Q.1
if  $2 \sin^2 (x) – 5 \sin (x) + 2 > 0$, $x \in ( 0 ,2 \pi)$ then $x \in $
  • $(0, \frac {\pi}{6} ) \cup (\frac {5\pi}{6} , 2 \pi)$
  • $(\frac {\pi}{80}, \frac {\pi}{6} )$
  • $(0, \frac {\pi}{6} )$
  • $(\frac {5\pi}{6} , 2 \pi)$
Q.2
for a positive integer n , let $f_n \theta = ( \tan \frac {\theta}{2}) ( 1+ \sec \theta) (1 + \sec 2 \theta) .....(1+ \sec 2^n \theta)$. Now four values are given as (i) $f_2 ( \frac {\pi}{16})=1$ (ii) $f_3 ( \frac {\pi}{32})=1$ (iii) $f_4 ( \frac {\pi}{64})=1$ (iv) $f_5 ( \frac {\pi}{128})=1$ Which of these are correct
  • (i) and (ii)
  • (i) and (iv)
  • All are correct
  • (i) ,(ii) and (iii)
Q.3
The minimum value of 3 cosx + 4 sinx + 5 is
  • 0
  • -5
  • 5
  • 4
Q.4
which of these is not the solution for the equation $7 \cos ^2 x + 3 \sin ^2 x =4$
  • $\frac {4 \pi}{5}$
  • $\frac {4 \pi}{3}$
  • $\frac {2 \pi}{3}$
  • $\frac {11 \pi}{3}$
Q.5
if $\alpha + \beta = \frac {\pi}{2}$ and $ \beta + \gamma = \alpha$,then $\tan \alpha$ equals to
  • $ \tan \beta + \tan \gamma$
  • $2 \tan \beta + \tan \gamma$
  • $2( \tan \beta + \tan \gamma)$
  • $ \tan \beta + 2 \tan \gamma$
Q.6
The number of integral values of k for which equation 7cos(x) + 5 sin(x) =2k +1 has a solution
  • 4
  • 10
  • 12
  • 8
Q.7
The solutions of the trigonometric equation tan x + tan 2x + tan x tan 2x=1
  • $\frac {n \pi}{2} + \frac {\pi}{12}, n \in Z$
  • $\frac {n \pi}{3} + \frac {\pi}{12}, n \in Z$
  • $\frac {n \pi}{3} + \frac {\pi}{4}, n \in Z$
  • $\frac {n \pi}{3} + \frac {\pi}{8}, n \in Z$
Q.8
which of the following number is rational?
  • $ \cos 15^0$
  • $ \sin 15^0$
  • $ \sin 15^0 \cos 75^0$
  • $ \sin 15^0 \cos 15^0$
Q.9
if y = |sin (x) | + |cos (x)| and $x \in R$ then
  • $y \in [0,2]$
  • $y \in [0,1]$
  • $y \in [1, \sqrt 2]$
  • $y \in [0,\sqrt 2]$
Q.10
The maximum value of sin (cos x) is equal to
  • 0
  • sin 1
  • 1
  • $\sin ( \frac {1}{\sqrt 2}) $
Q.11
If sin A and cos A are the roots of the equation $ax^2 – bx + c = 0$, then a, b and c satisfy the relation
  • $a^2 – b^2 – 2ac = 0$
  • $a^2 + b^2 + 2ac = 0$
  • $a^2 + c^2 + 2ab = 0$
  • $a^2 – b^2 + 2ac = 0$
Q.12
Minimum value of the expression $ \frac {1}{\cos ^2 ( \pi/4 +x) + \sin ^2( \pi/4 -x)}$ equals  is
  • $\frac {1}{\sqrt 2}$
  • $\sqrt 2$
  • $\frac {1}{2}$
  • 2
0 h : 0 m : 1 s