Inverse functions Practice Questions - NDA Mathematics Question Bank

Question 1 of 10 Authentic UPSC NDA Question

For the following two (02) items:

If the function is continuous, then what is the

value of k?

Step-by-Step Logic & Solution

Question 2 of 10 Authentic UPSC NDA Question

Direction for Questions (117-118): Consider the following for the two (02) items that follow:

The slope of the tangent of the curve y = f(x) at (x, f(x)) is 4 for every real number x and the curve passes through the origin.

What is the area bounded by the curve the x-axis and the line x = 4?

Step-by-Step Logic & Solution

Question 3 of 10 Authentic UPSC NDA Question

Direction for Questions (117-118): Consider the following for the two (02) items that follow:

The slope of the tangent of the curve y = f(x) at (x, f(x)) is 4 for every real number x and the curve passes through the origin.

What is the nature of the curve?

Step-by-Step Logic & Solution

Question 4 of 10 Authentic UPSC NDA Question

Direction for Questions (115-116): Consider the following for the two (02) items that follow: Let (x + y^{)p + q}= x^py^p, where p, q are positive integers.

If p + q = 10, then what is dy/dx equal to?

Step-by-Step Logic & Solution

Question 5 of 10 Authentic UPSC NDA Question

Direction for Questions (115-116): Consider the following for the two (02) items that follow: Let (x + y^{)p + q}= x^py^p, where p, q are positive integers.

The derivative of y with respect to x:

Step-by-Step Logic & Solution

Question 6 of 10 Authentic UPSC NDA Question

Direction for Questions (109-110): Consider the following for the two (02) items that follow:

Let the function f(x) = x² – 1

. What is equal to?

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Question 7 of 10 Authentic UPSC NDA Question

Direction for Questions (107-108): Consider the following for the two (02) items that follow: Let f = {(1, 1), (2, 4), (3, 7), (4, 10)}

Consider the following statements:

I. f is an one-one function.

II. f is onto function if the codomain is the set of natural numbers.

Which of the statements given above is/are correct?

Step-by-Step Logic & Solution

Explanation: \

f(x) = px + q is linear polynomial so, f(x) is one-one Range = {1, 4, 7, 10} codomain = N So it is not onto.

Question 8 of 10 Authentic UPSC NDA Question

Direction for Questions (107-108): Consider the following for the two (02) items that follow: Let f = {(1, 1), (2, 4), (3, 7), (4, 10)}

If f(x) = px + q, then what is the value of (p + q)?

Step-by-Step Logic & Solution

Explanation: f(x) = px + q put x = 1 and y = 1 p + q = 1

Question 9 of 10 Authentic UPSC NDA Question

Direction for Questions (105-106): Consider the following for the two (02) items that follow: Let the curve f(x) = |x – 3|.

What is the domain of the function f(x)?

Step-by-Step Logic & Solution

Explanation: Domain of f(x) = |x – 3| is (–∞,∞)

Question 10 of 10 Authentic UPSC NDA Question

Direction for Questions (103-104): Consider the following for the two (02) items that follow: Let the function f(x) = sin[x], where [.] is the greatest integer function and g(x) = [x].

What isequal to?

Step-by-Step Logic & Solution

Inverse functions Questions