1
IIT-JEE 1979
MCQ (Single Correct Answer)
+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.
2
IIT-JEE 1979
Subjective
+5
-0
(a) A balloon is observed simultaneously from three points $$A, B$$ and $$C$$ on a straight road directly beneath it. The angular elevation at $$B$$ is twice that at $$A$$ and the angular elevation at $$C$$ is thrice that at $$A$$. If the distance between $$A$$ and $$B$$ is a and the distance between $$B$$ and $$C$$ is $$b$$, find the height of the balloon in terms of $$a$$ and $$b$$.

(b) Find the area of the smaller part of a disc of radius $$10$$ cm, cut off by a chord $$AB$$ which subtends an angle of at the circumference.

3
IIT-JEE 1979
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+2
-0.5
If the cube roots of unity are $$1,\,\omega ,\,{\omega ^2},$$ then the roots of the equation $${\left( {x - 1} \right)^3} + 8 = 0$$ are
A
$$ - 1,1 + 2\omega ,\,1 + 2{\omega ^2}$$
B
$$ - 1,1 - 2\omega ,\,1 - 2{\omega ^2}$$
C
$$ - 1, - 1, - 1$$
D
None of these
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