Tag: maths

Questions Related to maths

If x is a whole number then $\displaystyle x^{2}\left ( x^{2}-1 \right )$ is always divisible by

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 12

  2. 24

  3. 12 - x

  4. Multiple of 12

Show answer
Correct Option: A
Explanation:

Putting x=2, we get $2^2\left(2^2-1\right)= 12. So, x^2\left(x^2-1\right)$ is always divisible by 12

Suresh travelled 1200 km by air which form (2/5) of his trip. One third of the whole trip, he travelled by car and the rest of the journey he performed by train. Find the distance travelled by train. Also, find the speed of the train if the time taken for the train to travel the whole distance is 8 hrs

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 1600 km, 350 km/hr

  2. 800 km, 375 km/hr

  3. 1800 km, 300 km/hr

  4. 480 km, 380 km/hr

Show answer
Correct Option: B
Explanation:

Suresh travelled 1200 km by air which form (2/5) of his trip. 
Then total distance of journey=$\frac{5}{2}\times 1200=3000 km$
Suresh travelled $\frac{1}{3}$of journey by car =$\frac{1}{3}\times 3000=1000 km$
Then suresh travelled distance by train =3000-1200-1000=800 km
If whole journey by train in 8 hours 
So speed of train=$\frac{3000}{8}$=375 km/Hr

Three lightships flash simultaneously at 6;00 a.m. The first lightship flashes every 12 seconds, the seconds lightship every 30 seconds and the third lightship every 66 seconds. At what time will the three lightships next flash together?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 6;09 a.m.

  2. 6:10 a.m.

  3. 6:11 a.m.

  4. 6:12 a.m.

Show answer
Correct Option: C
Explanation:

Three lightships flash simultaneously at 6;00 a.m. The first lightship flashes every 12 seconds, the seconds lightship every 30 seconds and the third lightship every 66 seconds. 
Then we take common multiple of 12,30 or 66 
That is $2\times 6\times 5\times 11=660$
So  the three lightships next flash together=660 seconds =$\frac{660}{60}=11$mints
The time next flash is after 11 mints=6.11 A.M 

If $\displaystyle \left ( 1^{2}+2^{2}+3^{2}+...+10^{2} \right )=385$ then the value of $\displaystyle \left ( 2^{2}+4^{2}+6^{2}+...+20^{2} \right )$

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 770

  2. 1155

  3. 1540

  4. (385 x 385)

Show answer
Correct Option: C
Explanation:

$\left(2^2 + 4^2 + 6^2 + ... + 20^2\right) = \left(1 \times 2\right)^2 + \left(2\times 2\right)^2 + \left(2 \times 3\right)^2 + ... + \left(2 \times 10\right)^2$



$= \left(2^2 \times 1^2\right) + \left(2^2 \times 2^2\right) + \left(2^2 \times 3^2\right) + ... + \left(2^2 \times 10^2\right)$

$= 2^2 \times \left [1^2 + 2^2 + 3^2 + ... + 10^2\right]$

$\left(1^2+2^2+3^2+....+n^2\right) = \frac{1}{6}n\left(n+1\right)\left(2n+1\right)$

$=\left(4\times\frac{1}{6}\times 10\times 11\times 21\right)$

$=\left(4\times 5\times 77\right)$

$= 1540$

When Sholey screened on the TV there was a commercial break of 5 min after every 15 min of the movie If from the start of the movie to the end of the movie there was in all 60 min of commercials that was screened what is the duration the movie?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 180 min

  2. 195 min

  3. 169 min

  4. 165 min

Show answer
Correct Option: B
Explanation:

In every 15 min there was a break of 5 min
If total 60 min break in all movie then number of commercial break =$\frac{60}{5}=12$
If 12 breaks are in movie then the duration of movie=$12\times 15+15=195    minutes$

If $\frac {2}{3}$ part of a number is 96 then what will be $\frac {3}{4}$ of the same number?

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 48

  2. 192

  3. 108

  4. 72

Show answer
Correct Option: C
Explanation:

Let, $\frac {2x}{3}=96$
$x=\frac {96\times 3}{2}=144$
$\therefore \frac {3}{4}\times 144=3\times 36=108$

Simplify $(9^{4/3} \div 27^{2/3}) \times 3^{3/2}$

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $3^{9/5}$

  2. $3^{13/6}$

  3. $3^{37/6}$

  4. None of these

Show answer
Correct Option: B
Explanation:

$\displaystyle \left ( \left ( 3^2 \right )^{4/3} \div \left ( 3^3 \right )^{2/3} \right ) \times 3^{3/2}$
$= 3^{8/3} \div 3^2 \times 3^{3/2}$
$= \displaystyle 3^{8/3 - 2 + 3/2} $
$= \displaystyle  3^{ \displaystyle \frac{16 - 12 + 9}{6}}$
$= 3^{13/ 6}$

The number of non-negative integers that are less than 1000 and end with only one zero is

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $90$

  2. $95$

  3. $91$

  4. $99$

Show answer
Correct Option: C
Explanation:

$1+9\times 10 = 91$

What is the value of $\displaystyle\frac{0.24\times0.35}{0.02\times0.14\times0.15}$

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. $20$

  2. $200$

  3. $100$

  4. $9$

Show answer
Correct Option: B
Explanation:

$\displaystyle\frac{0.24\times0.35}{0.02\times0.14\times0.15}= \frac{0.084}{0.00042}=200$

The product of two numbers is 0.008 and one is $\displaystyle \frac{1}{5}$ of the other, then the smaller number is

maths ways to multiply and divide mental multiplication multiplication methods multiplication of numbers

  1. 0.002

  2. 0.004

  3. 0.2

  4. 0.04

Show answer
Correct Option: D
Explanation:

Let the smaller number is x 

Then bigger number  of is 5 times of smaller number because one number is $\frac{1}{5}$ another
Then product of number =$5x\times x=0.008$
$\Rightarrow x^{2}=0.0016$
$\Rightarrow x=0.04$