PYQ Vault

Day 264: NDA Maths

5 questions (8 parts). Try each one first, then open its answer.

  1. Question 1

    Conics. Asked once: NDA 1 2024

    64
    In the parabola y2=8xy^2=8x, the focal distance of a point PP lying on it is 8 units. Which of the following statements is/are correct? (A) The coordinates of PP can be (6,43)(6,4\sqrt{3}). (B) The perpendicular distance of PP from the directrix of the parabola is 8 units. Select the correct answer using the code given below:

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  2. Question 2 (case study, 3 parts)

    Definite Integration. Asked once: NDA 1 2023

    Consider the following for the next three (03) items that follow: Let f(x)=Pex+Qe2x+Re3xf(x)=Pe^{x}+Qe^{2x}+Re^{3x}, where PP, QQ, RR are real numbers. Further f(0)=6f(0)=6, f′(ln⁡3)=282f'(\ln3)=282 and ∫0ln⁡2f(x) dx=11\int_{0}^{\ln2}f(x)\,dx=11.
    71
    What is the value of QQ?

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    72
    What is the value of RR?

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    73
    What is f′(0)f'(0) equal to?

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  3. Question 3

    Differential Equations. Asked once: NDA 2 2022

    100
    What is the solution of the differential equation (dy−dx)+cos⁡x(dy+dx)=0(dy-dx)+\cos x(dy+dx)=0?

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  4. Question 4

    Differentiation. Asked once: NDA 1 2026

    74
    What is the derivative of x∣x∣\dfrac{x}{|x|} with respect to xx, where x<0x<0?

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  5. Question 5 (case study, 2 parts)

    Functions. Asked once: NDA 2 2025

    For the following two (02) items: Consider the function f(x)=10x−10−x10x+10−xf(x)=\dfrac{10^x-10^{-x}}{10^x+10^{-x}}.
    89
    What is f∘f∘f∘f∘f(0)f\circ f\circ f\circ f\circ f(0) equal to?

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    90
    What is the inverse of the function?

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