36
Q:

# (51 + 52 + 53 + .........+100) is equal to

Q:

What smallest number of 6 digit is divisible by 111?

Smallest number of 6 digits is 100000

on dividing 100000 by 111 we get 100 as remainder

$\inline&space;\fn_jvn&space;\therefore$ Number to be added = (111 -100) = 11

$\inline&space;\fn_jvn&space;\therefore$ Required Number  = 100011

887
Q:

The value of

$\inline \fn_jvn \left [ \frac{2^{n}+2^{n-1}}{2^{n+1}-2^{n}} \right ]$ is:

$\inline \fn_jvn \frac{2^{n}+2^{n-1}}{2^{n+1}-2^{n}} =\frac{2^{n-1}(2+1)}{2^{n}(2-1)}=\frac{\frac{3\times 2^{n}}{2}}{2^{n}}=\frac{3}{2}$

517
Q:

The difference of two numbers is 11 and (1/5)th of their sum is 9. The numbers are

Let the numbers be x and (x-11)

$\inline \fn_jvn \frac{1}{5}\times (x+x-11)=9$

$\inline&space;\fn_jvn&space;\Rightarrow$   x = 28

$\inline&space;\fn_jvn&space;\therefore$ Another Number is (28 - 11) = 17

638
Q:

A number when divided by 779 gives a remainder 47. By dividing the same number by 19, what would be the remainder?

Number = ( 779 x a) + 47, where "a" is the quotient

= (19 x 41 x a) + (19 x 2) + 9

= 19 x (41a + 2) + 9

= 19 x (New quotient) + 9

$\inline&space;\fn_jvn&space;\therefore$  Required remainder = 9

1704
Q:

On dividing 4150 by a certain number , the quotient is 55 and the remainder is 25, the divisor is

Divisor = $\inline \fn_jvn \left [ \frac{Divided-Remainder}{Quotient} \right ]$
= $\inline \fn_jvn \frac{45\times 46}{2}=75$