1
IIT-JEE 1983
Subjective
+2
-0
Find all the solution of $$4$$ $${\cos ^2}x\sin x - 2{\sin ^2}x = 3\sin x$$
2
IIT-JEE 1983
Fill in the Blanks
+1
-0
The larger of $$\cos \left( {In\,\,\theta } \right)$$ and $$In $$ $$\left( {\cos \,\,\theta } \right)$$ If $${e^{ - \pi /2}} < \theta < {\pi \over 2}$$ is ..................
3
IIT-JEE 1983
Fill in the Blanks
+2
-0
The function $$y = 2{x^2} - In\,\left| x \right|$$ is monotonically increasing for values of $$x\left( {x \ne 0} \right)$$ satisfying the inequalities ......... and monotonically decreasing for values of $$x$$ satisfying the inequalities ............
4
IIT-JEE 1983
MCQ (Single Correct Answer)
+1
-0.25
If $$a+b+c=0$$, then the quadratic equation $$3a{x^2} + 2bx + c = 0$$ has
A
at least one root in $$\left[ {0,1} \right]$$
B
one root in $$\left[ {2,3} \right]$$ and the other in $$\left[ {-2,-1} \right]$$
C
imaginary roots
D
none of these
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