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Day 351: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Trigonometric Identities. Asked once: NDA 1 2021

    24
    What is (1+cot⁡θ−csc⁡θ)(1+tan⁡θ+sec⁡θ)(1+\cot\theta - \csc\theta)(1+\tan\theta+\sec\theta) equal to?

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  2. Question 2

    Vectors. Asked once: NDA 2 2019

    49
    Consider the following statements : 1. The magnitude of a⃗×b⃗\vec{a} \times \vec{b} is same as the area of a triangle with sides a⃗\vec{a} and b⃗\vec{b}. 2. If a⃗×b⃗=0⃗\vec{a} \times \vec{b} = \vec{0} where a⃗≠0⃗\vec{a} \neq \vec{0}, b⃗≠0⃗\vec{b} \neq \vec{0}, then a⃗=λb⃗\vec{a} = \lambda\vec{b}. Which of the above statements is/are correct ?

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  3. Question 3 (case study, 3 parts)

    Application of Derivatives. Asked once: NDA 1 2018

    Consider the following information for the next three (03) items that follow: Three sides of a trapezium are each equal to 6 cm. Let alpha in (0, pi/2) be the angle between a pair of adjacent sides.
    76
    If the area of the trapezium is the maximum possible, then what is alpha equal to?

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    77
    If the area is maximum, what is the length of the fourth side?

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    78
    What is the maximum area of the trapezium?

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  4. Question 4

    Differentiation. Asked once: NDA 1 2018

    74
    For f(x)=x2ln⁡∣x∣f(x)=x^2\ln|x| (x≠0x\ne0), f(0)=0f(0)=0, what is f′(0)f'(0)?

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  5. Question 5

    Functions. Asked once: NDA 1 2020

    97
    Consider the following statements: 1. The function f(x)=ln⁡xf(x)=\ln x increases in the interval (0,∞)(0,\infty). 2. The function f(x)=tan⁡xf(x)=\tan x increases in the interval (−π2,π2)\left(-\frac{\pi}{2},\frac{\pi}{2}\right). Which of the above statements is/are correct?

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