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Day 237: NDA Maths

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

  1. Question 1

    Lines. Asked once: NDA 2 2017 (same type asked 8 times)

    44
    The angle between the lines x+y−3=0x + y - 3 = 0 and x−y+3=0x - y + 3 = 0 is α\alpha and the acute angle between the lines x−3y+23=0x - \sqrt{3}y + 2\sqrt{3} = 0 and 3x−y+1=0\sqrt{3}x - y + 1 = 0 is β\beta. Which one of the following is correct?

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  2. Question 2

    Matrices & Determinants. Asked once: NDA 1 2017 (same type asked 8 times)

    37
    What is the order of [x  y  z][ahghbfgfc][xyz][x\; y\; z]\begin{bmatrix}a&h&g\\h&b&f\\g&f&c\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}?

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  3. Question 3

    Probability. Asked once: NDA 2 2017 (same type asked 7 times)

    116
    In a multiple-choice test, an examinee either knows the correct answer with probability pp, or guesses with probability 1−p1-p. The probability of answering a question correctly is 1m\dfrac{1}{m}, if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is

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  4. Question 4

    Application of Derivatives. Asked once: NDA 1 2017 (same type asked 7 times)

    98
    Let f(x)=x+1xf(x)=x+\dfrac{1}{x}, where x∈(0,1)x\in(0,1). Then which one of the following is correct?

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  5. Question 5

    Matrices & Determinants. Asked once: NDA 1 2019 (same type asked 6 times)

    25
    If A is a square matrix of order n>1n > 1, then which one of the following is correct?

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