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Day 67: NDA Maths

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

  1. Question 1

    Sets & Relations. This type asked 2 times: NDA 1 2022, NDA 2 2024. This one: NDA 2 2024

    34
    Let PP and QQ be two non-void relations on a set AA. Which of the following statements are correct? A. PP and QQ are reflexive ⇒P∩Q\Rightarrow P\cap Q is reflexive. B. PP and QQ are symmetric ⇒P∪Q\Rightarrow P\cup Q is symmetric. C. PP and QQ are transitive ⇒P∩Q\Rightarrow P\cap Q is transitive. Select the answer using the code given below.

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  2. Question 2

    Statistics. This type asked 2 times: NDA 2 2019, NDA 2 2024. This one: NDA 2 2024

    111
    Let ∑i=19xi2=855\displaystyle\sum_{i=1}^{9}x_i^2=855. If MM is the mean and σ\sigma is the standard deviation of x1,x2,…,x9x_1,x_2,\ldots,x_9, then what is the value of M2+σ2M^2+\sigma^2?

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  3. Question 3

    Vectors. This type asked 2 times: NDA 1 2022, NDA 2 2024. This one: NDA 2 2024

    51
    What is 3α+2β3\alpha+2\beta equal to if (2i^+6j^+27k^)×(i^+αj^+βk^)(2\hat{i}+6\hat{j}+27\hat{k})\times(\hat{i}+\alpha\hat{j}+\beta\hat{k}) is a null vector?

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  4. Question 4

    3D Geometry. This type asked 2 times: NDA 1 2023, NDA 1 2024. This one: NDA 1 2024

    52
    If (1,−1,2)(1,-1,2) and (2,1,−1)(2,1,-1) are the endpoints of a diameter of a sphere x2+y2+z2+2ux+2vy+2wz−1=0x^2+y^2+z^2+2ux+2vy+2wz-1=0, then what is u+v+wu+v+w equal to?

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  5. Question 5

    Application of Derivatives. This type asked 2 times: NDA 2 2021, NDA 1 2024. This one: NDA 1 2024

    79
    The non-negative values of bb for which the function 16x33−4bx2+x\dfrac{16x^3}{3}-4bx^2+x has neither maximum nor minimum in the range x>0x>0 is

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