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Day 101: NDA Maths

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

  1. Question 1

    Limits & Continuity. Asked once: NDA 1 2020 (same type asked 4 times)

    73
    If lim⁡x→1x4−1x−1=lim⁡x→kx3−k3x2−k2\lim_{x\to1}\frac{x^4-1}{x-1}=\lim_{x\to k}\frac{x^3-k^3}{x^2-k^2}, where k≠0k\neq0, then what is the value of kk?

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  2. Question 2

    Permutation & Combination. Asked once: NDA 1 2023 (same type asked 4 times)

    30
    5-digit numbers are formed using the digits 0, 1, 2, 4, 5 without repetition. What is the percentage of numbers which are greater than 50,000?

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  3. Question 3

    Quadratic Equations. Asked once: NDA 2 2022 (same type asked 4 times)

    8
    For how many quadratic equations, the sum of roots is equal to the product of roots?

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  4. Question 4

    Sets & Relations. Asked once: NDA 2 2022 (same type asked 4 times)

    Consider the following for the next three (03) items that follow: Let R be a relation from N to N defined by R={(x,y):x,y∈N and x2=y3}R = \{(x, y): x, y \in N \text{ and } x^2 = y^3\}. Which of the following are NOT correct? 1. (x,x)∈R(x,x) \in R for all x∈Nx \in N 2. (x,y)∈R⇒(y,x)∈R(x,y) \in R \Rightarrow (y,x) \in R 3. (x,y)∈R(x,y) \in R and (y,z)∈R⇒(x,z)∈R(y,z) \in R \Rightarrow (x,z) \in R
    14
    Select the correct answer using the code given below:

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  5. Question 5

    Statistics. Asked once: NDA 2 2024 (same type asked 4 times)

    101
    Let x−3y+4=0x-3y+4=0 and 2x−7y+8=02x-7y+8=0 be two lines of regression computed from some bivariate data. If byxb_{yx} and bxyb_{xy} are regression coefficients of lines of regression of yy on xx and xx on yy respectively, then what is the value of bxy+7byxb_{xy}+7b_{yx}?

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