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Day 88: NDA Maths

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

  1. Question 1

    Differentiation. This type asked 2 times: NDA 1 2017, NDA 2 2018. This one: NDA 2 2018

    98
    Let f(x+y)=f(x)f(y)f(x+y)=f(x)f(y) and f(x)=1+xg(x)ϕ(x)f(x)=1+xg(x)\phi(x), where lim⁡x→0g(x)=a\lim_{x\to0}g(x)=a and lim⁡x→0ϕ(x)=b\lim_{x\to0}\phi(x)=b. Then what is f′(x)f'(x) equal to?

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  2. Question 2

    Matrices & Determinants. This type asked 2 times: NDA 1 2018, NDA 2 2018. This one: NDA 2 2018

    14
    What is the adjoint of the matrix (cos⁡(−θ)−sin⁡(−θ)−sin⁡(−θ)cos⁡(−θ))\begin{pmatrix} \cos(-\theta) & -\sin(-\theta) \\ -\sin(-\theta) & \cos(-\theta) \end{pmatrix}?

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  3. Question 3

    Quadratic Equations. This type asked 2 times: NDA 1 2017, NDA 2 2018. This one: NDA 2 2018

    49
    The ratio of roots of the equations ax2+bx+c=0ax^2 + bx + c = 0 and px2+qx+r=0px^2 + qx + r = 0 are equal. If D1D_1 and D2D_2 are respective discriminants, then what is D1D2\frac{D_1}{D_2} equal to?

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  4. Question 4

    Statistics. This type asked 2 times: NDA 1 2017, NDA 2 2018. This one: NDA 2 2018

    118
    Which one of the following can be obtained from an ogive?

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  5. Question 5

    Vectors. This type asked 2 times: NDA 1 2017, NDA 2 2018. This one: NDA 2 2018

    70
    In a triangle ABC, if taken in order, consider the following statements: 1. AB⃗+BC⃗+CA⃗=0⃗\vec{AB}+\vec{BC}+\vec{CA}=\vec{0} 2. AB⃗+BC⃗−CA⃗=0⃗\vec{AB}+\vec{BC}-\vec{CA}=\vec{0} 3. AB⃗−BC⃗+CA⃗=0⃗\vec{AB}-\vec{BC}+\vec{CA}=\vec{0} 4. BA⃗−BC⃗+CA⃗=0⃗\vec{BA}-\vec{BC}+\vec{CA}=\vec{0} How many of the above statements are correct?

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