Evaluate: \(\int (3x^2 + 4x - 5) \, dx\)

• (A) \(x^3 + 2x^2 - 5x + C\)
• (B) \(3x^3 + 4x^2 - 5x + C\)
• (C) \(x^2 + 2x - 5 + C\)
• (D) \(x^3 + 4x^2 - 5 + C\)

If \(y = e^{2x}\), then find \(\frac{dy}{dx}\).

• (A) \(2e^{2x}\)
• (B) \(e^x\)
• (C) \(2xe^{2x}\)
• (D) \(e^{2x} + 2\)

Find the value of: \[ \int \frac{1}{x} \, dx \]

• (A) \( \log x + C \)
• (B) \( \dfrac{1}{x^2}+C \)
• (C) \( x\log x + C \)
• (D) \( e^x + C \)

Find the solution of the differential equation: \[ \frac{dy}{dx} = 3x^2 \]

• (A) \( y = x^3 + C \)
• (B) \( y = 3x^3 + C \)
• (C) \( y = x^2 + C \)
• (D) \( y = 9x + C \)

If \(\frac{dy}{dx} = y\), then which of the following is the correct solution?

• (A) \(y = Ce^x\)
• (B) \(y = Cx\)
• (C) \(y = x^2 + C\)
• (D) \(y = \log x\)

Which of the following functions has derivative equal to \(\cos x\)?

• (A) \(\sin x\)
• (B) \(-\sin x\)
• (C) \(\tan x\)
• (D) \(\sec x\)

Match the following:

• (A) P–I, Q–III, R–II
• (B) P–II, Q–I, R–III
• (C) P–III, Q–II, R–I
• (D) P–I, Q–II, R–III

If \[ A = \begin{bmatrix}2 & 1
3 & 4\end{bmatrix} \]
then find \( |A| \).

• (A) \( 5 \)
• (B) \( 8 \)
• (C) \( 11 \)
• (D) \( 13 \)

Find the simple interest on Rs 5000 at 10% per annum for 2 years.

• (A) Rs 500
• (B) Rs 1000
• (C) Rs 1500
• (D) Rs 2000

A shopkeeper earns 20% profit on an article whose cost price is Rs 800. Find the selling price.

• (A) Rs 920
• (B) Rs 940
• (C) Rs 960
• (D) Rs 1000