8
Q:

# In a Plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no lines passes through both points A and B , and no two are parallel. Find the number of points of intersection of the straight lines.

 A) 525 B) 535 C) 545 D) 555

Explanation:

The number of points of intersection of 37 lines is $\inline ^{37}\textrm{C}_{2}$. But 13 straight lines out of the given 37 straight lines pass through the same point A. Therefore instead of getting $\inline ^{13}\textrm{C}_{2}$ points, we get only one point A. Similarly 11 straight lines out of the given 37 straight lines intersect at point B. Therefore instead of getting $\inline ^{11}\textrm{C}_{2}$ points, we get only one point B.

Hence the number of intersection points of the lines is $\inline ^{37}\textrm{C}_{2}-^{13}\textrm{C}_{2}-^{11}\textrm{C}_{2}+2$ = 535

Q:

Some children goto ice-cream shop. 9 flavours are available there. Each child takes a cone with two different flavours. No two children take same combination and they have taken all such possible combinations. How many children went to ice cream shop ?

 A) 28 B) 56 C) 44 D) 36

Explanation:

Given there are 9 flavours of ice creams.
Each child takes the combination of two flavours and no two children will have the same combination
This can be done by 9C2 ways i.e children.
Number of children = 9C2 = 9 x 8 / 2 = 36.

2 22
Q:

In how many ways can the letters of the word 'LEADER' be arranged ?

 A) 360 B) 420 C) 576 D) 220

Explanation:

No. of letters in the word = 6
No. of 'E' repeated = 2
Total No. of arrangement = 6!/2! = 360

1 20
Q:

In how many different ways could couples be picked from 6 men and 9 women ?

 A) 26 B) 54 C) 52 D) 28

Explanation:

Number of mens = 8
Number of womens = 5

Different ways could couples be picked = 6c1 x 9c1 = 9 x 6 = 54 ways.

2 43
Q:

How many 6-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that the digits should not repeat and the second last digit is even ?

 A) 521 B) 720 C) 420 D) 225

Explanation:

Let last digit is 2
when second last digit is 4 remaining 4 digits can be filled in 120 ways, similarly second last digit is 6 remained 4 digits can be filled in 120 ways.
so for last digit = 2, total numbers=240

Similarly for 4 and 6
When last digit = 4, total no. of ways =240
and last digit = 6, total no. of ways =240
so total of 720 even numbers are possible.

3 29
Q:

How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed ?

 A) 5040 B) 2525 C) 2052 D) 4521