NDA/NA SOLVED PAPER 2015-I (MATHEMATICS)

Total Questions: 120

81. Solve the following equation

Correct Answer: (b) 1

82. What is the value of a?


where a, b are constants. The function is continuous everywhere.

Correct Answer: (d) 2
Solution:



83. What is the value of b?


where a, b are constants. The function is continuous everywhere.

Correct Answer: (a) -1
Solution:


From solution 82, b = -1

84. Consider the following functions:

1. f(x) = xΒ³, x ∈ 𝐑
2. f(x) = sin x, 0 < x < 2Ο€
3. f(x) = eΛ£, x ∈ 𝐑

Which of the above functions have inverse defined on their ranges?

Correct Answer: (c) 1 and 3 only

85. What is r equal to?


Correct Answer: (b)
Solution:

86. What is Ξ± equal to?


Correct Answer: (a)
Solution:a = r sin Ξ± Β  ...(i)
b = r cos Ξ±Β  ...(ii)
Dividing (i) from (ii),
a/b = tan alpha
α = tan⁻¹(a/b)

87. At what value of x does f(x) attain minimum value?

Correct Answer: (b) 0
Solution:


88. What is the minimum value of f(x)?

Correct Answer: (c) -1
Solution:f(x) is minimum at x = 0
∴ f(0) = -1/1 = - 1
∴ minimum value of f(x) is -1
∴ Option (c) is correct.

89. What is the value of Ξ± ?


Which is continuous at x = Ο€/2 where a is a constant.

Correct Answer: (a) 6
Solution:

90. Solve the following equation


Which is continuous at x = Ο€/2 where a is a constant.

Correct Answer: (d) 6/Ο€
Solution: