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Day 283: NDA Maths

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

  1. Question 1

    Properties of Triangle. Asked once: NDA 1 2024

    41
    Triangle ABCABC such that ∠C=60°\angle C=60°, then what is cos⁡A+cos⁡Bcos⁡ ⁣(A−B2)\dfrac{\cos A+\cos B}{\cos\!\left(\dfrac{A-B}{2}\right)} equal to?

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  2. Question 2 (case study, 2 parts)

    Quadratic Equations. Asked once: NDA 2 2025

    For the following two (02) items: Let f(x)=ax2+bx+cf(x)=ax^2+bx+c be a quadratic polynomial such that f(1)=f(4)=2f(1)=f(4)=2. Further, 2 is a root of f(x)=0f(x)=0.
    37
    What is the other root of f(x)=0f(x)=0?

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    38
    What is (a+b+c)(a+b+c) equal to?

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  3. Question 3

    Sequence & Series. Asked once: NDA 2 2023

    6
    If the nnth term of a sequence is 2n+57\frac{2n+5}{7}, then what is the sum of its first 140 terms?

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  4. Question 4 (case study, 2 parts)

    Sets & Relations. Asked once: NDA 1 2018

    Consider the information given below and answer the two items (02) that follow: In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.
    13
    What is the number of students who are good in either Hindi or Mathematics but not in English?

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    14
    What is the number of students who are good in Hindi and Mathematics but not in English?

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  5. Question 5

    Statistics. Asked once: NDA 1 2023

    108
    The observations 4, 1, 4, 3, 6, 2, 1, 3, 4, 5, 1, 6 are outputs of 12 dices thrown simultaneously. If mm and MM are means of lowest 8 observations and highest 4 observations respectively, then what is (2m+M)(2m+M) equal to?

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