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Day 51: NDA Maths

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

  1. Question 1

    Probability. Asked 2 times: NDA 1 2017*, NDA 1 2019 (* = numbers or wording changed that year)

    103
    A problem is given to three students A, B and C whose probabilities of solving the problem are 12\dfrac{1}{2}, 34\dfrac{3}{4} and 14\dfrac{1}{4} respectively. What is the probability that the problem will be solved if they all solve the problem independently?

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  2. Question 2

    Probability. Asked 2 times: NDA 1 2017, NDA 1 2019

    119
    What is the probability that an interior point in a circle is closer to the centre than to the circumference?

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  3. Question 3

    Sequence & Series. Asked 2 times: NDA 1 2017*, NDA 1 2019 (* = numbers or wording changed that year)

    47
    What is the fourth term of an AP of n terms whose sum is n(n+1)n(n+1)?

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  4. Question 4

    Vectors. Asked 2 times: NDA 1 2017*, NDA 1 2019 (* = numbers or wording changed that year)

    70
    What is the value of λ\lambda for which the vectors 3i^+4j^−k^3\hat{i}+4\hat{j}-\hat{k} and −2i^+λj^+10k^-2\hat{i}+\lambda\hat{j}+10\hat{k} are perpendicular?

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  5. Question 5

    Lines. Asked 2 times: NDA 1 2018*, NDA 2 2018 (* = numbers or wording changed that year)

    55
    What is the equation of straight line passing through the point of intersection of the lines x2+y3=1\frac{x}{2}+\frac{y}{3}=1 and x3+y2=1\frac{x}{3}+\frac{y}{2}=1, and parallel to the line 4x+5y−6=04x+5y-6=0?

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