PYQ Vault

Day 22: NDA Maths

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

  1. Question 1

    Definite Integration. This type asked 3 times: NDA 2 2018, NDA 2 2021, NDA 2 2026. This one: NDA 2 2026

    74
    What is ∫12xx(1+ln⁡x) dx\int_1^2 x^x (1 + \ln x)\,dx equal to?

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  2. Question 2

    Differential Equations. This type asked 3 times: NDA 1 2017, NDA 2 2017, NDA 2 2026. This one: NDA 2 2026

    78
    What is the solution of y dx−x dy−y2cos⁡x dx=0y\,dx - x\,dy - y^2\cos x\,dx = 0?

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  3. Question 3

    Differentiation. This type asked 3 times: NDA 1 2021, NDA 2 2025, NDA 2 2026. This one: NDA 2 2026

    85
    Let f(x)=p∣x∣+qf(x) = p|x| + q, where pp and qq are real constants. If f′(x)f'(x) exists at x=0x = 0, then what is the value of pp?

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  4. Question 4

    Functions. This type asked 3 times: NDA 2 2017, NDA 1 2019, NDA 2 2026. This one: NDA 2 2026

    99
    Consider the following statements in respect of the function f:R−{35}→R−{35}f : R - \left\{\frac{3}{5}\right\} \to R - \left\{\frac{3}{5}\right\} such that f(x)=3x+25x−3f(x) = \frac{3x + 2}{5x - 3} : I. f(x)f(x) is a bijective function. II. f−1(x)=f(x)f^{-1}(x) = f(x) Which of the statements given above is/are correct?

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  5. Question 5 (case study, 2 parts)

    Height & Distance. This type asked 3 times: NDA 2 2017, NDA 2 2018, NDA 2 2026. This one: NDA 2 2026

    For the following two (02) items that follow : From the top of a building, the angles of depression of the top and bottom of a tower of height hh are α\alpha and β\beta respectively. Let HH be the height of the building and DD be the horizontal distance between the building and the tower.
    1
    What is H2+D2H^2 + D^2 equal to?

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    2
    If α=15∘\alpha = 15^\circ and β=45∘\beta = 45^\circ, then which one of the following is correct?

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