Permutations & Combinations · NDA previous year questions

2014 12 questions

1. Q102014 · 28 Sept 2014

   What is the number of ways in which one can post 5 letters in 7 letter boxes ?

   1. A.$7^5$
   2. B.$3^5$
   3. C.$5^7$
   4. D.2520
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   Answer: A

2. Q112014 · 28 Sept 2014

   What is the number of ways that a cricket team of 11 players can be made out of 15 players ?

   1. A.364
   2. B.1001
   3. C.1365
   4. D.32760
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   Answer: C

3. Q292014 · 20 Apr 2014

   Consider the following statements: 1. $\sin |x|+\cos |x|$ is always positive. 2. $\sin (x^2)+\cos (x^2)$ is always positive. 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
   Show answer

   Answer: D

4. Q302014 · 20 Apr 2014

   What is $\frac{1+\sin A}{1-\sin A}-\frac{1-\sin A}{1+\sin A}$ equal to?

   1. A.$\sec A-\tan A$
   2. B.$2\sec A\cdot \tan A$
   3. C.$4\sec A\cdot \tan A$
   4. D.$4\mathrm{cosec}A\cdot \cot A$
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   Answer: C

5. Q312014 · 20 Apr 2014

   What is $\frac{\cot 224^{\circ }-\cot 134^{\circ }}{\cot 226^{\circ }+\cot 316^{\circ }}$ equal to?

   1. A.$-\mathrm{cosec}88^{\circ }$
   2. B.$-\mathrm{cosec}{2}^{\circ }$
   3. C.$-\mathrm{cosec}44^{\circ }$
   4. D.$-\mathrm{cosec}46^{\circ }$
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   Answer: B

6. Q322014 · 20 Apr 2014

   If $A+B+C=\pi$, then what is $\cos (A+B)+\cos C$ equal to?

   1. A.$0$
   2. B.$2\cos C$
   3. C.$\cos C-\sin C$
   4. D.$2\sin C$
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   Answer: A

7. Q332014 · 20 Apr 2014

   What is $\cos 20^{\circ }+\cos 100^{\circ }+\cos 140^{\circ }$ equal to?

   1. A.$2$
   2. B.$1$
   3. C.$1/2$
   4. D.$0$
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   Answer: D

8. Q342014 · 20 Apr 2014

   What is ${\sin }^2(3\pi )+{\cos }^2(4\pi )+{\tan }^2(5\pi )$ equal to?

   1. A.$0$
   2. B.$1$
   3. C.$2$
   4. D.$3$
   Show answer

   Answer: B

9. Q352014 · 20 Apr 2014

   The complete solution of $3{\tan }^{2}x=1$ is given by: where $n\in Z$

   1. A.$x=n\pi \pm \frac{\pi }{3}$
   2. B.$x=n\pi +\frac{\pi }{3}$ only
   3. C.$x=n\pi \pm \frac{\pi }{6}$
   4. D.$x=n\pi +\frac{\pi }{6}$ only
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   Answer: C

10. Q362014 · 20 Apr 2014

    What is the value of $\cos 36^{\circ }$?

    1. A.$\frac{\sqrt{5}-1}{4}$
    2. B.$\frac{\sqrt{5}+1}{4}$
    3. C.$\frac{\sqrt{10+2\sqrt{5}}}{4}$
    4. D.$\frac{\sqrt{10-2\sqrt{5}}}{4}$
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    Answer: B

11. Q372014 · 20 Apr 2014

    Consider the following statements: 1. Value of $\sin \theta$ oscillates between $-1$ and 1. 2. Value of $\cos \theta$ oscillates between 0 and 1. 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
    Show answer

    Answer: A

12. Q382014 · 20 Apr 2014

    Consider the following statements: 1. $n\left({\sin }^{2}67{\frac{1}{2}}^{\circ }-{\sin }^{2}22{\frac{1}{2}}^{\circ }\right)>1$ for all positive integers $n\ge 2$. 2. If $x$ is any positive real number, then $nx>1$ for all positive integers $n\ge 2$. 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
    Show answer

    Answer: A