1
IIT-JEE 2004 Screening
+2
-0.5
Given both $$\theta$$ and $$\phi$$ are acute angles and $$\sin \,\theta = {1 \over 2},\,$$ $$\cos \,\phi = {1 \over 3},$$ then the value of $$\theta + \phi$$ belongs to
A
$$\left( {{\pi \over 3},\left. {{\pi \over 2}} \right]} \right.$$
B
$$\left( {{\pi \over 2},{{2\pi } \over 3}} \right)$$
C
$$\left( {{{2\pi } \over 3},\left. {{{5\pi } \over 6}} \right]} \right.$$
D
$$\left( {{{5\pi } \over 6},\pi } \right]$$
2
IIT-JEE 2002 Screening
+2
-0.5
The number of integral values of $$k$$ for which the equation $$7\cos x + 5\sin x = 2k + 1$$ has a solution is
A
4
B
8
C
10
D
12
3
IIT-JEE 2001 Screening
+2
-0.5
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
4
IIT-JEE 2001 Screening
+2
-0.5
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
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