CUET 2026 Mathematics May 20 Shift 2 Question Paper Available- Download Answer Key and Solution PDF

Find the integrating factor (I.F.) for the linear differential equation: \[ \frac{dy}{dx} + \frac{2x}{1+x^2}y = \frac{1}{(1+x^2)^2} \]

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

Determine the sum of the order and the degree of the following differential equation: \[ \left[1 + \left(\frac{dy}{dx}\right)^2\right]^{
frac{3}{2}} = k \frac{d^2y}{dx^2} \]

• (A) \( 4 \)
• (B) \( 3 \)
• (C) \( 5 \)
• (D) \( The degree is undefined. \)

Find the area of the region enclosed by the ellipse given parametrically by the coordinates \( x = 2\sin\theta \) and \( y = 3\cos\theta \) where \( 0 \le \theta \le 2\pi \).

• (A) \( 6\pi \)
• (B) \( 12\pi \)
• (C) \( 5\pi \)
• (D) \( 13\pi \)

Evaluate the indefinite integral using pattern-based substitution: \[ \int \frac{\ln x - 1}{(\ln x)^2}\,dx \]

• (A) \( \frac{x}{\ln x} + C \)
• (B) \( x\ln x + C \)
• (C) \( \frac{\ln x}{x} + C \)
• (D) \( \frac{1}{\ln x} + C \)

If \( A \) is a square matrix of order 3 such that its determinant value is \( |A| = -2 \), find the value of the scalar-scaled determinant \( |4A| \).

• (A) \( -128 \)
• (B) \( -8 \)
• (C) \( -24 \)
• (D) \( 128 \)

Find the general solution of the separable differential equation: \[ \frac{dy}{dx} = e^{x-y} + x^2e^{-y} \]

• (A) \( e^y = e^x + \frac{x^3}{3} + C \)
• (B) \( e^{-y} = e^x + x^3 + C \)
• (C) \( e^y = e^x + 2x + C \)
• (D) \( y = \ln\left(e^x + \frac{x^3}{3}\right) + C \)

Let \( A \) be a square matrix of order 3 such that \( |A| = 5 \). Find the value of the determinant of its adjoint matrix, \( |adj(A)| \).

• (A) \( 25 \)
• (B) \( 5 \)
• (C) \( 125 \)
• (D) \( 15 \)

In a Linear Programming Problem (LPP), if the objective function to maximize is \( Z = 3x + 4y \) and the corner points of the feasible bounded region are \( (0,0), (4,0), (2,3), \) and \( (0,4) \), find the maximum value of \( Z \).

• (A) \( 18 \)
• (B) \( 16 \)
• (C) \( 12 \)
• (D) \( 22 \)

Find the integrating factor (I.F.) for the linear differential equation: \[ \frac{dy}{dx} - y\tan x = e^x \]

• (A) \( \cos x \)
• (B) \( \sec x \)
• (C) \( -\cos x \)
• (D) \( \ln|\cos x| \)

Find the particular solution of the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) given the initial boundary condition that \( y = 2 \) when \( x = 1 \).

• (A) \( y = 2x \)
• (B) \( y = x + 1 \)
• (C) \( y = x^2 \)
• (D) \( y = \frac{2}{x} \)