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Day 228: NDA Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: NDA 2 2022 (same type asked 5 times)

    55
    If 1+2(sin⁡x+cos⁡x)(sin⁡x−cos⁡x)=01+2(\sin x+\cos x)(\sin x - \cos x) = 0 where 0<x<360°0 < x < 360°, then how many values does x take?

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  2. Question 2

    Differential Equations. Asked once: NDA 1 2017 (same type asked 5 times)

    91
    What is the solution of the differential equation ln⁡ ⁣(dydx)−a=0\ln\!\left(\dfrac{dy}{dx}\right)-a=0?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 1 2021 (same type asked 5 times)

    3
    If Δ\Delta is the value of the determinant ∣a1b1c1a2b2c2a3b3c3∣\begin{vmatrix}a_1 & b_1 & c_1\\a_2 & b_2 & c_2\\a_3 & b_3 & c_3\end{vmatrix}, then what is the value of ∣pa1b1qc1pa2b2qc2pa3b3qc3∣\begin{vmatrix}pa_1 & b_1 & qc_1\\pa_2 & b_2 & qc_2\\pa_3 & b_3 & qc_3\end{vmatrix} (p≠0p \neq 0 or 11, q≠0q \neq 0 or 11)?

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  4. Question 4

    Sequence & Series. Asked once: NDA 2 2018 (same type asked 5 times)

    26
    Let TrT_r be the rthr^{\text{th}} term of an AP for r=1,2,3,…r = 1, 2, 3, \ldots. If for some distinct positive integers m and n we have Tm=1nT_m = \frac{1}{n} and Tn=1mT_n = \frac{1}{m}, then what is TmnT_{mn} equal to?

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  5. Question 5

    Applications of Integration. Asked once: NDA 2 2017 (same type asked 5 times)

    77
    The area bounded by the curve ∣x∣+∣y∣=1|x| + |y| = 1 is

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