Permutations & Combinations · NDA previous year questions

In how many ways can the letters of the word DELHI be arranged, keeping the positions of vowels and consonants unchanged?

1. A.6
2. B.9
3. C.12
4. D.14

What is the number of positive integer solutions of x+y+z=5?

1. A.3
2. B.5
3. C.6
4. D.9

In how many ways can the letters of the word INDIA be permutated such that in each combination, vowels should occupy odd positions?

1. A.3
2. B.6
3. C.9
4. D.12

The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?

1. A.240
2. B.720
3. C.1440
4. D.1620

In how many ways can a student choose (n - 2) courses out of n courses if 2 courses are compulsory (n > 4)?

1. A.(n - 3) (n - 4)
2. B.(n - 1) (n - 2)
3. C.(n - 3) (n - 4)/2
4. D.(n - 2) (n - 3)/2

1. A.-10000
2. B.-10
3. C.10
4. D.10000

A man has 7 relatives (4 women and 3 men). His wife also has 7 relatives (3 women and 4 men). In how many ways can they invite 3 women and 3 men so that 3 of them are man's relatives and 3 of them are his wife's relatives?

1. A.340
2. B.484
3. C.485
4. D.469

Let AX = B be a system of 3 linear equations with 3-unknowns. Let X  and X  be its two distinct solutions. If the combination aX  + bX  is a solution of AX = B; where a, b are real numbers, then which one of the following is correct ?

1. A.a = b
2. B.a + b = 1
3. C.a + b = 0
4. D.a - b = 1

Let x be the number of permutations of the word ‘PERMUTATIONS’ and y be the number of permutations of the word ‘COMBINATIONS’. Which one of the following is correct ?

1. A.x = y
2. B.y = 2x
3. C.x = 4y
4. D.y = 4x

5-digit numbers are formed using the digits 0, 1, 2, 4, 5 without repetition. What is the percentage of numbers which are greater than 50,000 ?

1. A.20%
2. B.25%
3. C.$\frac{100}{3}\%$
4. D.$\frac{110}{3}\%$

How many four-digit natural numbers are there such that all of the digits are odd ?

1. A.625
2. B.400
3. C.196
4. D.120

What is ${\sum }_{r=0}^n{2}^r\mathrm{C}(n,r)$ equal to ?

1. A.$2^n$
2. B.$3^n$
3. C.$2^{2n}$
4. D.$3^{2n}$

If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) are there in the list before the first word that starts with C ?

1. A.302400
2. B.403600
3. C.907200
4. D.1814400

Consider the following statements : 1. $2+4+6+........+2n=n^2+n$ 2. The expression $n^2+n+41$ always gives a prime number for every natural number n Which of the above statements is/are correct ?

1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2

A box contains 2 white balls, 3 black balls, and 4 red balls. What is the number of ways of drawing 3 balls from the box with at least one black ball?

1. A.84
2. B.72
3. C.64
4. D.48

1. A.0
2. B.always positive
3. C.always negative
4. D.positive if p, q, r are positive else negative

1. A.3
2. B.12
3. C.14
4. D.15

How many permutations are there of the letters of the word 'TIGER' in which the vowels should not occupy the even positions ?

1. A.72
2. B.36
3. C.18
4. D.12

In how many ways can a team of 5 players be selected out of 9 players so as to exclude two particular players ?

1. A.14
2. B.21
3. C.35
4. D.42

In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player?

1. A.42
2. B.35
3. C.21
4. D.20

What is the number of ways in which the letters of the word 'ABLE' can be arranged so that the vowels occupy even places?

1. A.2
2. B.4
3. C.6
4. D.8

Under which one of the following conditions will the quadratic equation $x^2+mx+2=0$ always have real roots?

1. A.$2\sqrt{3}\le m^2<8$
2. B.$\sqrt{3}\le m^2<4$
3. C.$m^2\ge 8$
4. D.$m^2\le \sqrt{3}$

From 6 programmers and 4 typists, an office wants to recruit 5 people. What is the number of ways this can be done so as to recruit at least one typist?

1. A.209
2. B.210
3. C.246
4. D.242

How many three-digit even numbers can be formed using the digits 1, 2, 3, 4 and 5 when repetition of digits is not allowed?

1. A.36
2. B.30
3. C.24
4. D.12

There are 17 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so as to include 3 bowlers?

1. A.$C(17,11)$
2. B.$C(12,8)$
3. C.$C(17,5)\times C(5,3)$
4. D.$C(5,3)\times C(12,8)$