Probability · NDA previous year questions

What is the $n^{th}$ term of the sequence 1, 5, 9, 13, 17, ...?

1. A.$2n-1$
2. B.$2n+1$
3. C.$4n-3$
4. D.None of the above

Three dice are thrown. What is the probability that the same number will appear on each of them?

1. A.1/6
2. B.1/18
3. C.1/24
4. D.1/36

For the next TWO (02) questions that follow: The equation formed by multiplying each root of $a{x}^2+bx+c=0$ by 2 is $x^2+36x+24=0$. What is b : c equal to?

1. A.3 : 1
2. B.1 : 2
3. C.1 : 3
4. D.3 : 2

For the next TWO (02) questions that follow: The equation formed by multiplying each root of $a{x}^2+bx+c=0$ by 2 is $x^2+36x+24=0$. Which one of the following is correct?

1. A.$bc=a^2$
2. B.$bc=36a^2$
3. C.$bc=72a^2$
4. D.$bc=108a^2$

For the next THREE (03) questions that follow: Let $\sin (A+B)=1$ and $\sin (A-B)=1/2$, where $A,B\in [0,\frac{\pi }{2}]$. What is the value of A?

1. A.$\frac{\pi }{6}$
2. B.$\frac{\pi }{3}$
3. C.$\frac{\pi }{4}$
4. D.$\frac{\pi }{8}$

For the next THREE (03) questions that follow: Let $\sin (A+B)=1$ and $\sin (A-B)=1/2$, where $A,B\in [0,\frac{\pi }{2}]$. What is $\tan (A+2B).\tan (2A+B)$ equal to?

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

For the next THREE (03) questions that follow: Let $\sin (A+B)=1$ and $\sin (A-B)=1/2$, where $A,B\in [0,\frac{\pi }{2}]$. What is ${\sin }^{2}A-{\sin }^{2}B$ equal to?

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

What is the probability that a leap year selected at random contains 53 Mondays?

1. A.1/7
2. B.2/7
3. C.7/366
4. D.26/183

If four dice are thrown together, then what is the probability that the sum of the numbers appearing on them is 25 ?

1. A.0
2. B.1/2
3. C.1
4. D.1/1296

Two letters are drawn at random from the word 'HOME'. What is the probability that both the letters are vowels?

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

If $z=1+i\tan \alpha$ where $\pi <\alpha <\frac{3\pi }{2}$, then what is $|z|$ equal to?

1. A.$\sec \alpha$
2. B.$-\sec \alpha$
3. C.${\sec }^2\alpha$
4. D.$-{\sec }^2\alpha$

A husband and wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is 1/5 and that of wife’s selection is 1/3. What is the probability that only one of them will be selected ?

1. A.1/5
2. B.2/5
3. C.3/5
4. D.4/5

There is a point inside a circle. What is the probability that this point is close to the circumference than to the centre ?

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

How many diagonals will be there in an n-sided regular polygon ?

1. A.$\frac{n(n-1)}{2}$
2. B.$\frac{n(n-3)}{2}$
3. C.$n^2-n$
4. D.$\frac{n(n+1)}{2}$

In a random arrangement of the letters of the word ‘UNIVERSITY’, what is the probability that two I’s do not come together ?

1. A.4/5
2. B.1/5
3. C.1/10
4. D.9/10

If $\tan A=1/2$ and $\tan B=1/3$, then what is the value of $4A+4B$ ?

1. A.$\pi /4$
2. B.$\pi /2$
3. C.$\pi$
4. D.$2\pi$

In a class of 125 students 70 passed in Mathematics, 55 passed in Statistics and 30 passed in both. What is the probability that a student selected at random from the class has passed in only one subject?

1. A.13/25
2. B.3/25
3. C.17/25
4. D.8/25

There are 4 letters and 4 directed envelopes. These 4 letters are randomly inserted into the 4 envelopes. What is the probability that the letters are inserted into the corresponding envelopes?

1. A.11/12
2. B.23/24
3. C.1/24
4. D.None of the above

The average daily income of workers of a factory including that of the owner is ₹ 110. However, if the income of the owner is excluded, the average daily income of the remaining 9 workers is ₹ 76. What is the daily income of the owner?

1. A.₹ 300
2. B.₹ 316
3. C.₹ 322
4. D.₹ 416

In an examination, there are 3 multiple-choice questions and each question has 4 choices. If a student randomly selects an answer for all the three questions, what is the probability that the student will not answer all the three questions correctly?

1. A.1/64
2. B.63/64
3. C.1/12
4. D.11/12

If $A$ and $B$ are two mutually exclusive events, then what is $P(AB)$ equal to?

1. A.0
2. B.$P(A)+P(B)$
3. C.$P(A)P(B)$
4. D.$P(A)P(B\mid A)$

If $x=\sin \theta +\cos \theta$ and $y=\sin \theta .\cos \theta$, then what is the value of $x^4-4x^{2}y-2x^2+4y^2+4y+1$?

1. A.0
2. B.1
3. C.2
4. D.None of the above

What is ${\lim }_{x\to \infty }\left(\sqrt{a^2{x}^2+ax+1}-\sqrt{a^2{x}^2+1}\right)$ equal to?

1. A.$\frac{1}{2}$
2. B.1
3. C.2
4. D.0

An experiment consists of flipping a coin and then flipping it a second time if head occurs. If a tail occurs on the first flip, then a six-faced die is tossed once. Assuming that the outcomes are equally likely, what is the probability of getting one head and one tail?

1. A.1/4
2. B.1/36
3. C.1/6
4. D.1/8

If, in general, the value of $\sin A$ is known, but the value of $A$ is not known, then how many values of $\tan (A/2)$ can be calculated ?

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