Tag: square and square root

Questions Related to square and square root

The digit in the ten's place of a two-digit number is three times that in the one's places if the digits are reversed the new number will be 36 less than the original number Find the number 

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

  1. 64

  2. 52

  3. 62

  4. 42

Show answer
Correct Option: C
Explanation:

Let the digits be $ x $ and $ y $
Given, "The digit in the ten's place of a two-digit number is three times that in the one's places "
$ => x = 3y $ 

Now, when the digits are reversed, the number will be $ 10y + x $
Also,  if the digits are reversed the new number will be $ 36 $ less than the original number. $ => 10y + x = (10x + y) - 36 $
$ => 9x -9y = 36 $

Putting $ x = 3y $ in this,
$ 9(3y) -9y = 36 $
$ => 27y - 9y = 36 $
$ 18y = 36 => y = 2 $

So, $ x = 3y = 6 $
Hence, the number is $ 62 $

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)

Show answer
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 $D$.

IX + XV + XX = _________.

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

  1. 45

  2. 35

  3. 44

  4. 76

Show answer
Correct Option: C
Explanation:

We have,

$IX+XV+XX$
$=9+15+20$
$=44$

Hence, this is the answer.

Choose the correct answer from the alternatives given.
Select the correct combination of mathematical signs to replace * signs and to balance the following equation.
7*5*5*4* 10

maths square and square root scientific notation use of exponents power of 10
    • $\div$ - =

  2. $\times $ - = $\times $

  3. $\times $ + = $\times$

    • $\times \div $ =
Show answer
Correct Option: C
Explanation:
Given,

$7**5*4* 10$

Now, we have

$7 \times5 + 5 = 4 \times 10$

$35+5=4 \times 10$

$40 =40$

If $x$ and $y$ are any two positive real numbers, then $x > y$ implies

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

  1. $- x > - y$

  2. $- x < - y$

  3. $\frac{1}{x} > \frac{1}{y}$

  4. $-\frac{1}{x} > \frac{1}{y}$

Show answer
Correct Option: B
Explanation:

$ Given\quad that\quad x\quad and\quad y\quad are\quad positive\quad number\quad and\quad x>y.\ We\quad may\quad calculate\ (a)\quad on\quad the\quad positive\quad side\quad of\quad number\quad line\quad x\quad will\quad be\ \quad \quad to\quad the\quad right\quad of\quad y\quad and\quad \ (b)\quad on\quad the\quad negative\quad side\quad of\quad the\quad number\quad line\quad x\quad will\ \quad \quad be\quad to\quad the\quad left\quad of\quad y.\ Statement\quad A\longrightarrow -x>-y\quad i.e\quad -x\quad to\quad the\quad right\quad side\quad of\quad -y\ which\quad is\quad not\quad complying\quad with\quad (b).\quad So\quad it\quad is\quad not\quad true.\ Statement\quad B\longrightarrow -x<-y\quad i.e\quad -x\quad lies\quad to\quad the\quad left\quad of\quad -y.\ This\quad complies\quad with\quad (b).\quad So\quad the\quad statement\quad is\quad true.\ Statement\quad C\longrightarrow \frac { 1 }{ x } >\frac { 1 }{ y } .\quad Here\quad the\quad numerators\quad of\quad the\ two\quad fractions\quad are\quad equal.\quad But\quad the\quad denominator\quad of\quad \frac { 1 }{ x } \ is\quad greater\quad than\quad that\quad of\quad \frac { 1 }{ y } .\ So\quad this\quad statement\quad is\quad not\quad true.\ Statement\quad D\longrightarrow -\frac { 1 }{ x } >\frac { 1 }{ y } ,\ -\frac { 1 }{ x } is\quad a\quad negative\quad number\quad so\quad it\quad will\quad always\quad be\quad smaller\ than\quad a\quad positive\quad number.\ \therefore \quad -\frac { 1 }{ x } \ngtr \frac { 1 }{ y } .\quad So\quad this\quad statement\quad is\quad not\quad true.\ Answer-\quad Statement\quad B\quad is\quad correct.\  $