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Day 48: NDA Maths

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

  1. Question 1

    Sequence & Series. Asked 2 times: NDA 2 2021*, NDA 1 2022 (* = numbers or wording changed that year)

    22
    What is the value of 2(2×1)+3(3×2×1)+4(4×3×2×1)+5(5×4×3×2×1)+…+9(9×8×7×6×5×4×3×2×1)+22(2\times1)+3(3\times2\times1)+4(4\times3\times2\times1)+5(5\times4\times3\times2\times1)+\ldots+9(9\times8\times7\times6\times5\times4\times3\times2\times1)+2?

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  2. Question 2

    Sets & Relations. Asked 2 times: NDA 1 2019*, NDA 1 2022 (* = numbers or wording changed that year)

    44
    Consider the following statements in respect of the relation RR in the set N\mathbb{N} of natural numbers defined by xRyxRy if x2−5xy+4y2=0x^2-5xy+4y^2=0: 1. RR is reflexive 2. RR is symmetric 3. RR is transitive Which of the above statements is/are correct?

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  3. Question 3

    Trigonometric Equations. Asked 2 times: NDA 1 2019, NDA 1 2022

    30
    Let sin⁡2θ=cos⁡3θ\sin2\theta=\cos3\theta, where θ\theta is acute. What is the value of 1+4sin⁡θ1+4\sin\theta? (given that sin⁡18°=5−14\sin18°=\frac{\sqrt5-1}{4})

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  4. Question 4

    Vectors. Asked 2 times: NDA 1 2019*, NDA 2 2021 (* = numbers or wording changed that year)

    70
    If the position vectors of AA and BB are (2−1)i^−j^(\sqrt{2}-1)\hat{i}-\hat{j} and i^+(2+1)j^\hat{i}+(\sqrt{2}+1)\hat{j} respectively, then what is the magnitude of AB→\overrightarrow{AB}?

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  5. Question 5

    Application of Derivatives. Asked 2 times: NDA 1 2020*, NDA 1 2021 (* = numbers or wording changed that year)

    90
    What is the maximum value of sin⁡2x⋅cos⁡2x\sin2x\cdot\cos2x?

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