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Day 132: NDA Maths

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

  1. Question 1

    Conics. Asked once: NDA 1 2021 (same type asked 2 times)

    65
    Consider the following with regard to eccentricity (e)(e) of a conic section: 1. e=0e=0 for circle. 2. e=1e=1 for parabola. 3. e<1e<1 for ellipse. Which of the above are correct?

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  2. Question 2

    Limits & Continuity. Asked once: NDA 1 2024 (same type asked 2 times)

    87
    Let f(x)=∣x∣+1f(x)=|x|+1 and g(x)=[x]−1g(x)=[x]-1, where [⋅][\cdot] is the greatest integer function. Let h(x)=f(x)⋅g(x)h(x)=f(x)\cdot g(x). Consider the following statements: (A) f(x)f(x) is differentiable for all x<0x<0. (B) g(x)g(x) is continuous at x=0.0001x=0.0001. (C) The derivative of g(x)g(x) at x=2.5x=2.5 is 1. Which of the statements given above are correct?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 1 2023 (same type asked 2 times)

    6
    Let AA and BB be symmetric matrices of same order, then which one of the following is correct regarding (AB−BA)(AB-BA)? 1. Its diagonal entries are equal but nonzero 2. The sum of its non-diagonal entries is zero

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  4. Question 4

    Permutation & Combination. Asked once: NDA 2 2018 (same type asked 2 times)

    6
    Let x be the number of integers lying between 2999 and 8001 which have at least two digits equal. Then x is equal to

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  5. Question 5

    Sets & Relations. Asked once: NDA 2 2021 (same type asked 2 times)

    39
    Consider the following statements in respect of relations and functions: 1. All relations are functions but all functions are not relations. 2. A relation from AA to BB is a subset of Cartesian product A×BA\times B. 3. A relation in AA is a subset of Cartesian product A×AA\times A. Which of the above statements are correct?

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