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Day 82: NDA Maths

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

  1. Question 1

    Quadratic Equations. This type asked 2 times: NDA 1 2021, NDA 2 2021. This one: NDA 2 2021

    6
    The quadratic equation 3x2−(k2+5k)x+3k2−5k=03x^{2}-(k^{2}+5k)x+3k^{2}-5k=0 has real roots of equal magnitude and opposite sign. Which one of the following is correct?

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  2. Question 2

    Quadratic Equations. This type asked 2 times: NDA 1 2021, NDA 2 2021. This one: NDA 2 2021

    1
    If x2+x+1=0x^{2} + x + 1 = 0, then what is the value of x199+x200+x201x^{199} + x^{200} + x^{201}?

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  3. Question 3

    Statistics. This type asked 2 times: NDA 1 2021, NDA 2 2021. This one: NDA 2 2021

    111
    For the set of numbers x,x,x+2,x+3,x+10x,x,x+2,x+3,x+10, where xx is a natural number, which of the following is/are correct? 1. Mean >> Mode 2. Median >> Mean Select the correct answer using the code given below.

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  4. Question 4

    Trigonometric Identities. This type asked 2 times: NDA 2 2019, NDA 2 2021. This one: NDA 2 2021

    35
    Let the equation sec⁡x⋅cosec⁡x=p\sec x\cdot\cosec x=p have a solution, where pp is a positive real number. What should be the smallest value of pp?

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  5. Question 5

    Binomial Theorem. This type asked 2 times: NDA 2 2018, NDA 1 2021. This one: NDA 1 2021

    45
    What is the coefficient of the middle term in the expansion of (1+4x+4x2)5(1+4x+4x^2)^5?

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