NDA/NA SOLVED PAPER 2015-II (MATHEMATICS)

Total Questions: 120

81. If : IR → IR, g : IR → IR be two functions given by f(x) = 2x - 3 and g(x) = x³ + 5 then (fog)⁻¹ (x) is equal to

Correct Answer: (b)
Solution:


82. Solve the following equation

Correct Answer: (a)
Solution:

83. Solve the following equation

Correct Answer: (c) 32/15
Solution:



84. Solve the following equation

Correct Answer: (d) 1
Solution:


85. Consider the following statements:

1. f(x) = ln(x) is an increasing function on (0, ∞)
2. f(x) = eˣ - x(ln(x)) is an increasing function on (1, ∞) .

Which of the above statements is/are correct?

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

86. Solve the following equation

Correct Answer: (c) 1/s³
Solution:


87. Consider the following statements :

Statement 1: The function f: IR → IR such that f(x) = x³ for all x ∈ IR is one-one.
Statement 2: f (a) ⇒ f(b) for all a, b ∈ IR if the function fis one-one.

Which one of the following is correct in respect of the above statements ?

Correct Answer: (a) Both the statements are true and Statement 2 is the correct explanation of Statement 1.
Solution:

88. Solve the following equation

Correct Answer: (c) ln(1 + eˣ) + c
Solution:

89. Solve the following equation

Correct Answer: (a) 0
Solution:

90. The area bounded by the coordinate axes and the curve √x + √y = 1, is

Correct Answer: (d) 1/6 square unit
Solution: