NDA/NA SOLVED PAPER 2015-II (MATHEMATICS)

Total Questions: 120

101. The degree of the differential equation

Correct Answer: (d) 5
Solution:

102. Solve the following equation

Correct Answer: (c)
Solution:

103. The differential equation of the family of circles passing through the origin and having centres on the x-axis is

Correct Answer: (b)
Solution:

104. The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a, 0) where a > 0, are respectively

Correct Answer: (a) 1, 1
Solution:


105. f(xy) = f(x) + f(y) is true for all

Correct Answer: (d) Logarithmic functions f
Solution:Let f(x) = logx
∴ f(y) = log y & f(xy) = log (xy) = log x + log y
⇒ f(xy) = f(x) + f(y)

106. Three digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8 and 9 without repeating any digit. What is the probability that the product is odd?.

Correct Answer: (c) 5/42
Solution:Total no. of 3-digit numbers = 9 ×8×7 = 504
For product to be odd, we have to choose only from odd numbers.
∴ Total no. of 3-digit no. whose product are odd = 5 × 4 × 3 = 60
∴ Required probability = 60/504 = 5/42

107. Two events A and B are such that P(notB) = 0.8 P( A ∪ B)= 0.5 and P( A|B)=0.4 Then P(A) is equal to

Correct Answer: (c) 0.38
Solution:

108. If mean and variance of a Binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than 1 is

Correct Answer: (d) 11/16
Solution:

109. Seven unbiased coins are tossed 128 times. In how many throws would you find at least three heads ?

Correct Answer: (a) 99
Solution:

110. A coin is tossed five times. What is the probability that heads are observed more than three times ?

Correct Answer: (a) 3/16
Solution: