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Day 31: NDA Maths

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

  1. Question 1

    Vectors. This type asked 3 times: NDA 1 2018, NDA 2 2018, NDA 2 2025. This one: NDA 2 2025

    70
    A force F⃗=2i^−λj^+5k^\vec{F}=2\hat{i}-\lambda\hat{j}+5\hat{k} is applied at the point A(1,2,5)A(1,2,5). If its moment about the point B(−1,−2,3)B(-1,-2,3) is 16i^−6j^+2λk^16\hat{i}-6\hat{j}+2\lambda\hat{k}, then what is the value of λ\lambda?

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  2. Question 2

    Vectors. This type asked 3 times: NDA 2 2017, NDA 2 2018, NDA 2 2025. This one: NDA 2 2025

    67
    How many of the following can be a vector perpendicular to both the vectors 2i^−j^+k^2\hat{i}-\hat{j}+\hat{k} and i^+j^+3k^\hat{i}+\hat{j}+3\hat{k}? I. 4i^+5j^−3k^4\hat{i}+5\hat{j}-3\hat{k} II. −8i^−10j^+6k^-8\hat{i}-10\hat{j}+6\hat{k} III. 150(−4i^−5j^+3k^)\frac{1}{50}(-4\hat{i}-5\hat{j}+3\hat{k}). Select the correct answer.

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  3. Question 3

    3D Geometry. This type asked 3 times: NDA 1 2018, NDA 2 2021, NDA 1 2025. This one: NDA 1 2025

    63
    ABC is a triangle right-angled at B. If A(k,1,−1),B(2k,0,2)A(k,1,-1), B(2k,0,2) and C(2+2k,k,1)C(2+2k,k,1) are the vertices of the triangle, then what is the value of kk?

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  4. Question 4

    Binomial Distribution. This type asked 3 times: NDA 1 2017, NDA 2 2024, NDA 1 2025. This one: NDA 1 2025

    119
    Let X be a random variable following binomial distribution whose mean and variance are 200 and 160 respectively. What is the value of the number of trials (nn)?

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  5. Question 5

    Inverse Trigonometry. This type asked 3 times: NDA 2 2018, NDA 1 2022, NDA 1 2025. This one: NDA 1 2025

    50
    If tan⁡−1k+tan⁡−112=π4\tan^{-1}k + \tan^{-1}\frac{1}{2} = \frac{\pi}{4}, then what is the value of kk?

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