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Day 359: NDA Maths

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

  1. Question 1

    Sequence & Series. Asked once: NDA 1 2017

    8
    What is the sum of the series 0.3+0.33+0.333+…0.3 + 0.33 + 0.333 + \ldots to nn terms?

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  2. Question 2

    Statistics. Asked once: NDA 2 2018

    116
    An analysis of monthly wages paid to the workers in two firms A and B belonging to the same industry gives the following result: Number of workers: Firm A = 500, Firm B = 600; Average monthly wage: Firm A = ₹1860, Firm B = ₹1750; Variance of distribution of wages: Firm A = 81, Firm B = 100. The average of monthly wage and variance of distribution of wages of all the workers in the firms A and B taken together are

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  3. Question 3

    Trigonometric Identities. Asked once: NDA 1 2021

    19
    What is the value of tan⁡31°tan⁡33°tan⁡35°⋯tan⁡57°tan⁡59°\tan 31° \tan 33° \tan 35° \cdots \tan 57° \tan 59°?

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  4. Question 4

    Vectors. Asked once: NDA 2 2018

    64
    If r⃗=xi^+yj^+zk^\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}, then what is r⃗⋅(i^+j^+k^)\vec{r}\cdot(\hat{i}+\hat{j}+\hat{k}) equal to?

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  5. Question 5

    Differentiation. Asked once: NDA 2 2017

    73
    If l1=ddx(esin⁡x)l_1 = \dfrac{d}{dx}(e^{\sin x}), l2=lim⁡h→0esin⁡(x+h)−esin⁡xhl_2 = \lim_{h \to 0}\dfrac{e^{\sin(x+h)} - e^{\sin x}}{h}, l3=∫esin⁡xcos⁡x dxl_3 = \displaystyle\int e^{\sin x}\cos x\,dx, then which one of the following is correct?

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