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Day 266: NDA Maths

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

  1. Question 1

    Logarithms. Asked once: NDA 1 2024

    7
    If log⁡ba=p\log_b a=p, log⁡dc=2p\log_d c=2p and log⁡fe=3p\log_f e=3p, then what is (ace)1p(ace)^{\frac{1}{p}} equal to?

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  2. Question 2

    Matrices & Determinants. Asked once: NDA 2 2026

    37
    What is ∣1abca31a+1bc(a+b)a3+b31a+1b+1cab+bc+caa3+b3+c3∣\begin{vmatrix} \frac{1}{a} & bc & a^3 \\ \frac{1}{a} + \frac{1}{b} & c(a + b) & a^3 + b^3 \\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} & ab + bc + ca & a^3 + b^3 + c^3 \end{vmatrix} equal to?

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  3. Question 3

    Permutation & Combination. Asked once: NDA 1 2025

    19
    What is the number of positive integer solutions of x+y+z=5x + y + z = 5?

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  4. Question 4

    Probability. Asked once: NDA 1 2026

    114
    Consider the following statements in respect of the events A, B, C: I. (A∪B∪C)∩(Aˉ∩Bˉ∩Cˉ)(A\cup B\cup C)\cap(\bar{A}\cap\bar{B}\cap\bar{C}) is an impossible event. II. (A∩B∩C)∩(Aˉ∪Bˉ∪Cˉ)(A\cap B\cap C)\cap(\bar{A}\cup\bar{B}\cup\bar{C}) is a possible event. Which of the statements given above is/are correct?

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  5. Question 5

    Properties of Triangle. Asked once: NDA 2 2024

    23
    In a triangle ABCABC, acos⁡A=bcos⁡B=ccos⁡Ca\cos A=b\cos B=c\cos C. What is the area of the triangle if a=6a=6 cm?

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