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Day 160: NDA Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: NDA 2 2019 (same type asked 2 times)

    42
    Consider the following statements : 1. cos⁡θ+sec⁡θ\cos\theta + \sec\theta can never be equal to 1.5. 2. tan⁡θ+cot⁡θ\tan\theta + \cot\theta can never be less than 2. Which of the above statements is/are correct ?

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  2. Question 2

    Binomial Theorem. Asked once: NDA 2 2018 (same type asked 2 times)

    11
    What is the coefficient of the middle term in the binomial expansion of (2+3x)4(2 + 3x)^4?

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  3. Question 3

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

    23
    If u, v and w (all positive) are the pthp^{\text{th}}, qthq^{\text{th}} and rthr^{\text{th}} terms of a GP, then the determinant of the matrix (ln⁡up1ln⁡vq1ln⁡wr1)\begin{pmatrix} \ln u & p & 1 \\ \ln v & q & 1 \\ \ln w & r & 1 \end{pmatrix} is

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  4. Question 4

    Matrices & Determinants. Asked once: NDA 2 2019 (same type asked 2 times)

    12
    What are the values of xx that satisfy the equation ∣x022x21111∣+∣3x02x221011∣=0\begin{vmatrix} x & 0 & 2 \\ 2x & 2 & 1 \\ 1 & 1 & 1 \end{vmatrix} + \begin{vmatrix} 3x & 0 & 2 \\ x^{2} & 2 & 1 \\ 0 & 1 & 1 \end{vmatrix} = 0 ?

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  5. Question 5

    Probability. Asked once: NDA 1 2020 (same type asked 2 times)

    103
    If P(A∪B)=56P(A\cup B)=\frac{5}{6}, P(A∩B)=13P(A\cap B)=\frac{1}{3} and P(not A)=12P(\text{not }A)=\frac{1}{2}, then which one of the following is not\textbf{\text{not}} correct?

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