PYQ Vault

Day 130: CBSE Class 12 Maths

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

  1. Question 1 (case study, 2 parts)

    Differential Equations. Asked once: 2024 (same type asked 2 times)

    A bacteria sample of certain number of bacteria is observed to grow exponentially in a given amount of time. Using exponential growth model, the rate of growth of this sample of bacteria is calculated. The differential equation representing the growth of bacteria is given as : dPdt=kP\dfrac{dP}{dt} = kP, where P is the population of bacteria at any time 't'. Based on the above information, answer the following questions :
    37 (i)
    Obtain the general solution of the given differential equation and express it as an exponential function of 't'.
    37 (ii)
    If population of bacteria is 1000 at t=0t = 0, and 2000 at t=1t = 1, find the value of k.

  2. Question 2

    Integrals. Asked once: 2024 (same type asked 2 times)

    26
    Find : ∫x−1(log⁡x)2−5log⁡x+4 dx\int \dfrac{x^{-1}}{(\log x)^2 - 5 \log x + 4}\, dx

  3. Question 3

    Integrals. Asked once: 2024 (same type asked 2 times)

    12
    Anti-derivative of 1+sin⁡2x\sqrt{1 + \sin 2x}, x∈[0,π4]x \in \left[0, \dfrac{\pi}{4}\right] is :

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  4. Question 4

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

    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) : In a Linear Programming Problem, if the feasible region is empty, then the Linear Programming Problem has no solution. Reason (R) : A feasible region is defined as the region that satisfies all the constraints.

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  5. Question 5

    Matrices. Asked once: 2024 (same type asked 2 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) : Every scalar matrix is a diagonal matrix. Reason (R) : In a diagonal matrix, all the diagonal elements are 0.

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