PYQ Vault

Day 20: CBSE Class 12 Maths

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

  1. Question 1

    Integrals. Asked 2 times: 2023, 2024

    33 (b)
    Evaluate : ∫0π2sin⁡2x tan⁡−1(sin⁡x)  dx\int_0^{\frac{\pi}{2}} \sin 2x \, \tan^{-1} (\sin x) \; dx

  2. Question 2

    Integrals. Asked 2 times: 2023*, 2024 (* = numbers or wording changed that year)

    27
    Find : ∫x2log⁡(x2−1) dx\displaystyle\int x^2 \log (x^2 - 1)\, dx

  3. Question 3

    Inverse Trigonometric Functions. Asked 2 times: 2023, 2024

    21 (b)
    Find the domain of the function f(x)=sin⁡−1(x2−4)f(x) = \sin^{-1}(x^2 - 4). Also, find its range.

  4. Question 4

    Linear Programming. Asked 2 times: 2023*, 2024 (* = numbers or wording changed that year)

    35
    Solve the following L.P.P. graphically : Minimise Z=6x+3y\mathrm{Z} = 6x + 3\mathrm{y} Subject to constraints 4x+y≥804x + \mathrm{y} \ge 80; x+5y≥115x + 5\mathrm{y} \ge 115; 3x+2y≤1503x + 2\mathrm{y} \le 150 x,y≥0x, \mathrm{y} \ge 0

  5. Question 5

    Matrices. Asked 2 times: 2023, 2024

    18
    If A and B are two non-zero square matrices of same order such that (A+B)2=A2+B2(A + B)^2 = A^2 + B^2, then :

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