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Day 87: NDA Maths

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

  1. Question 1

    Lines. This type asked 2 times: NDA 1 2018, NDA 1 2019. This one: NDA 1 2019

    51
    Consider the following statements: 1. For an equation of a line xcos⁡θ+ysin⁡θ=px\cos\theta+y\sin\theta=p in normal form, the length of the perpendicular from the point (α,β)(\alpha,\beta) to the line is ∣αcos⁡θ+βsin⁡θ+p∣|\alpha\cos\theta+\beta\sin\theta+p|. 2. The length of the perpendicular from the point (α,β)(\alpha,\beta) to the line xa+yb=1\frac{x}{a}+\frac{y}{b}=1 is ∣aα+bβ−aba2+b2∣\left|\frac{a\alpha+b\beta-ab}{\sqrt{a^2+b^2}}\right|. Which of the above statements is/are correct?

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  2. Question 2

    Probability. This type asked 2 times: NDA 1 2017, NDA 1 2019. This one: NDA 1 2019

    101
    From a deck of cards, cards are taken out with replacement. What is the probability that the fourteenth card taken out is an ace?

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  3. Question 3

    Statistics. This type asked 2 times: NDA 1 2018, NDA 1 2019. This one: NDA 1 2019

    118
    If all the natural numbers between 1 and 20 are multiplied by 3, then what is the variance of the resulting series?

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  4. Question 4

    Vectors. This type asked 2 times: NDA 1 2018, NDA 1 2019. This one: NDA 1 2019

    69
    The sine of the angle between vectors a⃗=2i^−6j^−3k^\vec{a}=2\hat{i}-6\hat{j}-3\hat{k} and b⃗=4i^+3j^−k^\vec{b}=4\hat{i}+3\hat{j}-\hat{k} is

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  5. Question 5

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

    29
    The sum of the binary numbers (11011)2(11011)_2, (10110110)2(10110110)_2 and (10011x0y)2(10011x0y)_2 is the binary number (101101101)2(101101101)_2. What are the values of x and y?

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