Vectors · NDA previous year questions

2013 12 questions

1. Q952013 · 11 Aug 2013

   If the angle between the vectors $\hat{i}-m\hat{j}$ and $\hat{j}+\hat{k}$ is $\frac{\pi }{3}$, then what is the value of $m$?

   1. A.0
   2. B.2
   3. C.$-2$
   4. D.None of the above
   Show answer

   Answer: D

2. Q962013 · 11 Aug 2013

   What is the vector perpendicular to both the vectors $\hat{i}-\hat{j}$ and $\hat{i}$?

   1. A.$\hat{i}$
   2. B.$-\hat{j}$
   3. C.$\hat{j}$
   4. D.$\hat{k}$
   Show answer

   Answer: D

3. Q972013 · 11 Aug 2013

   The position vectors of the points $A$ and $B$ are respectively $3\hat{i}-5\hat{j}+2\hat{k}$ and $\hat{i}+\hat{j}-\hat{k}$. What is the length of $AB$?

   1. A.11
   2. B.9
   3. C.7
   4. D.6
   Show answer

   Answer: C

4. Q982013 · 11 Aug 2013

   The vectors $\hat{i}-2x\hat{j}-3y\hat{k}$ and $\hat{i}+3x\hat{j}+2y\hat{k}$ are orthogonal to each other. Then the locus of the point $(x,y)$ is

   1. A.hyperbola
   2. B.ellipse
   3. C.parabola
   4. D.circle
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   Answer: D

5. Q992013 · 11 Aug 2013

   What is the value of $p$ for which the vector $p(2\hat{i}-\hat{j}+2\hat{k})$ is of 3 units length?

   1. A.1
   2. B.2
   3. C.3
   4. D.6
   Show answer

   Answer: A

6. Q1002013 · 11 Aug 2013

   If $\vec{a}=2\hat{i}+2\hat{j}+3\hat{k},\vec{b}=-\hat{i}+2\hat{j}+\hat{k}$ and $\vec{c}=3\hat{i}+\hat{j}$ are three vectors such that $\vec{a}+t\vec{b}$ is perpendicular to $\vec{c}$, then what is $t$ equal to?

   1. A.8
   2. B.6
   3. C.4
   4. D.2
   Show answer

   Answer: A

7. Q962013 · 14 Apr 2013

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

   1. A.$\vec{a}$
   2. B.$3\vec{a}$
   3. C.$-\vec{a}$
   4. D.$\vec{0}$
   Show answer

   Answer: A

8. Q972013 · 14 Apr 2013

   If the magnitude of $\vec{a}\times \vec{b}$ equals to $\vec{a}\cdot \vec{b}$, then which one of the following is correct ?

   1. A.$\vec{a}=\vec{b}$
   2. B.The angle between $\vec{a}$ and $\vec{b}$ is $45^{\circ }$
   3. C.$\vec{a}$ is parallel to $\vec{b}$
   4. D.$\vec{a}$ is perpendicular to $\vec{b}$
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   Answer: B

9. Q982013 · 14 Apr 2013

   If $|\vec{a}|=\sqrt{2},|\vec{b}|=\sqrt{3}$ and $|\vec{a}+\vec{b}|=\sqrt{6}$, then what is $|\vec{a}-\vec{b}|$ equal to ?

   1. A.1
   2. B.2
   3. C.3
   4. D.4
   Show answer

   Answer: B

10. Q992013 · 14 Apr 2013

    Which one of the following vectors is normal to the vector $\hat{i}+\hat{j}+\hat{k}$ ?

    1. A.$\hat{i}+\hat{j}-\hat{k}$
    2. B.$\hat{i}-\hat{j}+\hat{k}$
    3. C.$\hat{i}-\hat{j}-\hat{k}$
    4. D.None of the above
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    Answer: D

11. Q1002013 · 14 Apr 2013

    If $\theta$ is the angle between the vectors $4(\hat{i}-\hat{k})$ and $\hat{i}+\hat{j}+\hat{k}$, then what is $(\sin \theta +\cos \theta )$ equal to ?

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

12. Q1012013 · 14 Apr 2013

    The average marks obtained by the students in a class are 43. If the average marks obtained by 25 boys are 40 and the average marks obtained by the girl students are 48, then what is the number of girl students in the class ?

    1. A.15
    2. B.17
    3. C.18
    4. D.20
    Show answer

    Answer: A