Probability · NDA previous year questions

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.$0\cdot 45$

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.$\frac{5}{16}$

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.$\frac{8}{25}$

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.$\frac{5}{24}$

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

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.${}^{m+2}{C}_4$

Passage: The foci of the ellipse $p{x}^2+16y^2=16p$ and the foci of the hyperbola $25(81x^2-144y^2)=11664$ 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.$1\cdot 25$

Passage: The foci of the ellipse $p{x}^2+16y^2=16p$ and the foci of the hyperbola $25(81x^2-144y^2)=11664$ coincide (assume $p<16$). Question: What is the value of $p$ ?

1. A.$\sqrt{7}$
2. B.3
3. C.7
4. D.9

1. A.0
2. B.1
3. C.$\ln 10$
4. D.${\log }_{10}e$

1. A.0
2. B.1
3. C.$n-1$
4. D.$n+1$

If the random variable $X$ has mean 3 and standard deviation 5, then what is the variance of the random variable $Y=2X-5$ ?

1. A.15
2. B.40
3. C.45
4. D.100

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 $4P(A)=2P(B)=P(C)$ and $P(A\cup B\cup C)=5P(A)$, 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.$\frac{2}{3}$

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

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.$\frac{1}{40}$

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.$\frac{5}{1296}$

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.$\frac{7}{648}$

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 $9G$ equal to ?

1. A.$17^{\frac{1}{4}}$
2. B.$15^{\frac{1}{4}}$
3. C.$13^{\frac{1}{4}}$
4. D.$11^{\frac{1}{4}}$

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 $\frac{[2P(A)+3P(B)]}{[4P(C)+5P(D)]}$ equal to ?

1. A.$\frac{13}{18}$
2. B.$\frac{13}{60}$
3. C.$\frac{4}{21}$
4. D.$\frac{5}{28}$

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.$\frac{7}{18}$

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.$\frac{3}{8}$

In a sample survey of a village, the probability that a farmer is in debt is 0.60. What is the probability that three randomly selected farmers are all in debt (assume independence of events)?

1. A.0.000216
2. B.0.064
3. C.0.216
4. D.0.512

The probability that a family owns a laptop is 0.68; that it also owns a desktop is 0.56. If the probability that it owns both is 0.48, then what is the probability that a randomly selected family owns a laptop or a desktop?

1. A.0.80
2. B.0.76
3. C.0.36
4. D.0.28

An urn contains 10 white and 5 red balls. If two balls are drawn at random, then what is the probability that both the balls are red?

1. A.2/21
2. B.1/7
3. C.4/21
4. D.3/7

An urn contains 5 white, 6 red and 4 blue balls. Three balls are drawn at random. What is the probability that a white ball, a red ball and a blue ball are drawn?

1. A.28/91
2. B.2/7
3. C.24/91
4. D.23/91

A person X speaks the truth 4 out of 5 times and person Y speaks the truth 5 out of 6 times. What is the probability that they will contradict each other in stating the fact?

1. A.3/10
2. B.1/15
3. C.1/6
4. D.7/10