Vectors · NDA previous year questions

2024 10 questions

1. Q512024 · 1 Sept 2024

   What is 3α + 2β equal to if (2î + 6ĵ + 27k̂) × (î + αĵ + βk̂) is a null vector?

   1. A.36
   2. B.33
   3. C.30
   4. D.27
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   Answer: A

2. Q522024 · 1 Sept 2024

   For what value of the angle between the vectors $\vec{a}$ and $\vec{b}$ is the quantity $|\vec{a}\times \vec{b}|+\sqrt{3}|\vec{a}\cdot \vec{b}|$ maximum?

   1. A.$0^{\circ }$
   2. B.$30^{\circ }$
   3. C.$45^{\circ }$
   4. D.$60^{\circ }$
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   Answer: B

3. Q532024 · 1 Sept 2024

   Let $\theta$ be the angle between two unit vectors $\vec{a}$ and $\vec{b}$. if $\vec{a}+2\vec{b}$ is perpendicular to $5\vec{a}-4\vec{b}$ then what is $\cos \theta +\cos 2\theta$ equal to?

   1. A.0
   2. B.1/2
   3. C.1
   4. D.$\frac{\sqrt{3}+1}{2}$
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   Answer: A

4. Q542024 · 1 Sept 2024

   Let ABCDEF be a regular hexagon. If $\overrightarrow{\mathrm{AD}}=m\overrightarrow{\mathrm{BC}}$ and $\overrightarrow{\mathrm{CF}}=n\overrightarrow{\mathrm{AB}}$ then what is mn equal to

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

5. Q552024 · 1 Sept 2024

   The vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$ are of the same length. If taken pairwise they form equal angles. If $\vec{a}=\hat{i}+\hat{j}$ and $\vec{b}=\hat{j}+\hat{k}$, then what can $\vec{c}$ be equal to? I. $\hat{i}+\hat{k}$ II. $\frac{-\hat{i}+4\hat{j}-\hat{k}}{3}$ Select the correct answer using the code given below.

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

6. Q562024 · 1 Sept 2024

   The diagonals of a quadrilateral ABCD are along the lines x - 2y = 1 and 4x + 2y = 3. The quadrilateral ABCD may be a

   1. A.rectangle
   2. B.cyclic quadrilateral
   3. C.parallelogram
   4. D.rhombus
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   Answer: D

7. Q672024 · 21 Apr 2024

   If a vector of magnitude 2 units makes an angle $\frac{\pi }{3}$ with $2\hat{i}$, $\frac{\pi }{4}$ with $3\hat{j}$ and an acute angle $\theta$ with $4\hat{k}$, then what are the components of the vector?

   1. A.$(1,\sqrt{2},1)$
   2. B.$(1,-\sqrt{2},1)$
   3. C.$(1,-\sqrt{2},-1)$
   4. D.$(1,\sqrt{2},-1)$
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   Answer: A

8. Q682024 · 21 Apr 2024

   Consider the following in respect of moment of a force: 1. The moment of force about a point is independent of point of application of force. 2. The moment of a force about a line is a vector quantity. Which of the statements given above 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. Q692024 · 21 Apr 2024

   For any vector $\vec{r}$, what is $(\vec{r}\cdot \hat{i})\left(\vec{r}\times \hat{i}\right)+(\vec{r}\cdot \hat{j})\left(\vec{r}\times \hat{j}\right)+(\vec{r}\cdot \hat{k})\left(\vec{r}\times \hat{k}\right)$ equal to?

   1. A.$\vec{0}$
   2. B.$\vec{r}$
   3. C.$2\vec{r}$
   4. D.$3\vec{r}$
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   Answer: A

10. Q702024 · 21 Apr 2024

    Let $\vec{a}$ and $\vec{b}$ be two vectors of magnitude 4 inclined at an angle $\frac{\pi }{3}$, then what is the angle between $\vec{a}$ and $\vec{a}-\vec{b}$?

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