PYQ Vault

Day 275: CBSE Class 12 Maths

5 questions (11 parts). Try each one first, then open its answer.

  1. Question 1

    Integrals. Asked once: 2025

    33
    Find : ∫(tan⁡x+cot⁡x)dx\displaystyle\int \left(\sqrt{\tan x} + \sqrt{\cot x}\right) dx.

  2. Question 2

    Matrices. Asked once: 2026

    2
    Which of the following cannot be the order of a row-matrix ?

    Tap an option to check your answer.

  3. Question 3 (case study, 4 parts)

    Probability. Asked once: 2026

    In an online jackpot, there is one first prize of ₹ 3,00,000, two second prizes of ₹ 2,00,000 each and three third prizes of ₹ 50,000 each. A total of 1,00,000 jackpot tickets each costing ₹ 100 were sold there by raising a fund of ₹ 1,00,00,000. Rohan bought one ticket. Based on given information, answer the following questions :
    37 (i)
    What are the possible amounts, the person can win ?
    37 (ii) (a)
    What is the probability that the person wins atleast ₹ 2,00,000 ?
    37 (ii) (b)
    What is the probability that the person does not win any amount ?
    37 (iii)
    In another jackpot, Rohan also bought a ticket having a prize money of ₹ 5,00,000. The chances of winning the jackpot are 1 in 1,00,000. Find the probability that on exactly one of tickets he wins the jackpot.

  4. Question 4

    Relations and Functions. Asked once: 2026

    23 (b)
    A relation R on A={1,2,3}A = \{1, 2, 3\} is defined as R={(1,1) (3,3),(1,2)}R = \{(1, 1)\ (3, 3), (1, 2)\}. Is R a symmetric relation ? Justify. Write the smallest relation set R1R_1 such that R∪R1R \cup R_1 becomes an equivalence relation on the set {1,2,3}\{1, 2, 3\}.

  5. Question 5 (case study, 4 parts)

    Three Dimensional Geometry. Asked once: 2025

    An engineer is designing a new metro rail network in a city. Initially, two metro lines, Line A and Line B, each consisting of multiple stations are designed. The track for Line A is represented by l1:x−23=y+1−2=z−34l_1 : \frac{x - 2}{3} = \frac{y + 1}{-2} = \frac{z - 3}{4}, while the track for Line B is represented by l2:x−12=y−31=z+2−3l_2 : \frac{x - 1}{2} = \frac{y - 3}{1} = \frac{z + 2}{-3}. Based on the above information, answer the following questions :
    37 (i)
    Find whether the two metro tracks are parallel.
    37 (ii)
    Solar panels are to be installed on the rooftop of the metro stations. Determine the equation of the line representing the placement of solar panels on the rooftop of Line A's stations, given that panels are to be positioned parallel to Line A's track (l1)(l_1) and pass through the point (1,−2,−3)(1, -2, -3).
    37 (iii) (a)
    To connect the stations, a pedestrian pathway perpendicular to the two metro lines is to be constructed which passes through point (3, 2, 1). Determine the equation of the pedestrian walkway.
    37 (iii) (b)
    Find the shortest distance between Line A and Line B.