Question

Match List-I with List-II:

List-I		List-II
A	\( y = ln(x)\)	I	\(\frac{1}{x}\)
B	\(y=\frac{x^2}{4}\)	II	\(3x^2\)
C	\(y=x^3\)	III	\(\frac{x}{2}\)
D	\(y=x+1\)	IV	\(1\)

Choose the correct answer from the options given below

• A. A-(I), B-(III), C-(II), D-(IV
• B. A-(I), B-(III), C-(II), D-(IV)
• C. A-(I), B-(III), C-(II), D-(IV)
• D. A-(II), B-(III), C-(I), D-(IV)

Hint:

To find the derivative of a function, apply the standard rules of differentiation: for xn, the derivative is nxn−1, and for ln(x), the derivative is 1/x

Answer 1

The Correct Option is B

The derivatives for each function are as follows:

• For \( y = \ln(x) \), the derivative is \( \frac{1}{x} \), thus A is (I).
• For \( y = \frac{x^2}{4} \), the derivative is \( \frac{1}{2}x \), thus B is (III).
• For \( y = x^3 \), the derivative is \( 3x^2 \), thus C is (II).
• For \( y = x + 1 \), the derivative is \( 1 \), thus D is (IV).
  Therefore, the correct answer is (b).