PYQ Vault

Day 41: CBSE Class 12 Maths

5 questions. Try each one first, then open its answer.

  1. Question 1

    Differential Equations. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    13
    dydx=F(x,y)\dfrac{dy}{dx} = F(x, y) will be a homogeneous differential equation for which of the following functions ? (i) F(x,y)=3x+2yF(x, y) = 3x + 2y (ii) F(x,y)=sin⁡yx+log⁡y−log⁡xF(x, y) = \sin \dfrac{y}{x} + \log y - \log x (iii) F(x,y)=ey/x+1F(x, y) = e^{y/x} + 1 (iv) F(x,y)=x2+y2−yF(x, y) = \sqrt{x^2 + y^2} - y

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  2. Question 2

    Differential Equations. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    12
    The integrating factor of the differential equation 2xdydx−y=32x\dfrac{dy}{dx} - y = 3 is

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  3. Question 3

    Inverse Trigonometric Functions. This type asked 3 times: 2023, 2025, 2026. This one: 2026

    21
    Evaluate tan⁡[cos⁡−1(tan⁡3π4)]\tan\left[\cos^{-1}\left(\tan \dfrac{3\pi}{4}\right)\right].

  4. Question 4

    Inverse Trigonometric Functions. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    25 (a)
    Simplify : tan⁡−1(cos⁡2x−sin⁡2xcos⁡2x+sin⁡2x)\tan^{-1} \left( \frac{\cos 2x - \sin 2x}{\cos 2x + \sin 2x} \right), 0<x<π40 < x < \frac{\pi}{4}.

  5. Question 5

    Linear Programming. This type asked 3 times: 2024, 2025, 2026. This one: 2026

    18
    The degree of an objective function of a linear programming problem is

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