NDA/NA SOLVED PAPER 2015-II (MATHEMATICS)

Total Questions: 120

111. Solve the following equation

Correct Answer: (c)
Solution:

112. The arithmetic mean of 1, 8, 27, 64, ..... up to n terms is given by

Correct Answer: (c)
Solution:

113. An unbiased coin is tossed until the first head appears or until four tosses are completed, whichever happens earlier. Which of the following statements is/are correct?

1. The probability that no head is observed is 1/16.
2. The probability that the experiment ends with three tosses is 1/8.

Select the correct answer using the code given below:

Correct Answer: (c) Both 1 and 2
Solution:

Hence, both statements are correct.

114. If x ∈ [0, 5] then what is the probability that x² - 3x + 2 ≥ 0 ?

Correct Answer: (a) 4/5
Solution:

115. A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability that one ball is white and one ball is black is

Correct Answer: (b) 13/24
Solution:

116. problem in statistics is given to three students A, B and C whose chances of solving it independently are 1/2, 1/3 and 1/4 respectively. The probability that the problem will be solved is

Correct Answer: (d) 3/4
Solution:

117. An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probabilities of an accident involving a scooter driver, car driver and a truck driver are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. The probability that the person is a scooter driver is

Correct Answer: (a) 1/52
Solution:


118. A coin is tossed 5 times. The probability that tail appears an odd number of times, is

Correct Answer: (a) 1/2
Solution:

119. The regression coefficients of a bivariate distribution are -0.64 and -0.36. Then the correlation coefficient of the distribution is

Correct Answer: (b) -0.48
Solution:

120. What is the probability that the sum of any two different single digit natural numbers is a prime number?

Correct Answer: (b) 7/18
Solution:Total no. of two different single digit natural number = ⁹C₂ = 36
The number of prime numbers which is sum of two different single digit number.
(3, 5, 7, 11 ,13 & 17) = 14
∴ Required probability = 14/36 = 7/18