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Day 156: NDA Maths

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

  1. Question 1

    Lines. Asked once: NDA 1 2020 (same type asked 2 times)

    56
    Under which condition, are the points (a,b)(a,b), (c,d)(c,d) and (a−c,b−d)(a-c,b-d) collinear?

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  2. Question 2

    Permutation & Combination. Asked once: NDA 1 2019 (same type asked 2 times)

    99
    How many three-digit even numbers can be formed using the digits 1, 2, 3, 4 and 5 when repetition of digits is not\textbf{\text{not}} allowed?

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  3. Question 3

    Permutation & Combination. Asked once: NDA 2 2019 (same type asked 2 times)

    27
    If n!n! has 17 zeros, then what is the value of nn ?

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  4. Question 4

    Properties of Triangle. Asked once: NDA 2 2017 (same type asked 2 times)

    37
    In a triangle ABCABC, a−2b+c=0a - 2b + c = 0. The value of cot⁡ ⁣(A2)cot⁡ ⁣(C2)\cot\!\left(\dfrac{A}{2}\right)\cot\!\left(\dfrac{C}{2}\right) is

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  5. Question 5

    Quadratic Equations. Asked once: NDA 2 2017 (same type asked 2 times)

    24
    If α\alpha and β\beta are the roots of the equation 3x2+2x+1=03x^2 + 2x + 1 = 0, then the equation whose roots are α+β−1\alpha + \beta^{-1} and β+α−1\beta + \alpha^{-1} is

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