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Day 61: NDA Maths

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

  1. Question 1

    Sets & Relations. This type asked 2 times: NDA 2 2024, NDA 2 2025. This one: NDA 2 2025

    42
    Set XX contains 3n3n elements and set YY contains 2n2n elements, and they have nn elements in common. How many elements does (X−Y)×(Y−X)(X-Y)\times(Y-X) have?

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  2. Question 2

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

    11
    In a class of 45 students, 34 like to play cricket and 26 like to play football. Further, each student likes to play at least one of the two games. How many students like to play exactly one game?

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  3. Question 3

    Vectors. This type asked 2 times: NDA 2 2022, NDA 2 2025. This one: NDA 2 2025

    69
    The position vectors of the vertices AA, BB, CC and DD of a quadrilateral ABCDABCD are given by 3i^+4j^−2k^3\hat{i}+4\hat{j}-2\hat{k}, 4i^−4j^−3k^4\hat{i}-4\hat{j}-3\hat{k}, 2i^−3j^+2k^2\hat{i}-3\hat{j}+2\hat{k} and 6i^−2j^+k^6\hat{i}-2\hat{j}+\hat{k} respectively. What is the angle between the diagonals ACAC and BDBD of the quadrilateral?

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  4. Question 4

    Complex Numbers. This type asked 2 times: NDA 1 2021, NDA 1 2025. This one: NDA 1 2025

    16
    If z≠0z \neq 0 is a complex number, then what is amp(z)+amp(zˉ)\text{amp}(z) + \text{amp}(\bar{z}) equal to?

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  5. Question 5

    Conics. This type asked 2 times: NDA 1 2021, NDA 1 2025. This one: NDA 1 2025

    60
    If any point on an ellipse is (3sin⁡α,5cos⁡α)(3\sin\alpha, 5\cos\alpha), then what is the eccentricity of the ellipse?

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