PYQ Vault

Day 164: CBSE Class 12 Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Probability. Asked once: 2025 (same type asked 5 times)

    31
    A person is Head of two independent selection committees I and II. If the probability of making a wrong selection in committee I is 0⋅030{\cdot}03 and that in committee II is 0⋅010{\cdot}01, then find the probability that the person makes the correct decision of selection : (i) in both committees (ii) in only one committee

  2. Question 2

    Three Dimensional Geometry. Asked once: 2023 (same type asked 5 times)

    34 (a)
    Find the vector and the Cartesian equations of a line passing through the point (1,2,−4)(1, 2, -4) and parallel to the line joining the points A(3,3,−5)A(3, 3, -5) and B(1,0,−11)B(1, 0, -11). Hence, find the distance between the two lines.

  3. Question 3 (case study, 2 parts)

    Application of Derivatives. Asked once: 2024 (same type asked 4 times)

    A rectangular visiting card is to contain 24 sq.cm. of printed matter. The margins at the top and bottom of the card are to be 1 cm and the margins on the left and right are to be 1½ cm as shown below : On the basis of the above information, answer the following questions :
    37 (i)
    Write the expression for the area of the visiting card in terms of xx.
    37 (ii)
    Obtain the dimensions of the card of minimum area.

  4. Question 4

    Application of Derivatives. Asked once: 2024 (same type asked 4 times)

    23
    Show that the function f given by f(x)=sin⁡x+cos⁡xf(x) = \sin x + \cos x, is strictly decreasing in the interval (π4,5π4)\left(\dfrac{\pi}{4}, \dfrac{5\pi}{4}\right).

  5. Question 5

    Continuity and Differentiability. Asked once: 2025 (same type asked 4 times)

    6
    If f(x)={log⁡(1+ax)+log⁡(1−bx)x,for x≠0k,for x=0f(x) = \begin{cases} \dfrac{\log(1 + ax) + \log(1 - bx)}{x}, & \text{for } x \ne 0 \\ k, & \text{for } x = 0 \end{cases} is continuous at x=0x = 0, then the value of k is :

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