5
Q:

# How many 7 digit numbers can be formed using the digits 1, 2, 0, 2, 4, 2, 4?

 A) 120 B) 360 C) 240 D) 424

Explanation:

There are 7 digits 1, 2, 0, 2, 4, 2, 4 in which 2 occurs 3 times, 4 occurs 2 times.

$\inline \therefore$ Number of 7 digit numbers = $\inline \frac{7!}{3!\times 2!}$ = 420

But out of these 420 numbers there are some numbers which beign with '0' and they are not 7-digit numbers. The number of such numbers beginning with '0'.

=$\inline \frac{6!}{3!x2!}=60$

Hence the required number of 7 digits numbers = 420 - 60 = 360

Q:

There are 3 sections with 5 questions each. If four questions are selected from each section, the chance of getting different questions is ?

 A) 1000 B) 625 C) 525 D) 125

Explanation:

Methods for selecting 4 questions out of 5 in the first section = 5x4x3x2x1/4x3x2x1 = 5
similarly for other 2 sections also i.e 5 and 5
so total methods = 5 x 5 x 5 = 125.

3 30
Q:

If two cards are taken one after another without replacing from a pack of 52 cards. What is the probability for the two cards be Ace ?

 A) 51/1221 B) 42/221 C) 1/221 D) 52/1245

Explanation:

Total Combination of getting a card from 52 cards = 52C1
Because there is no replacement, so number of cards after getting first card= 51
Now, Combination of getting an another card= 51C1
Total combination of getting 2 cards from 52 cards without replacement= (52C1)x(51C1)
There are total 4 Ace in stack. Combination of getting 1 Ace is = 4C1
Because there is no replacement, So number of cards after getting first Ace = 3
Combination of getting an another Ace = 3C1
Total Combination of getting 2 Ace without replacement=(4C1)x(3C1)
Now,Probability of getting 2 cards which are Ace = (4C1)x(3C1)/(52C1)x(51C1) = 1/221.

3 40
Q:

A Cricket team of 23 people all shake hands with each other exactly once. How many hand shakes occur ?

 A) 142 B) 175 C) 212 D) 253

Explanation:

The first person shakes hands with 22 different people, the second person also shakes hands with 22 different people, but one of those handshakes was counted in the 22 for the first person, so the second person actually shakes hands with 21 new people. The third person, 20 people, and so on...
So,
22 + 21 + 20 + 19 + 18 + 17 + 16 + 15 + 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
= n(n+1)/2 = 22 x 23 /2 = 11 x 23 = 253.

3 42
Q:

There are three rooms in a Hotel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?

 A) 105 B) 7! x 6! C) 7!/5! D) 420

Explanation:

Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room,

Then, 7C1 x 6C2 x 4C4
= 7 x $\inline \fn_jvn \small \frac{6x5}{2}$ x 1
= 7 x 15 = 105.

4 141
Q:

How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines?

 A) 215 B) 315 C) 415 D) 115