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Day 86: NDA Maths

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

  1. Question 1

    Sets & Relations. This type asked 2 times: NDA 2 2018, NDA 2 2019. This one: NDA 2 2019

    3
    If AA, BB and CC are subsets of a given set, then which one of the following relations is not\textbf{\text{not}} correct ?

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  2. Question 2

    Sets & Relations. This type asked 2 times: NDA 2 2017, NDA 2 2019. This one: NDA 2 2019

    20
    If A={x:0≤x≤2}A = \{x : 0 \leq x \leq 2\} and B={y; y is a prime number}B = \{y;\, y \text{ is a prime number}\}, then what is A∩BA \cap B equal to ?

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  3. Question 3

    Statistics. This type asked 2 times: NDA 1 2018, NDA 2 2019. This one: NDA 2 2019

    106
    For the variables xx and yy, the two regression lines are 6x+y=306x + y = 30 and 3x+2y=253x + 2y = 25. What are the values of xˉ\bar{x}, yˉ\bar{y} and rr respectively ?

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  4. Question 4

    3D Geometry. This type asked 2 times: NDA 2 2018, NDA 1 2019. This one: NDA 1 2019

    64
    The distance between the parallel planes 4x−2y+4z+9=04x-2y+4z+9=0 and 8x−4y+8z+21=08x-4y+8z+21=0 is

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  5. Question 5

    Application of Derivatives. This type asked 2 times: NDA 2 2017, NDA 1 2019. This one: NDA 1 2019

    84
    A given quantity of metal is to be cast into a half cylinder (i.e. with a rectangular base and semicircular ends). If the total surface area is to be minimum, then the ratio of the height of the half cylinder to the diameter of the semicircular ends is

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