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Day 197: NDA Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: NDA 1 2020 (same type asked 3 times)

    28
    What is the value of cos⁡48°−cos⁡12°\cos 48°-\cos 12°?

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  2. Question 2

    Vectors. Asked once: NDA 2 2021 (same type asked 3 times)

    68
    If (a⃗+b⃗)(\vec{a}+\vec{b}) is perpendicular to a⃗\vec{a} and magnitude of b⃗\vec{b} is twice that of a⃗\vec{a}, then what is the value of (4a⃗+b⃗)⋅b⃗(4\vec{a}+\vec{b})\cdot\vec{b} equal to?

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  3. Question 3

    Applications of Integration. Asked once: NDA 2 2022 (same type asked 3 times)

    80
    What is the area of the region (in the first quadrant) bounded by y=1−x2y = \sqrt{1-x^2}, y=xy = x and y=0y = 0?

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  4. Question 4

    Binomial Theorem. Asked once: NDA 2 2019 (same type asked 3 times)

    25
    If the middle term in the expansion of (x2+1x)2n\left(x^{2}+\dfrac{1}{x}\right)^{2n} is 184756x10184756x^{10}, then what is the value of nn ?

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  5. Question 5

    Definite Integration. Asked once: NDA 2 2023 (same type asked 3 times)

    67
    What is ∫08π∣sin⁡x∣ dx\int_0^{8\pi}|\sin x|\,dx equal to?

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