1
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$$\alpha $$.

2
IIT-JEE 1979
Subjective
+4
-0
If $$\alpha ,\,\beta $$ are the roots of $${x^2} + px + q = 0$$ and $$\gamma ,\,\delta $$ are the roots of $${x^2} + rx + s = 0,$$ evaluate $$\left( {\alpha - \gamma } \right)\left( {\alpha - \delta } \right)\left( {\beta - \gamma } \right)$$ $$\left( {\beta - \delta } \right)$$ in terms of $$p,\,q,\,r$$ and $$s$$.

deduce the condition that the equations have a common root.

3
IIT-JEE 1979
MCQ (Single Correct Answer)
+2
-0.5
The equation x + 2y + 2z = 1 and 2x + 4y + 4z = 9 have
A
only one solution
B
only two solution
C
Infinite number of solutions
D
None of these.
4
IIT-JEE 1979
MCQ (Single Correct Answer)
+2
-0.5
If x, y and z are real and different and $$\,u = {x^2} + 4{y^2} + 9{z^2} - 6yz - 3zx - 2xy$$, then u is always.
A
non negative
B
zero
C
non positive
D
none of these
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