MHT CET 2026 April 16 Shift 1 Question Paper- Download PDF with Solutions

If the statement \( (p \land q) \rightarrow (r \lor \neg s) \) is False (F), what are the truth values of \(p, q, r,\) and \(s\) respectively?

• (A) \(T, T, F, T\)
• (B) \(T, F, F, T\)
• (C) \(T, T, T, F\)
• (D) \(F, T, F, T\)

Evaluate the integral: \( \displaystyle \int \frac{4x^2\cot^{-1}(x^3)}{1+x^6}\,dx \) (where \(C\) is a constant of integration).

• (A) \( \dfrac{2}{3}\big(\cot^{-1}(x^3)\big)^2 + C \)
• (B) \( -\dfrac{2}{3}\big(\cot^{-1}(x^3)\big)^2 + C \)
• (C) \( \dfrac{1}{3}\big(\cot^{-1}(x^3)\big)^2 + C \)
• (D) \( -\dfrac{1}{3}\big(\cot^{-1}(x^3)\big)^2 + C \)

If \( y = \sin^{-1}(3x - 4x^3) \), find the derivative \( \dfrac{dy}{dx} \) in its standard form.

• (A) \( \dfrac{3-12x^2}{\sqrt{1-(3x-4x^3)^2}} \)
• (B) \( \dfrac{3+12x^2}{\sqrt{1-(3x-4x^3)^2}} \)
• (C) \( \dfrac{3-12x^2}{1-(3x-4x^3)^2} \)
• (D) \( \dfrac{12x^2-3}{\sqrt{1-(3x-4x^3)^2}} \)

Find the angle between non-zero vectors \( \mathbf{a} \) and \( \mathbf{b} \) if their dot product \( \mathbf{a}\cdot\mathbf{b} = 0 \).

• (A) \(0^\circ\)
• (B) \(45^\circ\)
• (C) \(90^\circ\)
• (D) \(180^\circ\)

Evaluate the definite integral: \( \displaystyle \int_{3}^{5} |x-4|\,dx \).

• (A) \(1\)
• (B) \(2\)
• (C) \(3\)
• (D) \(4\)

Calculate the potential energy of a \(1.5\,kg\) block attached to a spring with \(k = 100\,N/m\) displaced by \(0.2\,m\).

• (A) \(1\,J\)
• (B) \(2\,J\)
• (C) \(4\,J\)
• (D) \(6\,J\)

At what temperature will the r.m.s. velocity of a hydrogen molecule be equal to that of an oxygen molecule at \(47°\)?

• (A) \(40\,K\)
• (B) \(20\,K\)
• (C) \(10\,K\)
• (D) \(5\,K\)

Determine the equivalent capacitance of an infinite circuit formed by repeating identical capacitors of capacitance \(C\).

• (A) \(C\)
• (B) \(\dfrac{C}{2}\)
• (C) \(\dfrac{C}{3}\)
• (D) \(2C\)

A wire of length \(L\) and resistance \(R\) is stretched to twice its length; what is the new resistance?

• (A) \(R\)
• (B) \(2R\)
• (C) \(3R\)
• (D) \(4R\)

Find the ratio of the de Broglie wavelengths of an alpha particle and a proton accelerated through the same potential.

• (A) \(1:1\)
• (B) \(1:\sqrt{2}\)
• (C) \(1:2\)
• (D) \(1:4\)

Which of the following compounds will undergo a Cannizzaro reaction: \( CH_3CHO,\ C_6H_5CHO,\ CH_3COCH_3 \)?

• (A) \( CH_3CHO \)
• (B) \( C_6H_5CHO \)
• (C) \( CH_3COCH_3 \)
• (D) Both \( CH_3CHO \) and \( C_6H_5CHO \)

Identify the strongest acid among: acetic acid, chloroacetic acid, dichloroacetic acid, and trichloroacetic acid.

• (A) Acetic acid
• (B) Chloroacetic acid
• (C) Dichloroacetic acid
• (D) Trichloroacetic acid

What is the difference in the oxidation number of Manganese (Mn) between \( KMnO_4 \) and \( MnO_2 \)?

• (A) \(1\)
• (B) \(2\)
• (C) \(3\)
• (D) \(4\)

What product is formed when a ketone reacts with hydrazine (\( NH_2NH_2 \))?

• (A) Hydrazone
• (B) Alcohol
• (C) Ester
• (D) Carboxylic acid

Predict the major product formed when an alkene reacts with a hydrogen halide (e.g., HCl or HBr).

• (A) Alkane
• (B) Alkyl halide
• (C) Alcohol
• (D) Ether