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Day 103: NDA Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: NDA 2 2021 (same type asked 4 times)

    29
    Let sin⁡x+sin⁡y=cos⁡x+cos⁡y\sin x+\sin y=\cos x+\cos y for all x,y∈Rx,y\in\mathbb{R}. What is tan⁡ ⁣(x2+y2)\tan\!\left(\frac{x}{2}+\frac{y}{2}\right) equal to?

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  2. Question 2

    Limits & Continuity. Asked once: NDA 1 2024 (same type asked 4 times)

    88
    Let f(x)=∣x∣+1f(x)=|x|+1, g(x)=[x]−1g(x)=[x]-1, h(x)=f(x)g(x)h(x)=\dfrac{f(x)}{g(x)}, where [⋅][\cdot] is the greatest integer function. What is lim⁡x→0−h(x)+lim⁡x→0+h(x)\displaystyle\lim_{x\to0^-}h(x)+\lim_{x\to0^+}h(x) equal to?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 2 2023 (same type asked 4 times)

    18
    If A=I3A = I_3 (identity), then what is 23A3−19A2−4A23A^3 - 19A^2 - 4A equal to?

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  4. Question 4

    Permutation & Combination. Asked once: NDA 1 2022 (same type asked 4 times)

    13
    If C(3n,2n)=C(3n,2n−7)C(3n, 2n) = C(3n, 2n-7), then what is the value of C(n,n−5)C(n, n-5)?

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  5. Question 5

    Permutation & Combination. Asked once: NDA 2 2024 (same type asked 4 times)

    14
    In how many ways can the letters of the word INDIA be permutated such that in each combination, vowels should occupy odd positions?

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