Tag: maths

Questions Related to maths

If k is an integer and $\displaystyle \left( 0.0025 \right) \left( 0.025 \right) \left( 0.00025 \right) \times { 10 }^{ k }$ is an integer, what is the least possible value of k ?

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. -12

  2. -6

  3. 0

  4. 6

  5. 12

Show answer
Correct Option: E
Explanation:

Given expression:

 $(25 \times 10^{-4}) $ $(25 \times 10^{-3}) $$(25 \times 10^{-5}) $
$\rightarrow$ $15625 \times 10^{-12}$.
So, to make the result an integer, we must multiply by $10^{12}$
Least possible value of k should be 12. (option E)

Match the following.

Column I Column II
(i) $715+12.59+685.35=$ (P) $417.16$
(ii) $518-( 216.80 -115.96 )=$ (Q) $213.07$
(iii) $4.090+0.050+6.500=$ (R) $1412.94$
(iv) $36.050+198.05-21.03=$ (S) $10.640$
maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. (i)$\rightarrow$ (Q), (ii) $\rightarrow$ (R), (iii)$\rightarrow$ (S), (iv) $\rightarrow$ (P)

  2. (i)$\rightarrow$ (R), (ii) $\rightarrow$ (P), (iii) $\rightarrow$(S), (iv) $\rightarrow$(Q)

  3. (i)$\rightarrow$ (R), (ii)$\rightarrow$(S), (iii) $\rightarrow$ (P), (iv) $\rightarrow$ (Q)

  4. (i)$\rightarrow$ (Q), (ii) $\rightarrow$(S), (iii) $\rightarrow$ (P), (iv)$\rightarrow$(R)

Show answer
Correct Option: B
Explanation:

(I) $715+12.59+685.35=1412.94$
(II) $518-(216.80-115.96)=518-100.84=417.16$
(III) $4.090+0.050+6.500=10.640$
(IV) $36.050+198.05-21.03=213.07$.

The base of the decimal number system is ten, meaning, for example, that 123=1.10$^{2}$ + 2.10 + 3.
In the binary system, which has base two, the first five positive integers are 1,10,11,100,101. The numeral 10011 in the binary system would then be written in the decimal system as:

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. 19

  2. 40

  3. 10011

  4. 11

  5. 7

Show answer
Correct Option: A
Explanation:

binary(10011)= (1)*2^4 + (0)*2^3 + (0)*2^2 + (1)*2^1 + (1)*2^0

                     =16 + 0 + 0 + 2 + 1
                     =19.

If $1.8 - 6.3x = -0.3x$, then find the value of $x$ is


maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $x=0.3$

  2. $x=0.6$

  3. $x=0.7$

  4. $x=0.5$

Show answer
Correct Option: A
Explanation:

from question 

$1.8-6.3x=-0.3x$

$\Rightarrow6.3x -0.3x =1.8$

$\Rightarrow6.0x =1.8$

$\Rightarrow x =\dfrac{1.8}{6}$

$x = 0.3$

$\text{Option A is correct.}$

Evaluate: $3.7-1.9$

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $0.6$

  2. $7.3$

  3. $3.4$

  4. $1.8$

Show answer
Correct Option: D
Explanation:

$3.7-1.9$


$=\dfrac{37}{10}-\dfrac{19}{10}=\dfrac{37-19}{10}$


$=\dfrac{18}{10}=1.8$

Sum of $0.5, 12.56$ and $0.003$ is:

maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. $13.063$

  2. $31.036$

  3. $12.063$

  4. $12.036$

Show answer
Correct Option: A
Explanation:

The sum of $0.5 ,12.56$ and $0.003$ is

$0.5+12.56+0.003$ $=13.063$ 
Hence, the answer is $13.063$.

The charges in a resort are shown.
Mr. Mohit drove to the resort with his wife and three children on Saturday at $1:30$p.m. They left the resort at $8$ p.m. How much did Mr. Mohit and his family have to pay in all?

Entrance Fee Rs. $40$ per car
Monday to Friday Rs. $15.50$ per passenger
Saturday and Sunday Rs. $22.50$ per passenger
Parking charges Rs. $10.60$ per half hour


maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

  1. Rs. $250.30$

  2. Rs. $300.90$

  3. Rs. $267.80$

  4. Rs. $290.30$

Show answer
Correct Option: D
Explanation:

Total number of members in family $\rightarrow$ $5$

Time they spent at the resort $\rightarrow$ $6.5$ hr
Entrance fee $\rightarrow$ $40$
Charge of the members $\rightarrow$  ($22.5$$\times$$5$) $\rightarrow$ $112.5$
Parking charges $\rightarrow$ ($13$$\times$$10.60$) $\rightarrow$ $137.80$ (we took $13$ Since charges are given for half an hour)
Total amount to be paid $\rightarrow$ $40$ + $112.5$ + $137.80$ $\rightarrow$ $290.30$
Hence, Option D is correct answer.


If $\displaystyle { a }^{ 2 }$ ends in 5, then $\displaystyle { a }^{ 3 }$ ends in 25.

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. True

  2. False

  3. Ambiguous

  4. Insufficient information

Show answer
Correct Option: B
Explanation:

False. 15 x 15=225 and 15 x 15 x 15=3375. so the statement $\displaystyle { a }^{ 2 }$ ends in 5, then $\displaystyle { a }^{ 3 }$ ends in 25 is not true in all cases.

If $\displaystyle n = 1 + x $, where $x$ is the product of four consecutive positive integers then which of the following is/are true:
A) n is odd

B) n is prime
C) n is a perfect square

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. A and C only

  2. A and B only

  3. A only

  4. None of these

Show answer
Correct Option: A
Explanation:

Let us take $\displaystyle x=1\times2\times3\times4=24 $

Then $\displaystyle n=1+24=25$
i.e. an odd number and a perfect square
Again let $\displaystyle x=2\times3\times4\times5=120.$
Then, $\displaystyle n=1+120=121$
i.e. an odd number and a perfect square
$\displaystyle \therefore $ Option (A) is correct

The squares of which of the following would be odd numbers:
$431$
$2826$
$7779$
$82004$

maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

  1. $431$ and $7779$

  2. $431$ and $2826$

  3. $2826$ and $7779$

  4. $2826$ and $82004$

Show answer
Correct Option: A
Explanation:

The squares of $431\;and\;7779$ would be odd numbers.
(Because we know that squares of odd numbers are always odd).