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Day 312: NDA Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Lines. Asked once: NDA 2 2024

    ABCD is an isosceles trapezium and AB is parallel to DC. Let A(2,3)A(2,3), B(4,3)B(4,3), C(5,1)C(5,1) be the vertices.
    63
    What are the coordinates of vertex DD?

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    64
    What is the point of intersection of the diagonals of the trapezium?

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  2. Question 2

    Logarithms. Asked once: NDA 2 2018

    31
    If (0.2)x=2(0.2)^x = 2 and log⁡102=0.3010\log_{10} 2 = 0.3010, then what is the value of x to the nearest tenth?

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  3. Question 3

    Matrices & Determinants. Asked once: NDA 2 2025

    14
    In obtaining the solution of the system of equations x+y+z=7x+y+z=7, x+2y+3z=16x+2y+3z=16 and x+3y+4z=22x+3y+4z=22 by Cramer's rule, the value of yy is obtained by dividing DD by D2D_2, where D=∣111123134∣D=\begin{vmatrix}1&1&1\\1&2&3\\1&3&4\end{vmatrix}. What is the value of the determinant D2D_2?

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  4. Question 4

    Permutation & Combination. Asked once: NDA 2 2022

    3
    If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) are there in the list before the first word that starts with C?

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  5. Question 5

    Probability. Asked once: NDA 2 2024

    119
    Three perfect dice D1,D2D_1,D_2 and D3D_3 are rolled. Let x,yx,y and zz represent the numbers on D1,D2D_1,D_2 and D3D_3 respectively. What is the number of possible outcomes such that x<y<zx<y<z?

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