There are 25 numbers which are divisible by 4 till 100. (100/4 = 25). But we should not consider 100 as we are asked to find the numbers between 1 to 100 which are divisible by 4. So answer is 24.

We can select any three of the 4 groups in $^4C_{3}$ ways. Now from each of these groups we can select 1 person in 4 ways.

So total ways = 4 x 4 x 4 x 4 = 256

We can select only one woman, and remaining 6 from men.

So $^{12}C_{6} \times ^3C_{1}$ = 2772

We can select two teams out of 15 in $^{15}C_{2}$ ways. So each team plays with other team once. Now to play two games, we have to conduct $^{15}C_{2}$ x 2 = 210 games.

As there is a difference of 2222.

7528 - 2222 = 5306.

So 4673 - 2222 = 2451

$x^2-y^2 $ = 16

(x+y)(x-y) = 16

So 16 comes in following table

1 $\times$ 16, 2 $\times$ 8, 4 $\times$ 4

Using 2 x 8 equation

x+y=8 and

x-y=2

So x = 5 or 3 and y = 3 or 5

So answer is 8.

1981 ? 4.54

2001 ? 7.44

Difference ( year ) = 20

Difference ( population ) = 2.9

So population per year = $\dfrac{20}{20}$ = 0.145

2009 ? x = ?

Hence x = 7.44 + 8 $\times$ 0.145 = 8.6 Lakhs

2520 = $2^3 \times 3^2 \times 5 \times 7$

Here 7 is the Highest prime So find the number of 7s in 50! only.

Number of 7s in 50! =$ \left[\dfrac{50}{7}\right] +\left[ \dfrac{50}{7^2}\right]$ = 7+1 = 8

For n(max) = 8, 50! is perfectly divisible by $2520^8$

Frog jumps 3 m in day & falls back 2 m at night

so,frog will be 3 - 2 = 1 m up in a day.

Thus, in 27 days it will be 27 m up

On 28th day it will be at top i.e 27 + 3 = 30 m & will not fall down.

(47, 94) (71, 142) (119, 238) (X, Y)

47 $\times$ 2 = 94

94 - 23 = 71

71 $\times$ 2=142

142 - 23 = 119

119 $\times$ 2 = 238

238 - 23 = 215

215 $\times$ 2 = 430

So the next 2 terms are 215 , 430

Let the total distance be x

So the speed of 1st train is x/4 and 2nd train x/3.5

In 2 hours 1st train covers half of the total distance .

So remaining is only half of the total distance(ie x/2).

Let t be the time taken

$d\dfrac{t\times x}{4}$ +$ \dfrac{t\times x}{3.5}$ = $\dfrac{x}{2}$

t=$\dfrac{14}{15}$ i.e. 56 min

i.e. Total time taken= 2 hrs + 56 min

Time they cross each other is 7:56 am (5+2.56)

Answer 7:56 am

A:B:C =(20000$\times$ 24):(15000 $\times$ 24):(20000 $\times$ 18) = 4 : 3 : 3

B`s Share = $\dfrac{3\times25000}{4+3+3}$ = 7500