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Day 277: NDA Maths

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

  1. Question 1

    Logarithms. Asked once: NDA 1 2024

    27
    What is the number of solutions of log⁡4(x−1)=log⁡2(x−3)\log_4(x-1)=\log_2(x-3)?

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  2. Question 2

    Matrices & Determinants. Asked once: NDA 1 2026

    14
    Let f(x)=∣3x2cos⁡x−sin⁡x6−10qq2q3∣f(x)=\begin{vmatrix}3x^2 & \cos x & -\sin x\\ 6 & -1 & 0\\ q & q^2 & q^3\end{vmatrix} where qq is any constant, then what is d2dx2(f(x))\dfrac{d^2}{dx^2}(f(x)) at x=0x=0 equal to?

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  3. Question 3

    Permutation & Combination. Asked once: NDA 1 2024

    5
    A man has 7 relatives (4 women and 3 men). His wife also has 7 relatives (3 women and 4 men). In how many ways can they invite 3 women and 3 men so that 3 of them are the man's relatives and 3 are his wife's relatives?

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  4. Question 4

    Probability. Asked once: NDA 2 2025

    102
    In a sample survey of a village, the probability that a farmer is in debt is 0.60. What is the probability that three randomly selected farmers are all in debt (assume independence of events)?

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  5. Question 5

    Properties of Triangle. Asked once: NDA 1 2024

    50
    Consider the following statements: A. In a triangle ABCABC, if cot⁡A⋅cot⁡B⋅cot⁡C>0\cot A\cdot\cot B\cdot\cot C>0, then the triangle is an acute angled triangle. B. In a triangle ABCABC, if tan⁡A⋅tan⁡B⋅tan⁡C>0\tan A\cdot\tan B\cdot\tan C>0, then the triangle is an obtuse angled triangle. Which of the statements given above is/are correct?

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