1
IIT-JEE 1980
+2
-0.5
Given $$A = {\sin ^2}\theta + {\cos ^4}\theta$$ then for all real values of $$\theta$$
A
$$1 \le A \le 2$$
B
$${3 \over 4} \le A \le 1$$
C
$${13\over 16} \le A \le 1$$
D
$${3 \over 4} \le A \le {{13} \over {16}}$$
2
IIT-JEE 1980
+2
-0.5
The equation $$\,2{\cos ^2}{x \over 2}{\sin ^2}x = {x^2} + {x^{ - 2}};\,0 < x \le {\pi \over 2}$$ has
A
no real solution
B
one real solution
C
more than one solution
D
none of these
3
IIT-JEE 1979
+2
-0.5
If $$\tan \theta = - {4 \over 3},then\sin \theta \,is\,$$
A
$$- {4 \over 5}\,but\,not\,{4 \over 5}$$
B
$$- {4 \over 5}\,or\,{4 \over 5}$$
C
$${4 \over 5}\,\,but\,not\, - {4 \over 5}$$
D
None of these.
4
IIT-JEE 1979
+2
-0.5
If $$\alpha + \beta + \gamma = 2\pi ,$$ then
A
$$tan{\alpha \over 2} + \tan {\beta \over 2} + \tan {\gamma \over 2} = \tan {\alpha \over 2}\tan {\beta \over 2}\tan {\gamma \over 2}$$
B
$$\tan {\alpha \over 2}\tan {\beta \over 2} + \tan {\beta \over 2}\tan {\gamma \over 2} + \tan {\gamma \over 2}\tan {\alpha \over 2} = 1$$
C
$$tan{\alpha \over 2} + \tan {\beta \over 2} + \tan {\gamma \over 2} = - \tan {\alpha \over 2}\tan {\beta \over 2}\tan {\gamma \over 2}$$
D
None of these.
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