Vectors · NDA previous year questions

2022 9 questions

1. Q672022 · 4 Sept 2022
   
   1. A.$\frac{\pi }{6}$
   2. B.$\frac{\pi }{4}$
   3. C.$\frac{\pi }{3}$
   4. D.$\frac{\pi }{2}$
   Show answer

   Answer: C

2. Q682022 · 4 Sept 2022

   Let $\vec{a},\vec{b}$ and $\vec{c}$ be unit vectors lying on the same plane. What is $\{(3\vec{a}+2\vec{b})\times (5\vec{a}-4\vec{c})\}\cdot (\vec{b}+2\vec{c})$ equal to ?

   1. A.-8
   2. B.-32
   3. C.8
   4. D.0
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   Answer: D

3. Q692022 · 4 Sept 2022

   What are the values of x for which the angle between the vectors $2x^2\hat{i}+3x\hat{j}+\hat{k}$ and $\hat{i}-2\hat{j}+x^2\hat{k}$ is obtuse ?

   1. A.$0<x<2$
   2. B.$x<0$
   3. C.$x>2$
   4. D.$0\le x\le 2$
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   Answer: A

4. Q702022 · 4 Sept 2022

   The position vectors of vertices A, B and C of triangle ABC are respectively $\hat{j}+\hat{k},3\hat{i}+\hat{j}+5\hat{k}$ and $3\hat{j}+3\hat{k}$. What is angle C equal to?

   1. A.$\frac{\pi }{6}$
   2. B.$\frac{\pi }{4}$
   3. C.$\frac{\pi }{3}$
   4. D.$\frac{\pi }{2}$
   Show answer

   Answer: D

5. Q962022 · 10 Apr 2022

   If $4\hat{i}+\hat{j}-3\hat{k}$ and $p\hat{i}+q\hat{j}-2\hat{k}$ are collinear vectors, then what are the possible values of p and q respectively?

   1. A.4, 1
   2. B.1, 4
   3. C.$\frac{8}{3},\frac{2}{3}$
   4. D.$\frac{2}{3},\frac{8}{3}$
   Show answer

   Answer: C

6. Q972022 · 10 Apr 2022

   If $\vec{a},\vec{b},\vec{c}$, are the position vectors of the vertices A, B, C respectively of a triangle ABC and G is the centroid of the triangle, then what is $\overrightarrow{AG}$ equal to ? .

   1. A.$\frac{\vec{a}+\vec{b}+\vec{c}}{3}$
   2. B.$\frac{2\vec{a}-\vec{b}-\vec{c}}{3}$
   3. C.$\frac{\vec{b}+\vec{c}-2\vec{a}}{3}$
   4. D.$\frac{\vec{a}-2\vec{b}-2\vec{c}}{3}$
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   Answer: C

7. Q982022 · 10 Apr 2022

   Consider the following statements : 1. Dot product over vector addition is distributive 2. Cross product over vector addition is distributive 3. Cross product of vectors is associative Which of the above statements is/are correct ?

   1. A.1 only
   2. B.2 only
   3. C.1 and 2 only
   4. D.1, 2 and 3
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   Answer: C

8. Q992022 · 10 Apr 2022

   Let $\vec{a},\vec{b},\vec{c}$ be three non-zero vectors such that $\vec{a}\times \vec{b}=\vec{c}$. Consider the following statements: 1. $\vec{a}$ is unique if $\vec{b}$ and $\vec{c}$ are given 2. $\vec{c}$ is unique if $\vec{a}$ and $\vec{b}$ are given Which of the above statements is/are correct?

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
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   Answer: B

9. Q1002022 · 10 Apr 2022

   Let $\vec{a}$ and $\vec{b}$ be two unit vectors such that $|\vec{a}-\vec{b}|<2$. If $2\theta$ is the angle between $\vec{a}$ and $\vec{b}$, then which one of the following is correct ?

   1. A.$0\le \sin \theta <1$ only
   2. B.$-\frac{1}{2}<\sin \theta <\frac{1}{2}$ only
   3. C.$-1<\sin \theta <0$ only
   4. D.$-1<\sin \theta <1$
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   Answer: D