1
IIT-JEE 1996
Fill in the Blanks
+1
-0
For any odd integer $$n$$ $$ \ge 1,\,\,{n^3} - {\left( {n - 1} \right)^3} + .... + {\left( { - 1} \right)^{n - 1}}\,{1^3} = ........$$
2
IIT-JEE 1996
Subjective
+3
-0
The real numbers $${x_1}$$, $${x_2}$$, $${x_3}$$ satisfying the equation $${x^3} - {x^2} + \beta x + \gamma = 0$$ are in AP. Find the intervals in which $$\beta \,\,and\,\gamma $$ lie.
3
IIT-JEE 1996
Subjective
+2
-0
A rectangle $$PQRS$$ has its side $$PQ$$ parallel to the line $$y = mx$$ and vertices $$P, Q$$ and $$S$$ on the lines $$y = a, x = b$$ and $$x = -b,$$ respectively. Find the locus of the vertex $$R$$.
4
IIT-JEE 1996
Fill in the Blanks
+1
-0
The intercept on the line y = x by the circle $${x^2} + {y^2} - 2x = 0$$ is AB. Equation of the circle with AB as a diameter is................................
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