Sets, Relations & Functions · NDA previous year questions

2023 17 questions

1. Q142023 · 3 Sept 2023

   A set S contains (2n + 1) elements. There are 4096 subsets of S which contain at most n elements. What is n equal to?

   1. A.5
   2. B.6
   3. C.7
   4. D.8
   Show answer

   Answer: B

2. Q152023 · 3 Sept 2023
   
   1. A.-1
   2. B.0
   3. C.1
   4. D.2
   Show answer

   Answer: B

3. Q212023 · 3 Sept 2023

   The Cartesian product A × A has 16 elements among which are (0, 2) and (1, 3). Which of the following statements is/are correct? 1. It is possible to determine set A. 2. A × A contains the element (3, 2). Select the correct answer using the code given below:

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
   Show answer

   Answer: C

4. Q222023 · 3 Sept 2023

   Let A = {1, 2, 3, ..., 20}. Define a relation R from A to A by R = {(x, y) : 4x - 3y = 1}, where x, y ∈ A. Which of the following statements is/are correct? 1. The domain of R is {1, 4, 7, 10, 13, 16). 2. The range of R is {1, 5, 9, 13, 17). 3. The range of R is equal to codomain of R. Select the correct answer using the code given below:

   1. A.1 only
   2. B.2 only
   3. C.1 and 2
   4. D.2 and 3
   Show answer

   Answer: B

5. Q232023 · 3 Sept 2023
   
   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2 1 2 3 100
   Show answer

   Answer: A

6. Q242023 · 3 Sept 2023

   Consider the following statements 1. A = (A ∪ B) ∪ (A - B), 2. A ∪ (B - A) = (A ∪ B) 3. B = (A ∪ B) - (A - B) Which of the statements given above are correct?

   1. A.1 and 2 only
   2. B.2 and 3 only
   3. C.1 and 3 only
   4. D.1, 2 and 3
   Show answer

   Answer: B

7. Q252023 · 3 Sept 2023

   A function satisfies $f(x-y)=\frac{f(x)}{f(y)}$, where $f(y)\ne 0$. If $f(1)=0.5$, then what is $f(2)+f(3)+f(4)+f(5)+f(6)$ equal to ?

   1. A.$\frac{15}{32}$
   2. B.$\frac{17}{32}$
   3. C.$\frac{29}{64}$
   4. D.$\frac{31}{64}$
   Show answer

   Answer: D

8. Q432023 · 3 Sept 2023

   Consider the following for the next items that follow: Let a function f be defined on $\mathbb{R}-\{0\}$ and $2f(x)+f\left(\frac{1}{x}\right)=x+3$. What is f(0.5) equal to ?

   1. A.$\frac{1}{2}$
   2. B.$\frac{2}{3}$
   3. C.1
   4. D.2
   Show answer

   Answer: B

9. Q492023 · 3 Sept 2023

   Consider the following for the next items that follow: A function is defined by $f(x)=\pi +{\sin }^{2}x$. What is the range of the function?

   1. A.$[0,1]$
   2. B.$[\pi ,\pi +1]$
   3. C.$[\pi -1,\pi +1]$
   4. D.$[\pi -1,\pi -1]$
   Show answer

   Answer: B

10. Q502023 · 3 Sept 2023

    Consider the following for the next items that follow: A function is defined by $f(x)=\pi +{\sin }^{2}x$. What is the period of the function?

    1. A.$2\pi$
    2. B.$\pi$
    3. C.$\frac{\pi }{2}$
    4. D.The function is non-periodic
    Show answer

    Answer: B

11. Q552023 · 3 Sept 2023

    Consider the following for the next items that follow: Let $f(x)=\sqrt{2-x}+\sqrt{2+x}$. What is the domain of the function?

    1. A.(-2, 2)
    2. B.[-2, 2]
    3. C.R - (-2, 2)
    4. D.R - [2, 2]
    Show answer

    Answer: B

12. Q562023 · 3 Sept 2023

    Consider the following for the next items that follow: Let $f(x)=\sqrt{2-x}+\sqrt{2+x}$. What is the greatest value of the function?

    1. A.$\sqrt{3}$
    2. B.$\sqrt{6}$
    3. C.$\sqrt{8}$
    4. D.4
    Show answer

    Answer: C

13. Q572023 · 3 Sept 2023

    Consider the following for the next items that follow: Let $f(x)=|x|$ and $g(x)=[x]-1$, where [.] is the greatest integer function. Let $h(x)=\frac{f(g(x))}{g(f(x))}$. What is ${\lim }_{x\to 0+}h(x)$ equal to ?

    1. A.-2
    2. B.-1
    3. C.0
    4. D.1
    Show answer

    Answer: B

14. Q582023 · 3 Sept 2023

    Consider the following for the next items that follow: Let $f(x)=|x|$ and $g(x)=[x]-1$, where [.] is the greatest integer function. Let $h(x)=\frac{f(g(x))}{g(f(x))}$. What is ${\lim }_{x\to 0-}h(x)$ equal to ?

    1. A.-2
    2. B.-1
    3. C.0
    4. D.2
    Show answer

    Answer: A

15. Q972023 · 16 Apr 2023

    What is the range of the function f(x) = x + |x| if the domain is the set of real numbers ?

    1. A.(0, ∞)
    2. B.[0, ∞)
    3. C.(-∞, ∞)
    4. D.[1, ∞)
    Show answer

    Answer: B

16. Q982023 · 16 Apr 2023

    If $f(x)=x(4x^2-3)$, then what is $f(\sin \theta )$ equal to ?

    1. A.$-\sin 3\theta$
    2. B.$-\cos 3\theta$
    3. C.$\sin 3\theta$
    4. D.$-\sin 4\theta$
    Show answer

    Answer: A

17. Q1072023 · 16 Apr 2023

    The central angles p, q, r and s (in degrees) of four sectors in a Pie Chart satisfy the relation 9p = 3q = 2r = 6s. What is the value of 4p - q ?

    1. A.12
    2. B.24
    3. C.30
    4. D.36
    Show answer

    Answer: D