PYQ Vault

Day 320: NDA Maths

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

  1. Question 1

    Lines. Asked once: NDA 1 2024

    63
    Triangle ABCABC is an acute angled isosceles triangle. Two equal sides ABAB and ACAC lie on the lines 7x−y−3=07x-y-3=0 and x+y−5=0x+y-5=0. If θ\theta is one of the equal angles, then what is cot⁡θ\cot\theta equal to?

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  2. Question 2

    Logarithms. Asked once: NDA 1 2018

    32
    If 0<a<10 < a < 1, the value of log⁡10a\log_{10}a is negative. This is justified by

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 1 2025

    24
    If A=(yzxzxyxyz)A = \begin{pmatrix} y & z & x \\ z & x & y \\ x & y & z \end{pmatrix} where x,y,zx, y, z are integers, is an orthogonal matrix, then what is the value of x2+y2+z2x^2 + y^2 + z^2?

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  4. Question 4

    Permutation & Combination. Asked once: NDA 2 2021

    25
    Consider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common side with any of the sides of the polygon?

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  5. Question 5

    Probability. Asked once: NDA 2 2024

    113
    A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?

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