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1

### IIT-JEE 2001 Screening

MCQ (Single Correct Answer)
The maximum value of $$\left( {\cos {\alpha _1}} \right).\left( {\cos {\alpha _2}} \right).....\left( {\cos {\alpha _n}} \right),$$ under the restrictions
$$0 \le {\alpha _1},{\alpha _2},....,{\alpha _n} \le {\pi \over 2}$$ vand $$\left( {\cot {\alpha _1}} \right).\left( {\cot {\alpha _2}} \right)....\left( {\cot {\alpha _n}} \right) = 1$$ is
A
$$1/{2^{n/2}}$$
B
$$1/{2^n}$$
C
$$1/2n\,$$
D
1
2

### IIT-JEE 2001 Screening

MCQ (Single Correct Answer)
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
3

### 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 $$\theta \le 0$$
4

### 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
$$b = c$$

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