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Day 261: NDA Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1

    Probability. Asked once: NDA 2 2026

    106
    If P(A∩B)=1/2P(A \cap B) = 1/2 and P(A‾∩B‾)=1/2P(\overline{A} \cap \overline{B}) = 1/2, and 2P(A)=P(B)=k2P(A) = P(B) = k, then what is the value of kk?

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  2. Question 2

    Properties of Triangle. Asked once: NDA 2 2024

    28
    In a triangle ABCABC, tan⁡A+tan⁡B+tan⁡C=k\tan A+\tan B+\tan C=k. What is the value of cot⁡Acot⁡Bcot⁡C\cot A\cot B\cot C?

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  3. Question 3

    Quadratic Equations. Asked once: NDA 2 2026

    29
    Let α\alpha and β\beta be the roots of the equation ax2+bx+c=0ax^2 + bx + c = 0 and pn=αn+βnp_n = \alpha^n + \beta^n, where n>1n > 1. What is apn+1+bpn+cpn−1ap_{n+1} + bp_n + cp_{n-1} equal to?

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  4. Question 4

    Sequence & Series. Asked once: NDA 2 2025

    7
    How many terms are identical in the two APs 19,21,23,…19, 21, 23, \ldots up to 110 terms and 19,22,25,28,…19, 22, 25, 28, \ldots up to 75 terms?

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  5. Question 5 (case study, 3 parts)

    Sets & Relations. Asked once: NDA 1 2020

    Directions for the following three (03) items: Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in Z be denoted by n(Z) which is equal to 90.
    16
    If the number of elements in Y and Z are in the ratio 4 : 5, then what is the value of b?

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    17
    What is the value of n(X)+n(Y)+n(Z)−n(X∩Y)−n(Y∩Z)−n(X∩Z)+n(X∩Y∩Z)n(X)+n(Y)+n(Z)-n(X\cap Y)-n(Y\cap Z)-n(X\cap Z)+n(X\cap Y\cap Z)?

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    18
    If the number of elements belonging to neither X, nor Y, nor Z is equal to p, then what is the number of elements in the complement of X?

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