Trigonometry · JEE Main previous year questions

2006 4 questions

1. Q12006 · 29 Apr 2006 · Shift 1

   If $0<x<\pi$ and $\cos x+\sin x=\frac{1}{2}$, then $\tan x$ is :

   1. A.$-\frac{(1-\sqrt{7})}{4}$
   2. B.$-\frac{(4-\sqrt{7})}{3}$
   3. C.$-\frac{(4+\sqrt{7})}{3}$
   4. D.$-\frac{(1+\sqrt{7})}{4}$
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   Answer: C

2. Q22006 · 29 Apr 2006 · Shift 1

   The value of ${\sum }_{k=1}^{10}(\sin \frac{2k\pi }{11}+i\cos \frac{2k\pi }{11})$ is :

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

   Answer: D

3. Q242006 · 29 Apr 2006 · Shift 1

   ${\int }_0^{\pi }xf(\sin x)dx$ is equal to

   1. A.$\pi {\int }_0^{\pi }f(\cos x)dx$
   2. B.$\pi {\int }_0^{\pi }f(\sin x)dx$
   3. C.$\frac{\pi }{2}{\int }_0^{\pi /2}f(\sin x)dx$
   4. D.$\pi {\int }_0^{\pi /2}f(\cos x)dx$
   Show answer

   Answer: D

4. Q362006 · 29 Apr 2006 · Shift 1

   The number of values of $x$ in the interval $[0,3\pi ]$ satisfying the equation $2{\sin }^{2}x+5\sin x-3=0$ is

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

   Answer: A