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Day 42: NDA Maths

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

  1. Question 1

    Quadratic Equations. This type asked 3 times: NDA 2 2017, NDA 2 2019, NDA 1 2021. This one: NDA 1 2021

    8
    If the roots of the quadratic equation x2+2x+k=0x^2 + 2x + k = 0 are real, then

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  2. Question 2

    Vectors. This type asked 3 times: NDA 2 2018, NDA 2 2019, NDA 1 2021. This one: NDA 1 2021

    73
    If a⃗\vec{a} and b⃗\vec{b} are two vectors such that ∣a⃗+b⃗∣=∣a⃗−b⃗∣=4|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|=4, then which one of the following is correct?

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  3. Question 3

    Logarithms. This type asked 3 times: NDA 2 2018, NDA 1 2019, NDA 1 2020. This one: NDA 1 2020

    7
    What is the value of 110log⁡51024−log⁡510+15log⁡53125\frac{1}{10}\log_5 1024 - \log_5 10 + \frac{1}{5}\log_5 3125?

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  4. Question 4

    Vectors. This type asked 3 times: NDA 1 2017, NDA 2 2017, NDA 1 2020. This one: NDA 1 2020

    70
    If the vectors a⃗=2i^−3j^+k^\vec{a}=2\hat{i}-3\hat{j}+\hat{k}, b⃗=i^+2j^−3k^\vec{b}=\hat{i}+2\hat{j}-3\hat{k} and c⃗=j^+pk^\vec{c}=\hat{j}+p\hat{k} are coplanar, then what is the value of pp?

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  5. Question 5

    Permutation & Combination. This type asked 3 times: NDA 1 2018, NDA 2 2018, NDA 1 2019. This one: NDA 1 2019

    20
    From 6 programmers and 4 typists, an office wants to recruit 5 people. What is the number of ways this can be done so as to recruit at least one typist?

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