advance math mcq pdf Model Questions & Answers, Practice Test for ibps rrb so officer sclae 2 3 single exam 2024

Answer: (a)

There can be five cases :

Case I : First triangle can have 5 balls and rest three 1 each.

So, number of ways for (5, 1, 1, 1) = ${4!}/{3!}$ = 4

(∵ Three triangles are having same number of balls)

Case II : Number of ways for (4, 2, 1, 1) = ${4!}/{2!}$ = 12

(∵ Two triangles are having same number of balls)

Case III : Similarly, number of ways for (2, 2, 2, 2) = ${4!}/{4!}$ = 1

Case IV : Number of ways for (3, 3, 1, 1) = ${4!}/{2! × 2!}$ = 6

Case V : Number of ways for (3, 2, 2, 1) = ${4!}/{2!}$ = 12

As, either of these five cases are possible,

Hence total number of ways = 4 + 12 + 1 + 6 + 12 = 35

Answer: (b)

Total number of arrangements of letters in the word GARDEN = 6 ! = 720 there are two vowels A and E, in half of the arrangements A preceeds E and other half A follows E.

So, vowels in alphabetical order in $1/2$ × 720 = 360

Answer: (c)

Task 1 can not be assigned to either person 1 or 2 i.e. there are 4 options.

Task 2 can be assigned to 3 or 4

So, there are only 2 options for task 2.

So required no. of ways = 2 options for task 2 × 3 options for task 1 × 4 options for task 3 × 3 options for task 4 × 2 options for task 5 × 1 option for task 6.

= 2 × 3 × 4 × 3 × 2 × 1 = 144

Answer: (b)

Since, probabilities of failure for engines A, B and C P(A), P(B) and P(C) are 0.03, 0.02 and 0.05 respectively. The aircraft will crash only when all the three engine fail. So, probability that it crashes = P(A). P(B). P(C)

= 0.03 × 0.02 × 0.05

= 0.00003

Hence, the probability that the aircraft will not crash,

= 1 – 0.00003

= 0.99997

Answer: (b)

These routes are:

A 1 2 B, A 1 4 5 B, A 3 4 5B,

A 3 4 7 B, A 1 4 3 6 B, A 3 6 B