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Day 303: NDA Maths

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

  1. Question 1

    Matrices & Determinants. Asked once: NDA 2 2025

    19
    If aa, bb, cc are the sides of a triangle ABCABC and pp is the perimeter of the triangle, then what is ∣p+cabcp+abcap+b∣\begin{vmatrix}p+c & a & b\\c & p+a & b\\c & a & p+b\end{vmatrix} equal to?

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  2. Question 2

    Permutation & Combination. Asked once: NDA 1 2023

    28
    mm parallel lines cut nn parallel lines giving rise to 60 parallelograms. What is the value of (m+n)(m+n)?

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  3. Question 3

    Probability. Asked once: NDA 2 2025

    112
    In a throw of three dice, what is the probability of getting one prime number, one composite number and one number which is neither prime nor composite?

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  4. Question 4

    Properties of Triangle. Asked once: NDA 2 2022

    50
    In a triangle ABC, a=4,b=3,c=2a = 4, b = 3, c = 2. What is cos⁡3C\cos 3C equal to?

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  5. Question 5

    Quadratic Equations. Asked once: NDA 1 2024

    32
    If a,ba,b and c  (a>0, c>0)c\;(a>0,\,c>0) are in GP, then consider the following in respect of the equation ax2+bx+c=0ax^2+bx+c=0: (A) The equation has imaginary roots. (B) The ratio of the roots of the equation is 1:ω1:\omega where ω\omega is a cube root of unity. (C) The product of roots of the equation is b2a2\dfrac{b^2}{a^2}. Which of the statements given above are correct?

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