Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Calculus

Question:

Match List – I with List – II.

LIST I

LIST II

 A. If $y=x^4+5 x^2+3$, then $\frac{d^2 y}{d x^2}$ is, 

 I. $12 x$

 B. If $y=2 x^3+6 x+5$, then $\frac{d^2 y}{d x^2}$ is, 

 II. $\frac{1}{x}$ 

 C. If $y=x \log x$, then $\frac{d^2 y}{d x^2}$ is,

 III. 0

 D. If $y=2 x+1$, then $\frac{d^2 y}{d x^2}$ is,

 IV. $12 x^2+10$ 

Choose the correct answer from the options given below:

Options:

A-II, B-IV, C-I, D-III

A-II, B-I, C-IV, D-III

A-IV, B-I, C-II, D-III

A-III, B-II, C-I, D-IV

Correct Answer:

A-IV, B-I, C-II, D-III

Explanation:

The correct answer is Option (3) → A-IV, B-I, C-II, D-III

$\text{A: } y = x^4 + 5x^2 + 3$

$y' = 4x^3 + 10x,\quad y'' = 12x^2 + 10 \Rightarrow \text{IV}$

$\text{B: } y = 2x^3 + 6x + 5$

$y' = 6x^2 + 6,\quad y'' = 12x \Rightarrow \text{I}$

$\text{C: } y = x\log x$

$y' = \log x + 1,\quad y'' = \frac{1}{x} \Rightarrow \text{II}$

$\text{D: } y = 2x + 1$

$y'' = 0 \Rightarrow \text{III}$

$\text{A-IV,\ B-I,\ C-II,\ D-III}$