Probability · NDA previous year questions

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2011 20 questions

Q192011 · 21 Aug 2011
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
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Answer: A
Q202011 · 21 Aug 2011
If $z = 1 + i tan α$ where $π < α < \frac{3 π}{2}$ , then what is $∣ z ∣$ equal to?
1. A. $sec α$
2. B. $- sec α$
3. C. $sec^{2} α$
4. D. $- sec^{2} α$
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Answer: B
Q422011 · 21 Aug 2011
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
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Answer: B
Q462011 · 21 Aug 2011
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
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Answer: A
Q472011 · 21 Aug 2011
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. $\frac{n ( n + 1 )}{2}$
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Answer: B
Q632011 · 21 Aug 2011
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
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Answer: A
Q642011 · 21 Aug 2011
If $tan A = 1/2$ and $tan B = 1/3$ , then what is the value of $4 A + 4 B$ ?
1. A. $π /4$
2. B. $π /2$
3. C. $π$
4. D. $2 π$
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Answer: C
Q702011 · 21 Aug 2011
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
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Answer: A
Q202011 · 17 Apr 2011
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
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Answer: C
Q212011 · 17 Apr 2011
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
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Answer: D
Q802011 · 17 Apr 2011
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
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Answer: B
Q832011 · 17 Apr 2011
If $A$ and $B$ are two mutually exclusive events, then what is $P (A B)$ equal to?
1. A.0
2. B. $P (A) + P (B)$
3. C. $P (A) P (B)$
4. D. $P (A) P (B ∣ A)$
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Answer: A
Q842011 · 17 Apr 2011
If $x = sin θ + cos θ$ and $y = sin θ . cos θ$ , then what is the value of $x^{4} - 4 x^{2} y - 2 x^{2} + 4 y^{2} + 4 y + 1$ ?
1. A.0
2. B.1
3. C.2
4. D.None of the above
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Answer: A
Q852011 · 17 Apr 2011
What is $lim_{x \to \infty} (a^{2} x^{2} + a x + 1 - a^{2} x^{2} + 1)$ equal to?
1. A. $\frac{1}{2}$
2. B.1
3. C.2
4. D.0
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Answer: A
Q962011 · 17 Apr 2011
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
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Answer: D
Q972011 · 17 Apr 2011
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
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Answer: B
Q982011 · 17 Apr 2011
Consider the following : 1. $cosec^{- 1} (- \frac{2}{3}) = - \frac{π}{3}$ 2. $sec^{- 1} (\frac{2}{3}) = \frac{π}{6}$ Which of the above is/are correct?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: C
Q992011 · 17 Apr 2011
Consider the following statements with regard to correlation coefficient $r$ between random variables $x$ and $y$ : 1. $r = + 1$ or $- 1$ means there is a linear relation between $x$ and $y$ . 2. $- 1 \leq r \leq 1$ and $r^{2}$ is a measure of the linear relationship between the variables. Which of the statements given above is/are correct ?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: C
Q1012011 · 17 Apr 2011
A box contains 6 distinct dolls. From this box, three dolls are randomly selected one by one with replacement. What is the probability of selecting 3 distinct dolls?
1. A.5/54
2. B.12/25
3. C.1/20
4. D.5/9
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Answer: D
Q1032011 · 17 Apr 2011
If $A$ and $B$ are events such that $P (A \cup B) = 0 \cdot 5$ , $P (\overline{B}) = 0 \cdot 8$ and $P (A ∣ B) = 0 \cdot 4$ , then what is $P (A \cap B)$ equal to ?
1. A. $0 \cdot 08$
2. B. $0 \cdot 02$
3. C. $0 \cdot 8$
4. D. $0 \cdot 2$
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Answer: A