PYQ Vault

Day 203: CBSE Class 12 Maths

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

  1. Question 1

    Inverse Trigonometric Functions. Asked once: 2023 (same type asked 3 times)

    Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the options given below.
    19
    Assertion (A) : Range of [sin⁡−1x+2cos⁡−1x]\left[ \sin^{-1} x + 2 \cos^{-1} x \right] is [0,π][0, \pi]. Reason (R) : Principal value branch of sin⁡−1x\sin^{-1} x has range [−π2,π2]\left[ -\frac{\pi}{2}, \frac{\pi}{2} \right].

    Tap an option to check your answer.

  2. Question 2

    Probability. Asked once: 2023 (same type asked 3 times)

    30 (b)
    A and B are independent events such that P(A∩B‾)=14P(A \cap \overline{B}) = \frac{1}{4} and P(A‾∩B)=16P(\overline{A} \cap B) = \frac{1}{6}. Find P(A) and P(B).

  3. Question 3

    Vector Algebra. Asked once: 2024 (same type asked 3 times)

    24
    Find the position vector of point C which divides the line segment joining points A and B having position vectors i^+2j^−k^\hat{i} + 2\hat{j} - \hat{k} and −i^+j^+k^-\hat{i} + \hat{j} + \hat{k} respectively in the ratio 4 : 1 externally. Further, find ∣AB→∣:∣BC→∣|\overrightarrow{AB}| : |\overrightarrow{BC}|.

  4. Question 4

    Determinants. Asked once: 2023 (same type asked 2 times)

    14
    If (a, b), (c, d) and (e, f) are the vertices of ΔABC\Delta ABC and Δ\Delta denotes the area of ΔABC\Delta ABC, then ∣acebdf111∣2\begin{vmatrix} a & c & e \\ b & d & f \\ 1 & 1 & 1 \end{vmatrix}^2 is equal to

    Tap an option to check your answer.

  5. Question 5

    Determinants. Asked once: 2025 (same type asked 2 times)

    33
    An amount of ₹ 10,000 is put into three investments at the rate of 10%, 12% and 15% per annum. The combined annual income of all three investments is ₹ 1,310, however the combined annual income of the first and the second investments is ₹ 190 short of the income from the third. Use matrix method and find the investment amount in each at the beginning of the year.