PYQ Vault

Day 263: CBSE Class 12 Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1

    Probability. Asked once: 2023 (same type asked 5 times)

    14
    If P(A∩B)=18P(A \cap B) = \frac{1}{8} and P(A‾)=34P(\overline{A}) = \frac{3}{4}, then P(BA)P\left( \frac{B}{A} \right) is equal to :

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  2. Question 2

    Probability. Asked once: 2022 (same type asked 5 times)

    6 (b)
    The probability that A hits the target is 13\dfrac{1}{3} and the probability that B hits it, is 25\dfrac{2}{5}. If both try to hit the target independently, find the probability that the target is hit.

  3. Question 3 (case study, 4 parts)

    Continuity and Differentiability. Asked once: 2023 (same type asked 4 times)

    Let f(x) be a real valued function. Then its Left Hand Derivative (L.H.D.) : Lf′(a)=lim⁡h→0f(a−h)−f(a)−hLf'(a) = \lim_{h \to 0} \dfrac{f(a-h) - f(a)}{-h} Right Hand Derivative (R.H.D.) : Rf′(a)=lim⁡h→0f(a+h)−f(a)hRf'(a) = \lim_{h \to 0} \dfrac{f(a+h) - f(a)}{h} Also, a function f(x) is said to be differentiable at x = a if its L.H.D. and R.H.D. at x = a exist and both are equal. For the function f(x)={∣x−3∣,x≥1x24−3x2+134,x<1f(x) = \begin{cases} |x - 3|, & x \ge 1 \\ \dfrac{x^2}{4} - \dfrac{3x}{2} + \dfrac{13}{4}, & x < 1 \end{cases} answer the following questions :
    36 (i)
    What is R.H.D. of f(x) at x = 1 ?
    36 (ii)
    What is L.H.D. of f(x) at x = 1 ?
    36 (iii) (a)
    Check if the function f(x) is differentiable at x = 1.
    36 (iii) (b)
    Find f′(2)f'(2) and f′(−1)f'(-1).

  4. Question 4

    Continuity and Differentiability. Asked once: 2023 (same type asked 4 times)

    27 (a)
    Differentiate sec⁡−1(11−x2)\sec^{-1}\left(\dfrac{1}{\sqrt{1 - x^2}}\right) w.r.t. sin⁡−1(2x1−x2)\sin^{-1}(2x\sqrt{1 - x^2}).

  5. Question 5

    Determinants. Asked once: 2023 (same type asked 4 times)

    5
    The value of the determinant ∣60−1214113∣\begin{vmatrix} 6 & 0 & -1 \\ 2 & 1 & 4 \\ 1 & 1 & 3 \end{vmatrix} is

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