Probability · NDA previous year questions

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2026 20 questions

Q262026 · 12 Apr 2026
Passage: A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that the number selected does not contain zero at any position ?
1. A. $0 \cdot 12$
2. B. $0 \cdot 25$
3. C. $0 \cdot 375$
4. D. $0 \cdot 45$
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Answer: B
Q272026 · 12 Apr 2026
Passage: A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that the number selected is divisible by 4 ?
1. A. $\frac{1}{2}$
2. B. $\frac{7}{16}$
3. C. $\frac{9}{16}$
4. D. $\frac{5}{16}$
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Answer: D
Q282026 · 12 Apr 2026
Passage: A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that the number selected is divisible by 3 ?
1. A. $\frac{9}{28}$
2. B. $\frac{3}{8}$
3. C. $\frac{3}{16}$
4. D. $\frac{8}{25}$
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Answer: B
Q292026 · 12 Apr 2026
Passage: A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that the number selected is divisible by 2 ?
1. A. $\frac{5}{8}$
2. B. $\frac{3}{8}$
3. C. $\frac{1}{8}$
4. D. $\frac{5}{24}$
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Answer: A
Q302026 · 12 Apr 2026
How many numbers greater than 1000 can be formed using the digits 0, 1, 2 and 3 (repetition of digits is not allowed) ?
1. A.24
2. B.18
3. C.15
4. D.12
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Answer: B
Q312026 · 12 Apr 2026
If $n =^{m} C_{2}$ then what is $^{n} C_{2}$ equal to ?
1. A. $^{m + 1} C_{4}$
2. B. $2 \times^{m + 1} C_{4}$
3. C. $3 \times^{m + 1} C_{4}$
4. D. $^{m + 2} C_{4}$
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Answer: C
Q512026 · 12 Apr 2026
Passage: The foci of the ellipse $p x^{2} + 16 y^{2} = 16 p$ and the foci of the hyperbola $25 (81 x^{2} - 144 y^{2}) = 11664$ coincide (assume $p < 16$ ). Question: What is the difference between the eccentricities of the hyperbola and the ellipse ?
1. A. $0 \cdot 5$
2. B. $0 \cdot 75$
3. C. $1 \cdot 0$
4. D. $1 \cdot 25$
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Answer: A
Q522026 · 12 Apr 2026
Passage: The foci of the ellipse $p x^{2} + 16 y^{2} = 16 p$ and the foci of the hyperbola $25 (81 x^{2} - 144 y^{2}) = 11664$ coincide (assume $p < 16$ ). Question: What is the value of $p$ ?
1. A. $7$
2. B.3
3. C.7
4. D.9
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Answer: C
Q532026 · 12 Apr 2026
1. A.0
2. B.1
3. C. $ln 10$
4. D. $lo g_{10} e$
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Answer: C
Q542026 · 12 Apr 2026
1. A.0
2. B.1
3. C. $n - 1$
4. D. $n + 1$
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Answer: C
Q572026 · 12 Apr 2026
If the random variable $X$ has mean 3 and standard deviation 5, then what is the variance of the random variable $Y = 2 X - 5$ ?
1. A.15
2. B.40
3. C.45
4. D.100
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Answer: D
Q1112026 · 12 Apr 2026
Three events $A, B$ and $C$ are such that $A$ and $B$ are disjoint, $A$ and $C$ are independent, $B$ and $C$ are independent. If $4 P (A) = 2 P (B) = P (C)$ and $P (A \cup B \cup C) = 5 P (A)$ , then what is the value of $P (C)$ ?
1. A. $\frac{5}{6}$
2. B. $\frac{1}{3}$
3. C. $\frac{1}{6}$
4. D. $\frac{2}{3}$
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Answer: D
Q1132026 · 12 Apr 2026
Consider the following statements in respect of the events $A, B, C$ : I. $(A \cup B \cup C) \cap (\overline{A} \cap \overline{B} \cap \overline{C})$ is an impossible event. II. $(A \cap B \cap C) \cap (\overline{A \cup B \cup C})$ is a possible event. Which of the statements given above is/are correct ?
1. A.I only
2. B.II only
3. C.Both I and II
4. D.Neither I nor II
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Answer: A
Q1142026 · 12 Apr 2026
In an entrance test there are multiple choice questions. There are four options for each question, of which only one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then what is the probability that he was guessing ?
1. A. $\frac{37}{40}$
2. B. $\frac{36}{37}$
3. C. $\frac{1}{37}$
4. D. $\frac{1}{40}$
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Answer: C
Q1152026 · 12 Apr 2026
Passage: Four dice are rolled. Question: What is the probability that getting a total of the numbers on the dice is at least 23 ?
1. A. $\frac{1}{1296}$
2. B. $\frac{1}{432}$
3. C. $\frac{1}{324}$
4. D. $\frac{5}{1296}$
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Answer: D
Q1162026 · 12 Apr 2026
Passage: Four dice are rolled. Question: What is the probability that getting a total of the numbers on the dice is 6 ?
1. A. $\frac{1}{216}$
2. B. $\frac{1}{324}$
3. C. $\frac{5}{648}$
4. D. $\frac{7}{648}$
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Answer: C
Q1172026 · 12 Apr 2026
Passage: Let $A, B, C$ and $D$ be mutually exclusive and exhaustive events and $\frac{P ( A )}{2} = \frac{P ( B )}{3} = \frac{P ( C )}{5} = \frac{P ( D )}{8}$ . Question: If $G$ is the geometric mean of $P (A), P (B), P (C)$ and $P (D)$ , then what is $9 G$ equal to ?
1. A. $1 7^{\frac{1}{4}}$
2. B. $1 5^{\frac{1}{4}}$
3. C. $1 3^{\frac{1}{4}}$
4. D. $1 1^{\frac{1}{4}}$
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Answer: B
Q1182026 · 12 Apr 2026
Passage: Let $A, B, C$ and $D$ be mutually exclusive and exhaustive events and $\frac{P ( A )}{2} = \frac{P ( B )}{3} = \frac{P ( C )}{5} = \frac{P ( D )}{8}$ . Question: What is $\frac{[ 2 P ( A ) + 3 P ( B )]}{[ 4 P ( C ) + 5 P ( D )]}$ equal to ?
1. A. $\frac{13}{18}$
2. B. $\frac{13}{60}$
3. C. $\frac{4}{21}$
4. D. $\frac{5}{28}$
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Answer: B
Q1192026 · 12 Apr 2026
Passage: Let $A, B, C$ and $D$ be mutually exclusive and exhaustive events and $\frac{P ( A )}{2} = \frac{P ( B )}{3} = \frac{P ( C )}{5} = \frac{P ( D )}{8}$ . Question: What is $P (A) + P (B) + P (C)$ equal to ?
1. A. $\frac{5}{9}$
2. B. $\frac{1}{18}$
3. C. $\frac{2}{21}$
4. D. $\frac{7}{18}$
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Answer: A
Q1202026 · 12 Apr 2026
Passage: A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that the number selected is divisible by 6 ?
1. A. $\frac{7}{48}$
2. B. $\frac{2}{3}$
3. C. $\frac{1}{4}$
4. D. $\frac{3}{8}$
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Answer: C