IIT-JEE 1980 | Trigonometric Functions & Equations Question 83 | Mathematics

IIT-JEE 1980

MCQ (Single Correct Answer)

-0.5

Given $$A = {\sin ^2}\theta + {\cos ^4}\theta $$ then for all real values of $$\theta $$

$$1 \le A \le 2$$

$${3 \over 4} \le A \le 1$$

$${13\over 16} \le A \le 1$$

$${3 \over 4} \le A \le {{13} \over {16}}$$

IIT-JEE 1980

MCQ (Single Correct Answer)

-0.5

The equation $$\,2{\cos ^2}{x \over 2}{\sin ^2}x = {x^2} + {x^{ - 2}};\,0 < x \le {\pi \over 2}$$ has

no real solution

one real solution

more than one solution

none of these

IIT-JEE 1979

MCQ (Single Correct Answer)

-0.5

If $$\tan \theta = - {4 \over 3},then\sin \theta \,is\,$$

$$ - {4 \over 5}\,but\,not\,{4 \over 5}$$

$$ - {4 \over 5}\,or\,{4 \over 5}$$

$${4 \over 5}\,\,but\,not\, - {4 \over 5}$$

None of these.

IIT-JEE 1979

MCQ (Single Correct Answer)

-0.5

If $$\alpha + \beta + \gamma = 2\pi ,$$ then

$$tan{\alpha \over 2} + \tan {\beta \over 2} + \tan {\gamma \over 2} = \tan {\alpha \over 2}\tan {\beta \over 2}\tan {\gamma \over 2}$$

$$\tan {\alpha \over 2}\tan {\beta \over 2} + \tan {\beta \over 2}\tan {\gamma \over 2} + \tan {\gamma \over 2}\tan {\alpha \over 2} = 1$$

$$tan{\alpha \over 2} + \tan {\beta \over 2} + \tan {\gamma \over 2} = - \tan {\alpha \over 2}\tan {\beta \over 2}\tan {\gamma \over 2}$$

None of these.

JEE Advanced Subjects