Matrices & Determinants · NDA previous year questions

2019 34 questions

1. Q382019 · 21 Apr 2019

   If $\sin \alpha +\cos \alpha =p$, then what is ${\cos }^2(2\alpha )$ equal to?

   1. A.$p^2$
   2. B.$p^2-1$
   3. C.$p^2(2-p^2)$
   4. D.$p^2+1$
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   Answer: C

2. Q392019 · 21 Apr 2019

   If $\tan \theta =\frac{1}{2}$ and $\tan \phi =\frac{1}{3}$, then what is the value of $(\theta +\phi )$?

   1. A.0
   2. B.$\frac{\pi }{6}$
   3. C.$\frac{\pi }{4}$
   4. D.$\frac{\pi }{2}$
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   Answer: C

3. Q402019 · 21 Apr 2019

   If $\cos A=\frac{3}{4}$, then what is the value of $\sin \left(\frac{A}{2}\right)\sin \left(\frac{3A}{2}\right)$?

   1. A.$\frac{5}{8}$
   2. B.$\frac{5}{16}$
   3. C.$\frac{5}{24}$
   4. D.$\frac{7}{32}$
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   Answer: B

4. Q412019 · 21 Apr 2019

   What is the value of $\tan 75^{\circ }+\cot 75^{\circ }$?

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

5. Q422019 · 21 Apr 2019

   What is the value of $\cos 46^{\circ }\cos 47^{\circ }\cos 48^{\circ }\cos 49^{\circ }\cos 50^{\circ }\dots$ $\cos 135^{\circ }$?

   1. A.$-1$
   2. B.0
   3. C.1
   4. D.Greater than 1
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   Answer: B

6. Q432019 · 21 Apr 2019

   If $\sin 2\theta =\cos 3\theta$, where $0<\theta <\frac{\pi }{2}$, then what is $\sin \theta$ equal to?

   1. A.$\frac{\sqrt{5}+1}{4}$
   2. B.$\frac{\sqrt{5}-1}{4}$
   3. C.$\frac{\sqrt{5}+1}{16}$
   4. D.$\frac{\sqrt{5}-1}{16}$
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   Answer: B

7. Q1182019 · 21 Apr 2019

   If A is a square matrix of order $n>1$, then which one of the following is correct?

   1. A.$\det (-A)=\det A$
   2. B.$\det (-A)=(-1{)}^n\det A$
   3. C.$\det (-A)=-\det A$
   4. D.$\det (-A)=n\det A$
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   Answer: B

8. Q1192019 · 21 Apr 2019

   Consider the following for the next 02 (two) items: Let A and B be $(3\times 3)$ matrices with $\det A=4$ and $\det B=3$. What is $\det (2AB)$ equal to?

   1. A.96
   2. B.72
   3. C.48
   4. D.36
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   Answer: A

9. Q1202019 · 21 Apr 2019

   Consider the following for the next 02 (two) items: Let A and B be $(3\times 3)$ matrices with $\det A=4$ and $\det B=3$. What is $\det (3A{B}^{-1})$ equal to?

   1. A.12
   2. B.18
   3. C.36
   4. D.48
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   Answer: C