Probability · NDA previous year questions

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2021 14 questions

Q192021 · 14 Nov 2021
Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct? 1. The number of straight lines that can be drawn by joining any two of these points is 380. 2. The number of triangles that can be drawn by joining any three of these points is 1140. Select the correct answer using the code given below.
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: B
Q1012021 · 14 Nov 2021
Consider the following relations for two events E and F : 1. P(E ∩ F) ≥ P(E) + P(F) - 1 2. P(E ∪ F) = P(E) + P(F) + P(E ∩ F) 3. P(E ∪ F) ≤ P(E) + P(F) Which of the above relations is/are correct?
1. A.1 only
2. B.3 only
3. C.1 and 3 only
4. D.1, 2 and 3
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Answer: C
Q1022021 · 14 Nov 2021
If P(A|B) < P(A), then which one of the following is correct?
1. A.P(B|A) < P(B)
2. B.P(B|A) > P(B)
3. C.P(B|A) = P(B)
4. D.P(B|A) > P(A)
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Answer: A
Q1042021 · 14 Nov 2021
A problem is given to three students A, B and C, whose probabilities of solving the problem independently are $\frac{1}{2}$ , $\frac{3}{4}$ and p respectively. If the probability that the problem can be solved is $\frac{29}{32}$ , then what is the value of p?
1. A. $\frac{2}{5}$
2. B. $\frac{2}{3}$
3. C. $\frac{1}{3}$
4. D. $\frac{1}{4}$
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Answer: D
Q1052021 · 14 Nov 2021
In a cricket match, a batsman hits a six 8 times out of 60 balls he plays. What is the probability that on a ball played he does not hit a six?
1. A. $\frac{2}{3}$
2. B. $\frac{1}{15}$
3. C. $\frac{2}{15}$
4. D. $\frac{13}{15}$
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Answer: D
Q1172021 · 14 Nov 2021
3-digit numbers are formed using the digits 1, 3, 7 without repetition of digits. A number is randomly selected. What is the probability that the number is divisible by 3?
1. A.0
2. B. $\frac{1}{3}$
3. C. $\frac{1}{4}$
4. D. $\frac{1}{8}$
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Answer: A
Q1182021 · 14 Nov 2021
What is the probability that the roots of the equation $x^{2} + x + n = 0$ are real, where $n \in N$ and $n < 4$ ?
1. A.0
2. B. $\frac{1}{4}$
3. C. $\frac{1}{3}$
4. D. $\frac{1}{2}$
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Answer: A
Q1192021 · 14 Nov 2021
If A and B are two events such that $P (not A) = \frac{7}{10}$ , $P (not B) = \frac{3}{10}$ and $P (A ∣ B) = \frac{3}{14}$ , then what is $P (B ∣ A)$ equal to?
1. A. $\frac{11}{14}$
2. B. $\frac{9}{14}$
3. C. $\frac{1}{4}$
4. D. $\frac{1}{2}$
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Answer: D
Q1202021 · 14 Nov 2021
Seven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed adjacently?
1. A. $\frac{7}{15}$
2. B. $\frac{8}{15}$
3. C. $\frac{11}{15}$
4. D. $\frac{13}{15}$
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Answer: A
Q652021 · 18 Apr 2021
Let two events A and B be such that P(A) = L and P(B) = M. Which one of the following is correct?
1. A. $P (A ∣ B) < \frac{L + M - 1}{M}$
2. B. $P (A ∣ B) > \frac{L + M - 1}{M}$
3. C. $P (A ∣ B) \geq \frac{L + M - 1}{M}$
4. D. $P (A ∣ B) = \frac{L + M - 1}{M}$
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Answer: C
Q702021 · 18 Apr 2021
If $P (A \cup B) = \frac{5}{6}$ , $P (A \cap B) = \frac{1}{3}$ and $P (\overset{ˉ}{A}) = \frac{1}{2}$ , then which of the following is/are correct? 1. A and B are independent events. 2. A and B are mutually exclusive events. Select the correct answer using the code given below.
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: A
Q722021 · 18 Apr 2021
A coin is tossed twice. If E and F denote occurrence of head on first toss and second toss respectively, then what is P(E ∪ F) equal to?
1. A. $\frac{1}{4}$
2. B. $\frac{1}{2}$
3. C. $\frac{3}{4}$
4. D. $\frac{1}{3}$
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Answer: C
Q732021 · 18 Apr 2021
In a binomial distribution, the mean is $\frac{2}{3}$ and variance is $\frac{5}{9}$ . What is the probability that random variable D = 2?
1. A. $\frac{5}{36}$
2. B. $\frac{25}{36}$
3. C. $\frac{25}{54}$
4. D. $\frac{25}{216}$
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Answer: D
Q752021 · 18 Apr 2021
If A and B are two events such that $P (A) = \frac{3}{4}$ and $P (B) = \frac{5}{8}$ , then consider the following statements: 1. The minimum value of $P (A \cup B)$ is $\frac{3}{4}$ . 2. The maximum value of $P (A \cap B)$ is $\frac{5}{8}$ . 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
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Answer: C