PYQ Vault

Day 59: CBSE Class 12 Maths

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

  1. Question 1

    Continuity and Differentiability. This type asked 2 times: 2023, 2024. This one: 2024

    27
    Find the values of a and b so that the following function is differentiable for all values of xx : f(x)={ax+b,x>−1bx2−3,x≤−1\mathrm{f}(x) = \begin{cases} \mathrm{a}x + \mathrm{b}, & x > -1 \\ \mathrm{b}x^2 - 3, & x \le -1 \end{cases}

  2. Question 2

    Determinants. This type asked 2 times: 2023, 2024. This one: 2024

    34 (a)
    Solve the following system of equations, using matrices : 2x+3y+10z=4\dfrac{2}{x} + \dfrac{3}{y} + \dfrac{10}{z} = 4, 4x−6y+5z=1\dfrac{4}{x} - \dfrac{6}{y} + \dfrac{5}{z} = 1, 6x+9y−20z=2\dfrac{6}{x} + \dfrac{9}{y} - \dfrac{20}{z} = 2 where x,y,z≠0x, y, z \ne 0

  3. Question 3

    Differential Equations. This type asked 2 times: 2023, 2024. This one: 2024

    1
    The number of solutions of differential equation dydx−y=1\dfrac{dy}{dx} - y = 1, given that y(0) = 1, is :

    Tap an option to check your answer.

  4. Question 4

    Matrices. This type asked 2 times: 2023, 2024. This one: 2024

    17
    If F(x)=[cos⁡x−sin⁡x0sin⁡xcos⁡x0001]F(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix} and [F(x)]2=F(kx)[F(x)]^2 = F(kx), then the value of k is :

    Tap an option to check your answer.

  5. Question 5

    Relations and Functions. This type asked 2 times: 2023, 2024. This one: 2024

    32 (b)
    A relation R is defined on N×NN \times N (where N is the set of natural numbers) as : (a,b) R (c,d)⇔a−c=b−d(a, b)\ R\ (c, d) \Leftrightarrow a - c = b - d Show that R is an equivalence relation.