Four ladies A, B, C and D and four gentlemen E, F, G and H are sitting in a circle round a table facing each other. Directions: (1) No two ladies or two gentlemen are sitting side by side. (2) C, who is sitting between G and E is facing D. (3) F is between D and A and is facing G. (4) H is to the right of B. Question: 1. Who are immediate neighbours of B? 2. E is facing whom?

Correct Answer: 22

Explanation:

Using,  C r n = C n - r n we get 

n ? 10 = 12

or, n = 12 + 10 = 22

Correct Answer: 28

Explanation:

Let x, y, z be the number of balls received by the three persons, then

  

x ? 5 , y ? 5 , z ? 5 a n d x + y + z = 21

 

Let  u ? 0 , v ? 0 , w ? 0 t h e n

 

? x + y + z =21

 

? u + 5 + v + 5 + w + 5 = 21

 

? u + v + w = 6 

 

?Total number of solutions =  C 3 - 1 6 + 3 - 1 = C 2 8 = 28

Correct Answer: 63

Explanation:

Given digits are 0, 4, 2, 6

Required 4 digit number should be greater than 6000.

So, first digit must be 6 only and the remaining three places can be filled by one of all the four digits.

This can be done by

1x4x4x4 = 64

Greater than 6000 means 6000 should not be there.

Hence, 64 - 1 = 63.

Correct Answer: 192

Explanation:

We are having with digits 2, 3, 4, 5 & 6 and numbers greater than 4000 are to be formed, no digit is repeated.

 

The number can be 4 digited but greater than 4000 or 5 digited.

 

Number of 4 digited numbers greater than 4000 are
4 or 5 or 6 can occupy thousand place => 3 x  P 3 4 = 3 x 24 = 72. 

 

5 digited numbers =  P 5 5 = 5! = 120 

So the total numbers greater than 4000 = 72 + 120 = 192

Correct Answer: 11

Explanation:

Let the number of sides be n. 

The number of diagonals is given by ⁿC₂ - n  

^{Therefore, n}C₂ - n = 44, n>0 

ⁿC₂ - n = 44

n² - 3n - 88 = 0 

n² -11n + 8n - 88 = 0  

 

As n>0, n will not be -8. Therefore, n=11.

Correct Answer: 191

Explanation:

Out of 15 fruits, 7 are alike of one kind, 5 are alike of a second kind and 3 are alike of a third kind.

Hence, the required number of ways = [ (7+1) (5+1) (3+1) -1] =191

Correct Answer: 59

Explanation:

The first letter is E and the last one is R.

 

Therefore, one has to find two more letters from the remaining 11 letters.

 

Of the 11 letters, there are 2 Ns, 2Es and 2As and one each of the remaining 5 letters.

 

The second and third positions can either have two different letters or have both the letters to be the same.

 

Case 1: When the two letters are different. One has to choose two different letters from the 8 available different choices. This can be done in 8 * 7 = 56 ways.

 

Case 2: When the two letters are same. There are 3 options - the three can be either Ns or Es or As. Therefore, 3 ways.

 

Total number of possibilities = 56 + 3 = 59

Correct Answer: 35

Explanation:

A triangle is formed by joining any three non-collinear points in pairs.

 

There are 7 non-collinear points

 

The number of triangles formed =  7 C 3 = 35

Correct Answer: 1170

Explanation:

Possibilities     Bowlers      Batsmen         Number of ways

 

                         6               9

 

         1              4                7               ( 6 C 4 * 9 C 7 )

 

         2              5                6               6 C 5 * 9 C 6

 

         3              6                5               6 C 6 * 9 C 5

 

6 C 4 * 9 C 7 = 15 x 36 = 540

 

6 C 5 * 9 C 6 = 6 x 84 = 504

 

  6 C 6 * 9 C 5= 1 x 126 = 126

 

Total = 1170

Correct Answer: n = 29/5

Explanation:

Given are the two AP'S:

15,12,9.... in which a=15, d=-3.............(1) 

-15,-13,-11..... in which a'=-15 ,d'=2.....(2)

 

now using the nth term's formula,we get

a+(n-1)d = a'+(n-1)d'

substituting the value obtained in eq. 1 and 2,

15+(n-1) x (-3) = -15+(n-1) x 2

=> 15 - 3n + 3 = -15 + 2n - 2

=> 12 - 3n = -17 + 2n

=> 12+17 = 2n+3n

=> 29=5n

=> n= 29/5