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Day 252: NDA Maths

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

  1. Question 1

    Binomial Theorem. Asked once: NDA 2 2024

    6
    In the expansion of (1+x)p(1+x)q(1+x)^{p}(1+x)^{q}, if the coefficient of x3x^{3} is 35, then what is the value of (p+q)(p+q)?

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  2. Question 2

    Circles. Asked once: NDA 1 2025

    57
    A square is inscribed in a circle x2+y2+2x+2y+1=0x^2 + y^2 + 2x + 2y + 1 = 0 and its sides are parallel to coordinate axes. Which one of the following is a vertex of the square?

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  3. Question 3

    Complex Numbers. Asked once: NDA 1 2026

    3
    Consider the following inequalities: I. 1+4i>3+2i1+4i>3+2i II. 2+3i<3+4i2+3i<3+4i III. 4+3i>3+4i4+3i>3+4i where i=−1i=\sqrt{-1}. How many of the above are valid?

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  4. Question 4

    Conics. Asked once: NDA 1 2025

    58
    A tangent to the parabola y2=4xy^2 = 4x is inclined at an angle 45°45° with the positive direction of xx-axis. What is the point of contact of the tangent and the parabola?

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  5. Question 5 (case study, 2 parts)

    Definite Integration. Asked once: NDA 2 2024

    Let I=∫0π/2f(x)g(x) dxI=\displaystyle\int_0^{\pi/2}f(x)g(x)\,dx, where f(x)=sin⁡xf(x)=\sin x and g(x)=sin⁡x+cos⁡x+1g(x)=\sin x+\cos x+1.
    97
    What is ∫0π/2dxg(x)\displaystyle\int_0^{\pi/2}\dfrac{dx}{g(x)} equal to?

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    98
    What is II equal to?

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