Permutations & Combinations · NDA previous year questions

The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is

1. A.45360
2. B.30240
3. C.27216
4. D.15120

A tea party is arranged for 16 people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is

1. A.$24\times 8!\times 8!$
2. B.$(8!{)}^3$
3. C.$210\times 8!\times 8!$
4. D.$16!$

A man running round a racecourse notes that the sum of the distances of two flag-posts from him is always 10 m and the distance between the flag-posts is 8 m. The area of the path he encloses is

1. A.$18\pi$ square metres
2. B.$15\pi$ square metres
3. C.$12\pi$ square metres
4. D.$8\pi$ square metres

How many different permutations can be made out of the letters of the word ‘PERMUTATION’?

1. A.19958400
2. B.19954800
3. C.19952400
4. D.39916800

1. A.$\left[\begin{array}{cc}2+3i& 5\\ 7& 2-3i\end{array}\right]$
2. B.$\left[\begin{array}{cc}2-3i& 5\\ 7& 2+3i\end{array}\right]$
3. C.$\left[\begin{array}{cc}2-3i& 7\\ 5& 2+3i\end{array}\right]$
4. D.$\left[\begin{array}{cc}2+3i& 5\\ 7& 2+3i\end{array}\right]$

A five-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3 and 4 without repetition of digits. What is the number of ways this can be done ?

1. A.96
2. B.48
3. C.32
4. D.No number can be formed

What is ${}^{47}{C}_4+{}^{51}{C}_3+{\sum }_{j=2}^5{}^{52-j}{C}_3$ equal to ?

1. A.${}^{52}{C}_4$
2. B.${}^{51}{C}_5$
3. C.${}^{53}{C}_4$
4. D.${}^{52}{C}_5$

What is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets?

1. A.60
2. B.120
3. C.500
4. D.1000

$A,B,C$ and $D$ are four sets such that $A\cap B=C\cap D=\varphi$. Consider the following: 1. $A\cup C$ and $B\cup D$ are always disjoint. 2. $A\cap C$ and $B\cap D$ are always disjoint. 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

If $a,b,c$ are the sides of a triangle $ABC$, then $a^{\frac{1}{p}}+b^{\frac{1}{p}}-c^{\frac{1}{p}}$ where $p>1$, is

1. A.always negative
2. B.always positive
3. C.always zero
4. D.positive if $1<p<2$ and negative if $p>2$

If different words are formed with all the letters of the word ‘AGAIN’ and are arranged alphabetically among themselves as in a dictionary, the word at the 50th place will be

1. A.NAAGI
2. B.NAAIG
3. C.IAAGN
4. D.IAANG

The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, is

1. A.165
2. B.364
3. C.1001
4. D.1365

A polygon has 44 diagonals. The number of its sides is

1. A.11
2. B.10
3. C.8
4. D.7

The number of ways in which 3 holiday tickets can be given to 20 employees of an organization if each employee is eligible for any one or more of the tickets, is

1. A.1140
2. B.3420
3. C.6840
4. D.8000

The number of 3-digit even numbers that can be formed from the digits 0, 1, 2, 3, 4 and 5, repetition of digits being not allowed, is

1. A.60
2. B.56
3. C.52
4. D.48

What is the number of ways in which one can post 5 letters in 7 letter boxes ?

1. A.$7^5$
2. B.$3^5$
3. C.$5^7$
4. D.2520

What is the number of ways that a cricket team of 11 players can be made out of 15 players ?

1. A.364
2. B.1001
3. C.1365
4. D.32760

Consider the following statements: 1. $\sin |x|+\cos |x|$ is always positive. 2. $\sin (x^2)+\cos (x^2)$ is always positive. 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

What is $\frac{1+\sin A}{1-\sin A}-\frac{1-\sin A}{1+\sin A}$ equal to?

1. A.$\sec A-\tan A$
2. B.$2\sec A\cdot \tan A$
3. C.$4\sec A\cdot \tan A$
4. D.$4\mathrm{cosec}A\cdot \cot A$

What is $\frac{\cot 224^{\circ }-\cot 134^{\circ }}{\cot 226^{\circ }+\cot 316^{\circ }}$ equal to?

1. A.$-\mathrm{cosec}88^{\circ }$
2. B.$-\mathrm{cosec}{2}^{\circ }$
3. C.$-\mathrm{cosec}44^{\circ }$
4. D.$-\mathrm{cosec}46^{\circ }$

If $A+B+C=\pi$, then what is $\cos (A+B)+\cos C$ equal to?

1. A.$0$
2. B.$2\cos C$
3. C.$\cos C-\sin C$
4. D.$2\sin C$

What is $\cos 20^{\circ }+\cos 100^{\circ }+\cos 140^{\circ }$ equal to?

1. A.$2$
2. B.$1$
3. C.$1/2$
4. D.$0$

What is ${\sin }^2(3\pi )+{\cos }^2(4\pi )+{\tan }^2(5\pi )$ equal to?

1. A.$0$
2. B.$1$
3. C.$2$
4. D.$3$

The complete solution of $3{\tan }^{2}x=1$ is given by: where $n\in Z$

1. A.$x=n\pi \pm \frac{\pi }{3}$
2. B.$x=n\pi +\frac{\pi }{3}$ only
3. C.$x=n\pi \pm \frac{\pi }{6}$
4. D.$x=n\pi +\frac{\pi }{6}$ only

What is the value of $\cos 36^{\circ }$?

1. A.$\frac{\sqrt{5}-1}{4}$
2. B.$\frac{\sqrt{5}+1}{4}$
3. C.$\frac{\sqrt{10+2\sqrt{5}}}{4}$
4. D.$\frac{\sqrt{10-2\sqrt{5}}}{4}$