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Day 52: NDA Maths

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

  1. Question 1

    Permutation & Combination. Asked 2 times: NDA 1 2017*, NDA 2 2018 (* = numbers or wording changed that year)

    48
    What is the sum of all three-digit numbers that can be formed using all the digits 3, 4 and 5, when repetition of digits is not\textbf{\text{not}} allowed?

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  2. Question 2

    Differentiation. Asked 2 times: NDA 1 2017*, NDA 2 2018 (* = numbers or wording changed that year)

    76
    If f(x)=25−x2f(x)=\sqrt{25-x^2}, then what is lim⁡x→1f(x)−f(1)x−1\lim_{x\to1}\frac{f(x)-f(1)}{x-1} equal to?

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  3. Question 3

    Binomial Theorem. Asked 2 times: NDA 2 2017*, NDA 1 2018 (* = numbers or wording changed that year)

    21
    What is the number of non-zero terms in (1+23 x)11+(1−23 x)11(1+2\sqrt{3}\,x)^{11} + (1-2\sqrt{3}\,x)^{11} after simplification?

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  4. Question 4

    Lines. Asked 2 times: NDA 2 2017*, NDA 1 2018 (* = numbers or wording changed that year)

    53
    What is the equation of the line cutting intercept 2 from negative y-axis direction, inclined at 30 degrees with positive x-axis?

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  5. Question 5

    Logarithms. Asked 2 times: NDA 2 2017*, NDA 1 2018 (* = numbers or wording changed that year)

    11
    If x+log⁡15(1+3x)=xlog⁡155+log⁡1512x + \log_{15}(1+3^x) = x\log_{15}5 + \log_{15}12, where x is an integer, then what is x equal to?

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