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Day 134: NDA Maths

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

  1. Question 1

    Applications of Integration. Asked once: NDA 1 2019 (same type asked 2 times)

    95
    What is the area of one of the loops between the curve y=csin⁡xy=c\sin x and x-axis?

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  2. Question 2

    Limits & Continuity. Asked once: NDA 1 2020 (same type asked 2 times)

    93
    What is lim⁡x→03x+3−x−2x\lim_{x\to0}\frac{3^x+3^{-x}-2}{x} equal to?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 2 2024 (same type asked 2 times)

    12
    If ω=−12+i32\omega=-\dfrac{1}{2}+i\dfrac{\sqrt{3}}{2}, then what is ∣1+ω1+ω2ω+ω21∣⋅∣ωω21ω2∣⋅∣1ω1ω2∣\begin{vmatrix}1+\omega & 1+\omega^2 \\ \omega+\omega^2 & 1 \end{vmatrix} \cdot \begin{vmatrix}\omega & \omega^2 \\ 1 & \omega^2 \end{vmatrix} \cdot \begin{vmatrix}1 & \omega \\ 1 & \omega^2 \end{vmatrix} equal to?

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  4. Question 4

    Probability. Asked once: NDA 2 2021 (same type asked 2 times)

    117
    3-digit numbers are formed using the digits 1, 3, 7 without repetition of digits. A number is randomly selected. What is the probability that the number is divisible by 3?

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  5. Question 5

    Properties of Triangle. Asked once: NDA 1 2022 (same type asked 2 times)

    27
    In a triangle ABCABC, sin⁡A−cos⁡B−cos⁡C=0\sin A - \cos B - \cos C = 0. What is angle BB equal to?

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