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Day 382: NDA Maths

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

  1. Question 1

    Matrices & Determinants. Asked once: NDA 1 2019

    9
    If A=(0110)A = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}, then the matrix A is a/an

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  2. Question 2

    Probability. Asked once: NDA 2 2018

    115
    Two integers x and y are chosen with replacement from the set {0,1,2,…,10}\{0,1,2,\ldots,10\}. The probability that ∣x−y∣>5|x-y|>5 is

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  3. Question 3

    Trigonometric Identities. Asked once: NDA 2 2018

    43
    If θ=π8\theta = \frac{\pi}{8}, then what is the value of (2cos⁡θ+1)10(2cos⁡2θ−1)10(2cos⁡θ−1)10(2cos⁡4θ−1)10(2\cos\theta+1)^{10}(2\cos 2\theta-1)^{10}(2\cos\theta-1)^{10}(2\cos 4\theta-1)^{10}?

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 1 2019

    18
    If A is an identity matrix of order 3, then its inverse (A−1)(A^{-1})

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  5. Question 5

    Probability. Asked once: NDA 1 2018

    118
    Consider the following in respect of two events AA and BB: 1. P(A occurs but not B)=P(A)−P(B)P(A \text{ occurs but not } B) = P(A) - P(B) if B⊂AB \subset A 2. P(A alone or B alone occurs)=P(A)+P(B)−P(A∩B)P(A \text{ alone or } B \text{ alone occurs}) = P(A) + P(B) - P(A \cap B) 3. P(A∪B)=P(A)+P(B)P(A \cup B) = P(A) + P(B) if AA and BB are mutually exclusive Which of the above is/are correct?

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