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Day 240: NDA Maths

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

  1. Question 1

    Binomial Theorem. Asked once: NDA 2 2026

    42
    What is the coefficient of x2nx^{2n} in the expansion of the following? (1+x)2n(1+1x)2n(1 + x)^{2n} \left(1 + \frac{1}{x}\right)^{2n}

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  2. Question 2

    Circles. Asked once: NDA 2 2026

    51
    A circle touches each of the lines x−y=0x - y = 0 and x+y=0x + y = 0 at unit distance from the origin. The centre of the circle may be at

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  3. Question 3

    Complex Numbers. Asked once: NDA 2 2026

    35
    What is i×i4×i9×i16×…×i576i \times i^4 \times i^9 \times i^{16} \times \ldots \times i^{576}, where i=−1i = \sqrt{-1}, equal to?

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  4. Question 4

    Conics. Asked once: NDA 2 2026

    53
    The centre and one of the foci (F)(F) of an ellipse are at (0,0)(0, 0) and (−c,0)(-c, 0) respectively. If P(x,y)P(x, y) is any point on the ellipse and 2a2a is the length of major axis, then what is PFPF equal to?

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  5. Question 5

    Definite Integration. Asked once: NDA 2 2026

    72
    What is ∫01dx(ax+bx+c)2\int_0^1 \frac{dx}{(ax + bx + c)^2} equal to?

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