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Day 37: NDA Maths

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

  1. Question 1

    Trigonometric Identities. This type asked 3 times: NDA 1 2017, NDA 2 2017, NDA 1 2024. This one: NDA 1 2024

    36
    What is 3cos⁡10°−sin⁡10°sin⁡25°cos⁡25°\dfrac{\sqrt{3}\cos10°-\sin10°}{\sin25°\cos25°} equal to?

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  2. Question 2

    Vectors. This type asked 3 times: NDA 1 2020, NDA 1 2021, NDA 1 2024. This one: NDA 1 2024

    67
    If a vector of magnitude 2 units makes an angle π3\dfrac{\pi}{3} with 2i^2\hat{i}, π4\dfrac{\pi}{4} with 3j^3\hat{j} and an acute angle θ\theta with 4k^4\hat{k}, then what are the components of the vector?

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  3. Question 3

    Conics. This type asked 3 times: NDA 2 2018, NDA 1 2019, NDA 2 2023. This one: NDA 2 2023

    85
    Consider x224−k+y2k−16=2\frac{x^2}{24-k}+\frac{y^2}{k-16}=2. (1) Represents ellipse if k=19k=19. (2) Represents hyperbola if k=12k=12. (3) Represents circle if k=20k=20. How many statements are correct?

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  4. Question 4

    Statistics. This type asked 3 times: NDA 1 2020, NDA 1 2022, NDA 2 2023. This one: NDA 2 2023

    101
    The sum of deviations of nn numbers from 10 and 20 are pp and qq respectively. If (p−q)2=10000(p-q)^2=10000, then what is the value of nn?

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  5. Question 5

    Statistics. This type asked 3 times: NDA 2 2019, NDA 1 2022, NDA 1 2023. This one: NDA 1 2023

    101
    The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11, 16 and 20. What are the other two observations?

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