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Day 172: NDA Maths

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

  1. Question 1

    Trigonometric Equations. Asked once: NDA 2 2024 (same type asked 5 times)

    26
    What is the number of solutions of the equation cot⁡2x⋅cot⁡3x=1\cot 2x\cdot\cot 3x=1 for 0<x<π0<x<\pi?

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  2. Question 2

    Applications of Integration. Asked once: NDA 1 2018 (same type asked 5 times)

    75
    What is the area bounded by y2=6(x−1)y^2=6(x-1) and y2=3xy^2=3x?

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  3. Question 3

    Differential Equations. Asked once: NDA 1 2020 (same type asked 5 times)

    99
    What is the solution of the differential equation ln⁡(dydx)=x\ln\left(\frac{dy}{dx}\right)=x?

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 1 2022 (same type asked 5 times)

    1
    If Δ1=∣1pq1qr1rp∣\Delta_1 = \begin{vmatrix}1 & p & q\\1 & q & r\\1 & r & p\end{vmatrix} and Δ2=∣111qrprpq∣\Delta_2 = \begin{vmatrix}1 & 1 & 1\\q & r & p\\r & p & q\end{vmatrix} where p≠q≠rp \neq q \neq r, then Δ1+Δ2\Delta_1 + \Delta_2 is

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  5. Question 5

    Sequence & Series. Asked once: NDA 1 2022 (same type asked 5 times)

    52
    If the 5th term of an AP is 110\frac{1}{10} and its 10th term is 15\frac{1}{5}, then what is the sum of first 50 terms?

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