Vectors · NDA previous year questions

2020 5 questions

1. Q662020 · 6 Sept 2020

   If $\hat{a}$ is a unit vector in the $xy$-plane making an angle $30^{\circ }$ with the positive $x$-axis, then what is $\hat{a}$ equal to?

   1. A.$\frac{\sqrt{3}\hat{i}+\hat{j}}{2}$
   2. B.$\frac{\sqrt{3}\hat{i}-\hat{j}}{2}$
   3. C.$\frac{\hat{i}+\sqrt{3}\hat{j}}{2}$
   4. D.$\frac{\hat{i}-\sqrt{3}\hat{j}}{2}$
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   Answer: A

2. Q682020 · 6 Sept 2020

   Two adjacent sides of a parallelogram are $2\hat{i}-4\hat{j}+5\hat{k}$ and $\hat{i}-2\hat{j}-3\hat{k}$. What is the magnitude of dot product of vectors which represent its diagonals?

   1. A.21
   2. B.25
   3. C.31
   4. D.36
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   Answer: C

3. Q692020 · 6 Sept 2020

   If $|\vec{a}\times \vec{b}{|}^2+|\vec{a}\cdot \vec{b}{|}^2=144$ and $|\vec{a}|=4$, then what is $|\vec{b}|$ equal to?

   1. A.3
   2. B.4
   3. C.6
   4. D.8
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   Answer: A

4. Q702020 · 6 Sept 2020

   If the vectors $\vec{a}=2\hat{i}-3\hat{j}+\hat{k}$, $\vec{b}=\hat{i}+2\hat{j}-3\hat{k}$ and $\vec{c}=\hat{j}+p\hat{k}$ are coplanar, then what is the value of $p$?

   1. A.1
   2. B.$-1$
   3. C.5
   4. D.$-5$
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   Answer: B

5. Q712020 · 6 Sept 2020

   What is ${\lim }_{x\to 1}\frac{x+x^2+x^3-3}{x-1}$ equal to?

   1. A.1
   2. B.2
   3. C.3
   4. D.6
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   Answer: D