1
IIT-JEE 1980
Subjective
+2
-0
Given $$\alpha + \beta - \gamma = \pi ,$$ prove that
$$\,{\sin ^2}\alpha + {\sin ^2}\beta - {\sin ^2}\gamma = 2\sin \alpha {\mkern 1mu} \sin \beta {\mkern 1mu} \cos y$$
2
IIT-JEE 1980
Subjective
+2
-0
Given $$A = \left\{ {x:{\pi \over 6} \le x \le {\pi \over 3}} \right\}$$ and
$$f\left( x \right) = \cos x - x\left( {1 + x} \right);$$ find $$f\left( A \right).$$
3
IIT-JEE 1980
Subjective
+4
-0
For all $$\theta$$ in $$\left[ {0,\,\pi /2} \right]$$ show that, $$\cos \left( {\sin \theta } \right) \ge \,\sin \,\left( {\cos \theta } \right).$$
4
IIT-JEE 1979
Subjective
+2
-0
(a) Draw the graph of $$y = {1 \over {\sqrt 2 }}\left( {cinx + \cos x} \right)$$ from $$x = - {\pi \over 2}$$ to $$x = {\pi \over 2}$$.

(b) If $$\cos \left( {\alpha + \beta } \right) = {4 \over 5},\,\,\sin \,\left( {\alpha - \beta } \right) = \,{5 \over {13}},$$ and $$\alpha ,\,\beta$$ lies between 0 and $${\pi \over 4}$$, find tan2$$\alpha$$.

Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination