What is the value of lim(x→9) (x² − 81)/(x − 9)?
- A19
- B9
- C81
- D18
Show answer
Answer: (D) 18
(x² − 9²)/(x − 9) = x + 9 → 18.
NDA & NA Calculus Questions with Answers & Explanations
20 Calculus questions from the Mathematics section of NDA & NA, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.
What is the value of ∫₀^2 (6x² + 2x) dx?
- A17
- B19
- C20
- D16
Show answer
Answer: (C) 20
∫ = [6x³/3 + 2x²/2] from 0 to 2 = 20.
If f(x) = 1x³ + 4x² + 8, what is f′(2)?
- A12
- B31
- C36
- D28
Show answer
Answer: (D) 28
f′(x) = 3x² + 8x, so f′(2) = 28.
What is the value of lim(x→3) (x² − 9)/(x − 3)?
- A0
- B9
- C7
- D6
Show answer
Answer: (D) 6
(x² − 3²)/(x − 3) = x + 3 → 6.
What is the value of ∫₀^1 (3x² + 2x) dx?
- A5
- B6
- C1
- D2
Show answer
Answer: (D) 2
∫ = [3x³/3 + 2x²/2] from 0 to 1 = 2.
If f(x) = 5x³ + 2x² + 7, what is f′(1)?
- A19
- B26
- C34
- D15
Show answer
Answer: (A) 19
f′(x) = 15x² + 4x, so f′(1) = 19.
If f(x) = 1x³ − 1x² − 4, what is f′(3)?
- A27
- B21
- C24
- D14
Show answer
Answer: (B) 21
f′(x) = 3x² + -2x, so f′(3) = 21.
What is the value of lim(x→8) (x² − 64)/(x − 8)?
- A0
- B17
- C64
- D16
Show answer
Answer: (D) 16
(x² − 8²)/(x − 8) = x + 8 → 16.
What is the value of ∫₀^1 (6x² + 2x) dx?
- A3
- B5
- C6
- D1
Show answer
Answer: (A) 3
∫ = [6x³/3 + 2x²/2] from 0 to 1 = 3.
If f(x) = 5x³ + 3x² + 2, what is f′(3)?
- A153
- B155
- C164
- D135
Show answer
Answer: (A) 153
f′(x) = 15x² + 6x, so f′(3) = 153.
If f(x) = 1x³ − 3x² + 5, what is f′(1)?
- A2
- B3
- C0
- D-3
Show answer
Answer: (D) -3
f′(x) = 3x² + -6x, so f′(1) = -3.
What is the value of ∫₀^3 (3x² + 4x) dx?
- A43
- B45
- C49
- D46
Show answer
Answer: (B) 45
∫ = [3x³/3 + 4x²/2] from 0 to 3 = 45.
If f(x) = 2x³ + 3, what is f′(1)?
- A12
- B5
- C6
- D9
Show answer
Answer: (C) 6
f′(x) = 6x² + 0x, so f′(1) = 6.
What is the value of lim(x→2) (x² − 4)/(x − 2)?
- A4
- B0
- C5
- D2
Show answer
Answer: (A) 4
(x² − 2²)/(x − 2) = x + 2 → 4.
If f(x) = 1x³ − 5x² − 8, what is f′(3)?
- A27
- B-11
- C-3
- D0
Show answer
Answer: (C) -3
f′(x) = 3x² + -10x, so f′(3) = -3.
What is the value of lim(x→8) (x² − 64)/(x − 8)?
- A16
- B64
- C0
- D17
Show answer
Answer: (A) 16
(x² − 8²)/(x − 8) = x + 8 → 16.
What is the value of lim(x→4) (x² − 16)/(x − 4)?
- A4
- B8
- C16
- D0
Show answer
Answer: (B) 8
(x² − 4²)/(x − 4) = x + 4 → 8.
If f(x) = 4x³ − 1x² − 8, what is f′(4)?
- A176
- B184
- C196
- D232
Show answer
Answer: (B) 184
f′(x) = 12x² + -2x, so f′(4) = 184.
If f(x) = 2x³ − 2x² − 7, what is f′(1)?
- A-7
- B-5
- C6
- D2
Show answer
Answer: (D) 2
f′(x) = 6x² + -4x, so f′(1) = 2.
If f(x) = 2x³ − 2x² + 1, what is f′(2)?
- A24
- B9
- C17
- D16
Show answer
Answer: (D) 16
f′(x) = 6x² + -4x, so f′(2) = 16.
These are RankerClub practice questions written in the NDA & NA pattern. They are not official SSC/IBPS/RRB papers.
