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Day 79: NDA Maths

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

  1. Question 1

    Permutation & Combination. This type asked 2 times: NDA 2 2019, NDA 1 2022. This one: NDA 1 2022

    21
    What is the maximum value of nn such that 5n5^n divides (30!+35!)(30!+35!), where nn is a natural number?

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  2. Question 2

    Properties of Triangle. This type asked 2 times: NDA 2 2017, NDA 1 2022. This one: NDA 1 2022

    86
    Let a,b,ca, b, c be the lengths of sides BC,CA,ABBC, CA, AB respectively of a triangle ABCABC. If pp is the perimeter and qq is the area of the triangle, then what is p(p−2a)tan⁡(A2)p(p-2a)\tan\left(\frac{A}{2}\right) equal to?

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  3. Question 3

    Quadratic Equations. This type asked 2 times: NDA 2 2017, NDA 1 2022. This one: NDA 1 2022

    17
    Let α\alpha and β\beta be the roots of the equation x2+px+q=0x^2+px+q=0. If α3\alpha^3 and β3\beta^3 are the roots of the equation x2+mx+n=0x^2+mx+n=0, then what is the value of m+nm+n?

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  4. Question 4

    Sets & Relations. This type asked 2 times: NDA 1 2019, NDA 1 2022. This one: NDA 1 2022

    23
    If A={{1,2,3}}A=\{\{1,2,3\}\}, then how many elements are there in the power set of AA?

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  5. Question 5

    Sets & Relations. This type asked 2 times: NDA 1 2020, NDA 1 2022. This one: NDA 1 2022

    41
    Consider all the subsets of the set A={1,2,3,4}A=\{1,2,3,4\}. How many of them are supersets of the set {4}\{4\}?

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