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Day 130: NDA Maths

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

  1. Question 1

    Logarithms. Asked once: NDA 1 2019 (same type asked 3 times)

    72
    If f(x)=log⁡10(1+x)f(x)=\log_{10}(1+x), then what is 4f(4)+5f(1)−log⁡1024f(4)+5f(1)-\log_{10}2 equal to?

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  2. Question 2

    Vectors. Asked once: NDA 2 2017 (same type asked 3 times)

    51
    If the vectors ai^+j^+k^a\hat{i}+\hat{j}+\hat{k}, i^+bj^+k^\hat{i}+b\hat{j}+\hat{k} and i^+j^+ck^\hat{i}+\hat{j}+c\hat{k} (a,b,c≠1a, b, c \neq 1) are coplanar, then the value of 11−a+11−b+11−c\dfrac{1}{1-a}+\dfrac{1}{1-b}+\dfrac{1}{1-c} is

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  3. Question 3

    Permutation & Combination. Asked once: NDA 2 2018 (same type asked 3 times)

    16
    There are 17 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so as to include 3 bowlers?

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  4. Question 4

    Sequence & Series. Asked once: NDA 2 2018 (same type asked 3 times)

    7
    The sum of the series 3−1+13−19+⋯3 - 1 + \frac{1}{3} - \frac{1}{9} + \cdots is equal to

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  5. Question 5

    Statistics. Asked once: NDA 1 2018 (same type asked 3 times)

    108
    Consider statements: 1. Mean is independent of change in scale and origin. 2. Variance is independent of change in scale but not in origin. Which is/are correct?

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