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Day 353: NDA Maths

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

  1. Question 1

    Statistics. Asked once: NDA 1 2019

    107
    If two variables X and Y are independent, then what is the correlation coefficient between them?

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  2. Question 2

    Trigonometric Identities. Asked once: NDA 1 2021

    30
    If 3cos⁡θ=4sin⁡θ3\cos\theta = 4\sin\theta, then what is the value of tan⁡(45°+θ)\tan(45°+\theta)?

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  3. Question 3

    Vectors. Asked once: NDA 2 2019

    48
    Consider the following equations for two vectors a⃗\vec{a} and b⃗\vec{b} : 1. (a⃗+b⃗)⋅(a⃗−b⃗)=∣a⃗∣2−∣b⃗∣2\left(\vec{a}+\vec{b}\right)\cdot\left(\vec{a}-\vec{b}\right)=\left|\vec{a}\right|^{2}-\left|\vec{b}\right|^{2} 2. (∣a⃗+b⃗∣)(∣a⃗−b⃗∣)=∣a⃗∣2−∣b⃗∣2\left(\left|\vec{a}+\vec{b}\right|\right)\left(\left|\vec{a}-\vec{b}\right|\right)=\left|\vec{a}\right|^{2}-\left|\vec{b}\right|^{2} 3. ∣a⃗⋅b⃗∣2+∣a⃗×b⃗∣2=∣a⃗∣2∣b⃗∣2\left|\vec{a}\cdot\vec{b}\right|^{2}+\left|\vec{a}\times\vec{b}\right|^{2}=\left|\vec{a}\right|^{2}\left|\vec{b}\right|^{2} Which of the above statements are correct ?

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  4. Question 4

    Application of Derivatives. Asked once: NDA 2 2017

    71
    The maximum value of ln⁡xx\dfrac{\ln x}{x} is

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  5. Question 5

    Differentiation. Asked once: NDA 1 2018

    97
    If f(x) is an even function, then which is correct?

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