

  1. $2.53$

  2. $0.0000253$

  3. $0.00253$

  4. $0.000253$

Show answer
Correct Option: D
Explanation:

$2.53\times { 10 }^{ -4 }=\frac { 2.53 }{ { 10 }^{ 4 } } =0.000253$

So correct answer will be option D

Convert $62000+39000$ to scietific form.

maths square and square root scientific notation use of exponents power of 10

  1. $1.01\times 10^5$

  2. $1.1\times 10^5$

  3. $1.01\times 10^4$

  4. $1.1\times 10^4$

Show answer
Correct Option: A
Explanation:

On adding, we get

$62000+39000=101000$
Therefore, $ 101000=1.01\times 10^5$
Hence, option A is correct.

Convert $6.634\times 10^{-3}$ in decimal form.

maths square and square root scientific notation use of exponents power of 10

  1. $6634$

  2. $0.006634$

  3. $0.006643$

  4. $0.0006634$

Show answer
Correct Option: B
Explanation:

$6.634\times 10^{-3}$ can be written as 

$=\dfrac{6.634}{1000}=0.006634$
Hence, option B is correct.

Write $1200\times 3200$ in scientific notation.

maths square and square root scientific notation use of exponents power of 10

  1. $384000$

  2. $384\times 10^3$

  3. $3.84\times 10^6$

  4. $3840\times10^2$

Show answer
Correct Option: C
Explanation:

The value of $3200\times 1200$ is 

$=32\times12\times10^4\=384\times 10^4\=3.84\times 10^6$

Which of the following options is INCORRECT?

maths square and square root scientific notation use of exponents power of 10

  1. The number $48693$ rounded off to nearest hundred is $48700$

  2. LXXV is greater than LXXIV

  3. One million is equal to $10$ crore

  4. Place value of a digit $=$(face value of the digit)$\times$ (Value of the place)

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Correct Option: C
Explanation:

Option A: For rounding to the nearest hundred, If tens digit is 0,1,2,3,4

, then round down to the previous hundred and If tens digit is 5,6,7,8,9, then round up to the next hundred.
Following the above rule, as 6 is present in the hundredth place, we will round up it to $700$.

Hence $48693$ $\rightarrow$ $48700$.

Option B: LXXV $\rightarrow$ $75$
                 LXXIV $\rightarrow$ $74$
So, LXXV $>$ LXXIV

Option C: 1 million $\rightarrow$ 10,00,000 $\rightarrow$ 10lakh

Option D: Face value is the value of the digit itself.
Value of place if the position of the digit in the number
Hence, Place value $\rightarrow$ face value $\times$ Value of place

Hence Option C is incorrect.





In scientific notation, $670,000,000 + 700,000,000 =$?

maths square and square root scientific notation use of exponents power of 10

  1. $1.37 \times {10}^{-9}$

  2. $1.37 \times {10}^{7}$

  3. $1.37 \times {10}^{8}$

  4. $1.37 \times {10}^{9}$

  5. $137 \times {10}^{15}$

Show answer
Correct Option: D
Explanation:

$670,000,000+700,000,000=1,370,000,000$

$\therefore 1,370,000,000=1.37\times 10^9$
Ans-Option $D$.

State True or False
$\displaystyle A\cup A'=\phi $

maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

False because $\displaystyle A\cup A'=\cup  $

Given, universal set = {$x \,\,\epsilon\,\, Z$ : $- 6 < x \leq 6$}, N = {$n$ : $n$ is a non-negative number} and P = {$x$ : $x$ is a nonpositive number}. Find :$P'$
maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. ${-1,-2,-3,-4,-5,-6}$ 

  2.  ${1,2,3,4,5,6}$ 

  3. ${0,1,2,3,4,5,6}$ 

  4. ${0,-1,-2,-3,-4,-5,-6}$ 

Show answer
Correct Option: B
Explanation:

Universal set includes ${-5,-4,-3,-2,-1,0,1,2,3,4,5,6}$


P=${-5.-4.-3,-2,-1,0}$.

Hence P' only has the elements in option B. It does not contain 0.
P'=${1,2,3,4,5,6}$.

If the universal set ${x\in W ,3<x≤12} ,A={5,7,9}$, then $A'=$

maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. ${3,6,8,10,11,12}$

  2. ${4,6,8,10,11,12}$

  3. ${6,8,10,11,12}$

  4. None of the above

Show answer
Correct Option: B
Explanation:
Given universal set is $\{x\in W ,3<x≤12\}$
It can be written as a set $\{4,5,6,7,8,9,10,11,12\}$
$A$ is given as $A=\left\{5,7,9\right\}$
$\therefore A'=W-A=$ All the elements in the universal set but not in set $A$
         $ =\{4,6,8,10,11,12\}$
Hence, option B is correct

Let  $U={x: \in, W: 3<x< 12} $, $B={4,6,8,10}$ . $B'$

maths introduction to set different sets de morgan's law de morgan's law for set theory

  1. ${6,7,9,11,12}$

  2. ${5,7,9,11}$

  3. ${5,7,9,10,11,12 }$

  4. None of the above

Show answer
Correct Option: B
Explanation:
Given universal set is $\{x\in W ,3<x<12\}$
It can be written as a set $\{4,5,6,7,8,9,10,11\}$
$B$ is given as $B=\left\{4,6,8,10\right\}$
$\therefore B'=W-B=$ All the elements in the universal set but not in set $B$
         $ =\{5,7,9,11\}$
Hence, option B is correct