PYQ Vault

Day 10: CBSE Class 12 Maths

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

  1. Question 1

    Linear Programming. Asked 2 times: 2023, 2026

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    20
    Assertion (A) : Consider a Linear Programming Problem with minimise Z=x+2yZ = x + 2y subject to constraints 2x+y≥32x + y \ge 3, x+2y≥6x + 2y \ge 6, x, y≥0x,\ y \ge 0 which gives minimum Z at infinitely many points. The corner points of feasible region are (0, 3) and (6, 0). Reason (R) : If two corner points produce the same minimum value of the objective function, then every point on the line segment joining the points will give the same minimum value.

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  2. Question 2

    Matrices. Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)

    4
    If A=[cos⁡x−sin⁡xsin⁡xcos⁡x]A = \begin{bmatrix} \cos x & -\sin x \\ \sin x & \cos x \end{bmatrix} and A+A′=IA + A' = I, then the value of x∈[0,π2]x \in \left[0, \dfrac{\pi}{2}\right] is

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  3. Question 3

    Probability. Asked 2 times: 2023, 2026

    18
    If E and F are two independent events such that P(E)=310P(E) = \dfrac{3}{10}, P(E∪F)=12P(E \cup F) = \dfrac{1}{2}, then P(E∣F)−P(F∣E)P(E|F) - P(F|E) is equal to :

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  4. Question 4

    Probability. Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)

    18
    A box contains 4 red, 5 blue and 1 green marble. A child randomly takes out a marble from the box, notes down the colour and puts it back in the box. If the activity is repeated 3 times, what is the probability that at least one marble is red ?

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  5. Question 5

    Relations and Functions. Asked 2 times: 2023, 2026

    34
    Show that f:R+→[−5,∞)f : R_+ \to [-5, \infty) given by f(x)=4x2+4x−5f(x) = 4x^2 + 4x - 5 is both one-one and onto where R+=[0,∞)R_+ = [0, \infty). Also, find p∈R+p \in R_+ such that f(p)=3f(p) = 3.