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Day 368: NDA Maths

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

  1. Question 1

    Trigonometric Identities. Asked once: NDA 2 2019

    63
    If tan⁡A−tan⁡B=x\tan A - \tan B = x and cot⁡B−cot⁡A=y\cot B - \cot A = y, then what is the value of cot⁡(A−B)\cot(A - B) ?

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  2. Question 2

    Vectors. Asked once: NDA 2 2017

    47
    A force F⃗=i^+3j^+2k^\vec{F} = \hat{i}+3\hat{j}+2\hat{k} acts on a particle to displace it from the point A(i^+2j^−3k^)A(\hat{i}+2\hat{j}-3\hat{k}) to the point B(3i^−j^+5k^)B(3\hat{i}-\hat{j}+5\hat{k}). The work done by the force will be

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  3. Question 3

    Differentiation. Asked once: NDA 2 2017

    65
    Consider the following statements: 1. dydx\dfrac{dy}{dx} at a point on the curve gives slope of the tangent at that point. 2. If a(t)a(t) denotes acceleration of a particle, then ∫a(t) dt+c\int a(t)\,dt + c gives velocity of the particle. 3. If s(t)s(t) gives displacement of a particle at time tt, then dsdt\dfrac{ds}{dt} gives its acceleration at that instant. Which of the above statements is/are correct?

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  4. Question 4

    Functions. Asked once: NDA 2 2018

    80
    A function f:A→Rf: A\to\mathbb{R} is defined by the equation f(x)=x2−4x+5f(x)=x^2-4x+5 where A=(1,4)A=(1,4). What is the range of the function?

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  5. Question 5

    Lines. Asked once: NDA 1 2018

    62
    Perpendiculars from any point on 2x+11y=5 to lines 24x+7y=20 and 4x-3y=2 are

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