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1

### IIT-JEE 2002 Screening

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
2

### IIT-JEE 2001 Screening

If $$\alpha + \beta = \pi /2$$ and $$\beta + \gamma = \alpha ,$$ then $$\tan \,\alpha \,$$ equals
A
$$2\left( {\tan \beta + \tan \gamma } \right)$$
B
$$\,\tan \beta + \tan \gamma$$
C
$$\tan \beta + 2\tan \gamma$$
D
$$2\tan \beta + \tan \gamma$$
3

### IIT-JEE 2001 Screening

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
4

### IIT-JEE 2001 Screening

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

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