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    Test-III - Class XII

    Uploaded by

    Harsh Mandhian
    The document is a math test containing 10 questions covering topics like matrices, determinants, functions, inverse trigonometric functions, and differentiation. The questions are multi-part and range in difficulty. The test is timed for 1 hour and contains a total of 36 marks.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Test-III - Class XII

    Uploaded by

    Harsh Mandhian
    18 views1 page
    The document is a math test containing 10 questions covering topics like matrices, determinants, functions, inverse trigonometric functions, and differentiation. The questions are multi-part and range in difficulty. The test is timed for 1 hour and contains a total of 36 marks.

    Original Description:

    dmdmd

    Original Title

    Test-3(25062021)

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    The document is a math test containing 10 questions covering topics like matrices, determinants, functions, inverse trigonometric functions, and differentiation. The questions are multi-part and range in difficulty. The test is timed for 1 hour and contains a total of 36 marks.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    18 views1 page

    Test-III - Class XII

    Uploaded by

    Harsh Mandhian
    The document is a math test containing 10 questions covering topics like matrices, determinants, functions, inverse trigonometric functions, and differentiation. The questions are multi-part and range in difficulty. The test is timed for 1 hour and contains a total of 36 marks.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
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    Test-III – Class XII

    (Topic: Matrix, Determinant, Function, Inverse Trigonometric function, Differentiation ) F.M: 36


    Date : 25/6/2021 Time : 1 hr

    Q-1(i) Assume that X , Y ,W and P are matrices of order 2 × 𝑛 , 3 × 𝑘 , 𝑛 × 3 and 𝑝 × 𝑘 respectively.


    Then the restriction on n , k and p so that PY + WY will be defined are:
    A) k=3 , p = n B) k is arbitrary , p = 2 C) p is arbitrary , k = 3. D) k=3 , p =3.
    1
    (ii) The number of points at which the function f (x) = is discontinuous is
    log|𝑥|

    A) 1 B) 2 C) 3 D) 4
    𝑑𝑥
    (iii) Find at 𝜃 = 𝜋 , if 𝑥 = 𝑎(𝜃 + sin 𝜃) , 𝑦 = 𝑎(1 − cos 𝜃)
    𝑑𝑦
    A) 0 B) -1 C) 1 D) ∞
    𝜋
    (iv) sin−1 (1 − 𝑥) − 2 sin−1 𝑥 = , then 𝑥 is equal to
    2

    (A) 0 , 1/2 (B) 1 , 1/2 (C) 0 (D) 1/2


    (v) Let f, g : R→ R be two functions defines as f(x) = |x| + x and g(x) = |x|-x for all x ∈ R. Then
    fog(5) =
    A) -20 B) 1 C) 0 D) -1 [5 × 1=5]
    𝑑𝑦 2 2
    Q-2 (i) Find , given 𝑠𝑖𝑛 𝑥 + 𝑐𝑜𝑠 𝑦 = 1
    𝑑𝑥

    (ii) Find the domain of sin 𝑥 + sin−1 𝑥


    2 1
    (iii) If tan−1 = tan−1 𝑘 , then find k.
    3 2

    0 6 − 5𝑥
    (iv) If the matrix [ 2 ] is symmetric, then find x , where x is an negative integer.
    𝑥 𝑥+3
    𝜋
    (v) Find the derivative of sin(sin 𝑥 2 ) at x = √ [5 × 1=5]
    2

    1−𝑥 𝑑𝑦
    Q-3 If y = 𝑠𝑖𝑛2 (2 tan−1 √ ) , find [2]
    1+𝑥 𝑑𝑥

    Q-4 Show that the function f(x)= x |x| is continuous at x = 0. Is it differentiable at x = 0? [2]
    𝑑𝑦
    Q-5 Find , in terms of y , given that x sin ( a+y) + sin a cos ( a+y) = 0 [2]
    𝑑𝑥

    √1+𝑥 2 −1 2𝑥
    Q-6 Differentiate tan−1 ( ) with respect to sin−1 ( ) [4]
    𝑥 1+𝑥 2

    Q-7 Solve foe x : sin−1 𝑥 − cos −1 𝑥 = sin−1 (3𝑥 − 2) [4]


    1 1 3 3 5
    Q-8 Find the matrix A such that [ ]𝐴 = [ ] [4]
    0 1 1 0 1
    Q-9 Examine the function f for continuity and differentiability at x = 1 where
    𝑥2 , 𝑥 ≤ 1
    f(x) = { 1 [4]
    ,𝑥 > 1
    𝑥
    1
    Q-10 If f(x) = log 𝑥 2 (log 𝑥) , prove that 𝑓 ′ (𝑒) = [4]
    2𝑒

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