PYQ Vault
EbooksTutor

Day 47: NDA Maths

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

  1. Question 1

    Vectors. Asked 2 times: NDA 2 2019*, NDA 2 2023 (* = numbers or wording changed that year)

    91
    What is the length of projection of the vector i^+2j^+3k^\hat{i}+2\hat{j}+3\hat{k} on the vector 2i^+3j^−2k^2\hat{i}+3\hat{j}-2\hat{k}?

    Tap an option to check your answer.

  2. Question 2

    Limits & Continuity. Asked 2 times: NDA 1 2022*, NDA 1 2023 (* = numbers or wording changed that year)

    100
    What is lim⁡x→1x9−1x3−1\lim_{x\to1}\dfrac{x^{9}-1}{x^{3}-1} equal to?

    Tap an option to check your answer.

  3. Question 3

    Probability. Asked 2 times: NDA 1 2020*, NDA 1 2023 (* = numbers or wording changed that year)

    119
    What is the probability that the month of December has 5 Sundays?

    Tap an option to check your answer.

  4. Question 4

    Vectors. Asked 2 times: NDA 1 2021*, NDA 2 2022 (* = numbers or wording changed that year)

    68
    Let a⃗,b⃗\vec{a}, \vec{b} and c⃗\vec{c} be unit vectors lying on the same plane. What is {(3a⃗+2b⃗)×(5a⃗−4c⃗)}⋅(b⃗+2c⃗)\left\{(3\vec{a}+2\vec{b})\times(5\vec{a}-4\vec{c})\right\}\cdot(\vec{b}+2\vec{c}) equal to?

    Tap an option to check your answer.

  5. Question 5

    Binomial Theorem. Asked 2 times: NDA 1 2019*, NDA 1 2022 (* = numbers or wording changed that year)

    11
    How many terms are there in the expansion of (1+2x)9(1−2x)9\left(1+\frac{2}{x}\right)^9\left(1-\frac{2}{x}\right)^9?

    Tap an option to check your answer.