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Day 30: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Lines. This type asked 3 times: NDA 1 2021, NDA 1 2022, NDA 2 2025. This one: NDA 2 2025

    58
    The equation of the locus of a point equidistant from the points (a,b)(a,b) and (c,d)(c,d) is (a−c)x+(b−d)y+k=0(a-c)x+(b-d)y+k=0. What is the value of kk?

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  2. Question 2 (case study, 2 parts)

    Permutation & Combination. This type asked 3 times: NDA 1 2018, NDA 1 2024, NDA 2 2025. This one: NDA 2 2025

    For the following two (02) items: There are 8 points on a plane out of which 4 points are collinear.
    35
    How many triangles can be formed by joining these points?

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    36
    How many quadrilaterals can be formed by joining these points?

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  3. Question 3

    Probability. This type asked 3 times: NDA 2 2019, NDA 1 2020, NDA 2 2025. This one: NDA 2 2025

    104
    An urn contains 10 white and 5 red balls. If two balls are drawn at random, then what is the probability that both the balls are red?

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  4. Question 4

    Sets & Relations. This type asked 3 times: NDA 1 2021, NDA 2 2023, NDA 2 2025. This one: NDA 2 2025

    43
    Let A={−3,−2,−1,0,1,2,3}A=\{-3,-2,-1,0,1,2,3\} and B={0,1,4,9}B=\{0,1,4,9\}. How many elements does the subset of A×BA\times B corresponding to the relation R={(x,y):∣x∣<y}R=\{(x,y):|x|<y\} have, where x∈Ax\in A and y∈By\in B?

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  5. Question 5

    Statistics. This type asked 3 times: NDA 2 2021, NDA 1 2023, NDA 2 2025. This one: NDA 2 2025

    101
    What is the harmonic mean of the numbers C(10,3)C(10,3), C(10,4)C(10,4), C(10,5)C(10,5), C(10,6)C(10,6) and C(10,7)C(10,7)?

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