MHT CET 2025 20 April Shift 2 Question Paper (Available): Download Question Paper (PCM) with Answers PDF

Which of the following gases is most soluble in water?

• (A) Oxygen
• (B) Nitrogen
• (C) Carbon dioxide
• (D) Hydrogen

Which of the following elements does not have a completely filled outermost shell in its ground state?

• (A) Neon
• (B) Helium
• (C) Oxygen
• (D) Argon

Which of the following is an example of a redox reaction?

• (A) NaCl dissolving in water
• (B) \( \mathrm{2H_2O_2\ (aq) \rightarrow 2H_2O\ (l) + O_2\ (g)} \)
• (C) NaOH dissolving in water
• (D) \( \mathrm{CaCO_3\ (s) \rightarrow CaO\ (s) + CO_2\ (g)} \)

In the reaction \( \mathrm{2H_2 + O_2 \rightarrow 2H_2O} \), if 4 moles of hydrogen react completely with oxygen, how many moles of water will be produced?

• (A) 2 mol
• (B) 4 mol
• (C) 8 mol
• (D) 1 mol

What is the volume of oxygen required for complete combustion of 0.25 mole of methane at S.T.P.?

• (A) 22.4 L
• (B) 5.6 L
• (C) 11.2 L
• (D) 7.46 L

Evaluate the integral: \( \int \sin^5 x \, dx \)

• (A) \( -\frac{1}{5} \cos x (5 - 10 \sin^2 x + \sin^4 x) + C \)
• (B) \( -\cos x + \frac{\cos^3 x}{3} - \frac{\cos^5 x}{5} + C \)
• (C) \( \frac{1}{5} \sin^5 x + C \)
• (D) \( \int \sin^5 x \, dx = \int \sin^3 x \cdot \sin^2 x \, dx \)

Evaluate the determinant of the matrix: \[ \left| \begin{array}{cc} 1 & \tan x
-\tan x & 1 \end{array} \right| \]

• (A) \( 1 - \tan^2 x \)
• (B) \( 1 + \tan^2 x \)
• (C) \( \sec^2 x \)
• (D) \( 0 \)

Evaluate the expression: \[ f\left(f(f(x))\right) + \left(f(f(x))\right)^2 \quad if \quad x = 1 \]

• (A) \( f(f(f(1))) + \left(f(f(1))\right)^2 \)
• (B) \( f(f(f(1))) + \left(f(1)\right)^2 \)
• (C) \( f(1)^2 + f(1) \)
• (D) Cannot be determined

A copper ball at \(80^\circ C\) is brought to \(60^\circ C\) in 5 minutes, with surrounding temperature at \(20^\circ C\). Find the temperature of the ball after 20 minutes.

• (A) \(35^\circ C\)
• (B) \(30^\circ C\)
• (C) \(25^\circ C\)
• (D) \(20^\circ C\)

Given \( f'(1) = 3 \), \( f(1) = 1 \), and
\[ y = f\left(f(f(x))\right) + \left(f(x)\right)^2, \]
then find \( \frac{dy}{dx} \) at \( x = 1 \).

• (A) \( 9 \)
• (B) \( 12 \)
• (C) \( 15 \)
• (D) \( 18 \)

If \( y = x^x + x^x \), then find \( \frac{dy}{dx} \):

• (A) \( x^x(\ln x + 1) \)
• (B) \( 2x^x(\ln x + 1) \)
• (C) \( x^x(\ln x - 1) \)
• (D) \( 2x^x \ln x \)

Evaluate the definite integral: \( \int_{-2}^{2} |x^2 - x - 2| \, dx \)

• (A) \( \frac{40}{3} \)
• (B) \( \frac{28}{3} \)
• (C) \( \frac{36}{5} \)
• (D) \( \frac{44}{3} \)

Find the value of the integral: \( \int \frac{2x + 3}{(xy)(x^2 + 1)} \, dx \)

• (A) \( \frac{1}{y} \ln(x^2 + 1) + C \)
• (B) \( \frac{2}{y} \ln|x| + \frac{3}{y} \tan^{-1}(x) + C \)
• (C) \( \frac{2}{y} \ln|x| + \frac{3}{y} \ln(x^2 + 1) + C \)
• (D) \( \frac{1}{y} \ln|x(x^2 + 1)| + C \)

If \( \int \frac{2x + 3}{(x - 1)(x^2 + 1)} \, dx = \log_x \{(x - 1)^{\frac{5}{2}}(x^2 + 1)^a\} - \frac{1}{2} \tan^{-1}x + C \), then the value of \( a \) is:

• (A) \( \frac{5}{4} \)
• (B) \( -\frac{5}{3} \)
• (C) \( -\frac{5}{6} \)
• (D) \( -\frac{5}{4} \)