MHT CET 2026 May 18 Shift 1 PCM Question Paper- Download PDF with Solutions

If a polygon has 54 diagonals, find the number of sides of the polygon.

• (A) (A) 10
• (B) (B) 11
• (C) (C) 12
• (D) (D) 15

If \( y = \cos^{-1} x \), find \( \frac{d^2y}{dx^2} \) in terms of \( y \).

• (A) \(-\csc^2 y \cot y\)
• (B) \(\csc^2 y \cot y\)
• (C) \(-\csc y \cot^2 y\)
• (D) \(\csc y \cot^2 y\)

If \( A = \begin{bmatrix} 4 & 5 \\ 2 & 1 \end{bmatrix} \), find \( A^{-1} \).

• (A) \[ \begin{bmatrix} \frac{1}{6} & -\frac{5}{6} \\ -\frac{1}{3} & \frac{2}{3} \end{bmatrix} \]
• (B) \[ \begin{bmatrix} -\frac{1}{6} & \frac{5}{6} \\ \frac{1}{3} & -\frac{2}{3} \end{bmatrix} \]
• (C) \[ \begin{bmatrix} -1 & 5 \\ 2 & -4 \end{bmatrix} \]
• (D) \[ \begin{bmatrix} 4 & -5 \\ -2 & 1 \end{bmatrix} \]

If \(\int x^3 e^x \, dx = e^x(px^3 + qx^2 + rx + s) + C\),
then find the value of \(p + q + r + s\).

• (A) \(-2\)
• (B) \(0\)
• (C) \(1\)
• (D) \(6\)

Find the distance between the point \(2\hat{i} + \hat{j} - \hat{k}\) and the plane \(\vec{r} \cdot (\hat{i} - 2\hat{j} + 4\hat{k}) = 9\).

• (A) \(\frac{13}{\sqrt{21}}\)
• (B) \(\frac{9}{\sqrt{21}}\)
• (C) \(\frac{13}{21}\)
• (D) \(\frac{21}{\sqrt{13}}\)

If the scalar triple product of three vectors \( \vec{a}, \vec{b}, \vec{c} \) is given as \([\vec{a}\ \vec{b}\ \vec{c}] = 3\), then find the value of the scalar triple product of their cross products, denoted as \([ \vec{a} \times \vec{b} \quad \vec{b} \times \vec{c} \quad \vec{c} \times \vec{a} ]\).

• (A) 3
• (B) 6
• (C) 9
• (D) 27

Evaluate the indefinite integral: \[ \int \frac{x^3 \sin [\tan^{-1}(x^4)]}{1 + x^8} \, dx \]

• (A) \( \frac{1}{4} \cos [\tan^{-1}(x^4)] + C \)
• (B) \( -\frac{1}{4} \cos [\tan^{-1}(x^4)] + C \)
• (C) \( \frac{1}{4} \sin [\tan^{-1}(x^4)] + C \)
• (D) \( -\frac{1}{4} \sin [\tan^{-1}(x^4)] + C \)

If

find the value of the matrix expression \(A(I + \operatorname{adj} A)\), where \(I\) is the identity matrix of the same order as \(A\).

• (A) \[ \begin{bmatrix} 8 & -2 & 2 \\ 0 & 8 & -3 \\ 3 & -2 & 8 \end{bmatrix} \]
• (B) \[ \begin{bmatrix} 9 & -2 & 2 \\ 0 & 10 & -3 \\ 3 & -2 & 12 \end{bmatrix} \]
• (C) \[ \begin{bmatrix} 1 & -16 & 16 \\ 0 & 16 & -24 \\ 24 & -16 & 32 \end{bmatrix} \]
• (D) \[ \begin{bmatrix} 9 & 0 & 0 \\ 0 & 10 & 0 \\ 0 & 0 & 12 \end{bmatrix} \]

Evaluate the indefinite integral: \[ \int e^x (\sin x + \cos x)\, dx \]

• (A) \( e^x \cos x + C \)
• (B) \( e^x \sin x + C \)
• (C) \( -e^x \sin x + C \)
• (D) \( e^x (\sin x - \cos x) + C \)

In \(\triangle ABC\), if \(\angle C = \frac{2\pi}{3}\), then the value of \(\cos^2 A + \cos^2 B - \cos A \cos B\) is:

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

Which of the following compounds is NOT in the gaseous phase at \(25^{\circ}C\)?

• (A) ClF
• (B) BrF
• (C) IF\(_3\)
• (D) ClF\(_3\)

A solution is prepared by dissolving 2 g of a non-volatile solute in 500 mL of solution at \(27^{\circ}C\). The osmotic pressure of the solution is 0.82 atm. The molar mass of the solute is:

• (A) \(100\,g\,mol^{-1}\)
• (B) \(120\,g\,mol^{-1}\)
• (C) \(150\,g\,mol^{-1}\)
• (D) \(180\,g\,mol^{-1}\)

What is the oxidation state of sulfur in Marshall's acid (H\(_2\)S\(_2\)O\(_8\))?

• (A) +4
• (B) +5
• (C) +6
• (D) +7

Oil of wintergreen is chemically known as:

• (A) Methyl acetate
• (B) Methyl salicylate
• (C) Ethyl salicylate
• (D) Salicylic acid

Which of the following does not belong to Group 16 elements?

• (A) Oxygen
• (B) Sulfur
• (C) Selenium
• (D) Chlorine