The number of distinct real roots of $$\left| {\matrix{
{\sin x} & {\cos x} & {\cos x} \cr
{\cos x} & {\sin x} & {\cos x} \cr
{\cos x} & {\cos x} & {\sin x} \cr
} } \right|\,$$
$$\, = 0$$ in the interval $$ - {\pi \over 4} \le x \le {\pi \over 4}$$ is
A
0
B
2
C
1
D
3
2
IIT-JEE 2000 Screening
MCQ (Single Correct Answer)
Let $$f\left( \theta \right) = \sin \theta \left( {\sin \theta + \sin 3\theta } \right)$$. Then $$f\left( \theta \right)$$ is
A
$$ \ge 0\,\,$$ only when $$\theta \ge 0$$
B
$$ \le 0$$ for all real $$\theta $$
C
$$ \ge 0$$ for all real $$\theta $$
D
$$ \le 0$$ only when $$\theta \le 0$$
3
IIT-JEE 1999
MCQ (Single Correct Answer)
In a triangle $$PQR,\angle R = \pi /2$$. If $$\,\,\tan \left( {P/2} \right)$$ and $$\tan \left( {Q/2} \right)$$ are the roots of the equation $$a{x^2} + bx + c = 0\left( {a \ne 0} \right)$$ then.
A
$$a + b = c$$
B
$$a + c = b$$
C
$$b + c = a$$
D
$$b = c$$
4
IIT-JEE 1998
MCQ (Single Correct Answer)
Which of the following number(s) is /are rational?
