PYQ Vault
EbooksTutor

Day 70: NDA Maths

5 questions (9 parts). Try each one first, then open its answer.

  1. Question 1

    Vectors. This type asked 2 times: NDA 2 2017, NDA 1 2024. This one: NDA 1 2024

    66
    Let a⃗=i^−j^+k^\vec{a}=\hat{i}-\hat{j}+\hat{k} and b⃗=i^+2j^−k^\vec{b}=\hat{i}+2\hat{j}-\hat{k}. If a⃗×(b⃗×a⃗)=αi^−βj^+γk^\vec{a}\times(\vec{b}\times\vec{a})=\alpha\hat{i}-\beta\hat{j}+\gamma\hat{k}, then what is the value of α+β+γ\alpha+\beta+\gamma?

    Tap an option to check your answer.

  2. Question 2

    Vectors. This type asked 2 times: NDA 2 2017, NDA 1 2024. This one: NDA 1 2024

    69
    For any vector r⃗\vec{r}, what is (r⃗⋅i^)(r⃗×i^)+(r⃗⋅j^)(r⃗×j^)+(r⃗⋅k^)(r⃗×k^)(\vec{r}\cdot\hat{i})(\vec{r}\times\hat{i})+(\vec{r}\cdot\hat{j})(\vec{r}\times\hat{j})+(\vec{r}\cdot\hat{k})(\vec{r}\times\hat{k}) equal to?

    Tap an option to check your answer.

  3. Question 3 (case study, 3 parts)

    Binomial Theorem. This type asked 2 times: NDA 1 2021, NDA 2 2023. This one: NDA 2 2023

    Let (1+x)n=1+T1x+T2x2+⋯+Tnxn(1+x)^n = 1 + T_1 x + T_2 x^2 + \cdots + T_n x^n.
    38
    What is T1+2T2+3T3+⋯+nTnT_1+2T_2+3T_3+\cdots+nT_n equal to?

    Tap an option to check your answer.

    39
    What is 1−T1+2T2−3T3+⋯+(−1)nnTn1-T_1+2T_2-3T_3+\cdots+(-1)^n nT_n equal to?

    Tap an option to check your answer.

    40
    What is T1+T2+T3+⋯+TnT_1+T_2+T_3+\cdots+T_n equal to?

    Tap an option to check your answer.

  4. Question 4 (case study, 3 parts)

    Complex Numbers. This type asked 2 times: NDA 1 2019, NDA 2 2023. This one: NDA 2 2023

    Consider equation-I: z3+2z2+2z+1=0z^3+2z^2+2z+1=0 and equation-II: z1985+z100+1=0z^{1985}+z^{100}+1=0.
    33
    What are the roots of equation-I?

    Tap an option to check your answer.

    34
    Which one of the following is a root of equation-II?

    Tap an option to check your answer.

    35
    What is the number of common roots of equation-I and equation-II?

    Tap an option to check your answer.

  5. Question 5

    Complex Numbers. This type asked 2 times: NDA 2 2021, NDA 2 2023. This one: NDA 2 2023

    12
    Which one of the following is a square root of −−1\sqrt{-\sqrt{-1}}?

    Tap an option to check your answer.