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Day 141: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Properties of Triangle. Asked once: NDA 1 2021 (same type asked 2 times)

    33
    The sides of a triangle are mm, nn and m2+n2+mn\sqrt{m^2+n^2+mn}. What is the sum of the acute angles of the triangle?

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  2. Question 2 (case study, 2 parts)

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

    Direction: Consider the following for the next two (02) items that follow. The marks obtained by 60 students in a certain subject out of 75 are given below: Marks: 15-20 (4), 20-25 (5), 25-30 (11), 30-35 (6), 35-40 (5), 40-45 (8), 45-50 (9), 50-55 (6), 55-60 (4), 60-65 (2).
    108
    What is the median?

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    109
    What is the mode?

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  3. Question 3 (case study, 2 parts)

    Vectors. Asked once: NDA 1 2023 (same type asked 2 times)

    Consider the following for the next two (02) items that follow: Let a vector a⃗=4i^−8j^+k^\vec{a}=4\hat{i}-8\hat{j}+\hat{k} make angles α\alpha, β\beta, γ\gamma with the positive directions of xx, yy, zz axes respectively.
    67
    What is cos⁡α\cos\alpha equal to?

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    68
    What is cos⁡2β+cos⁡2γ\cos2\beta+\cos2\gamma equal to?

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  4. Question 4

    Vectors. Asked once: NDA 1 2018 (same type asked 2 times)

    69
    If a⃗+2b⃗+3c⃗=0⃗\vec{a}+2\vec{b}+3\vec{c}=\vec{0} and a⃗×b⃗+b⃗×c⃗+c⃗×a⃗=λ(b⃗×c⃗)\vec{a}\times\vec{b}+\vec{b}\times\vec{c}+\vec{c}\times\vec{a}=\lambda(\vec{b}\times\vec{c}), then lambda is?

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  5. Question 5

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

    69
    Let a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} be three vectors such that a⃗\vec{a}, b⃗\vec{b} and c⃗\vec{c} are coplanar. Which of the following is/are correct? 1. (a⃗×b⃗)×c⃗(\vec{a}\times\vec{b})\times\vec{c} is coplanar with a⃗\vec{a} and b⃗\vec{b} 2. (a⃗×b⃗)×c⃗(\vec{a}\times\vec{b})\times\vec{c} is perpendicular to a⃗×b⃗\vec{a}\times\vec{b} Select the correct answer using the code given below.

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