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Day 179: NDA Maths

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

  1. Question 1

    Matrices & Determinants. Asked once: NDA 2 2018 (same type asked 4 times)

    21
    The system of equations 2x+y−3z=52x + y - 3z = 5, 3x−2y+2z=53x - 2y + 2z = 5 and 5x−3y−z=165x - 3y - z = 16

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  2. Question 2

    Permutation & Combination. Asked once: NDA 1 2018 (same type asked 4 times)

    12
    How many four-digit numbers divisible by 10 can be formed using 1, 5, 0, 6, 7 without repetition?

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  3. Question 3

    Quadratic Equations. Asked once: NDA 2 2019 (same type asked 4 times)

    6
    If the roots of the equation a(b−c)x2+b(c−a)x+c(a−b)=0a(b-c)x^{2} + b(c-a)x + c(a-b) = 0 are equal, then which one of the following is correct ?

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  4. Question 4

    Trigonometric Identities. Asked once: NDA 1 2018 (same type asked 4 times)

    37
    What is sin⁡5x−sin⁡3xcos⁡5x+cos⁡3x\frac{\sin 5x - \sin 3x}{\cos 5x + \cos 3x} equal to?

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  5. Question 5 (case study, 2 parts)

    Limits & Continuity. Asked once: NDA 2 2023 (same type asked 4 times)

    Let f(x)=∣x∣f(x)=|x| and g(x)=[x]−1g(x)=[x]-1. Let h(x)=f(g(x))g(f(x))h(x)=\frac{f(g(x))}{g(f(x))}.
    57
    What is lim⁡x→0+h(x)\lim_{x\to0^+}h(x) equal to?

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    58
    What is lim⁡x→0−h(x)\lim_{x\to0^-}h(x) equal to?

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