1
IIT-JEE 1987
Subjective
+3
-0
Prove by mathematical induction that $$ - 5 - {{\left( {2n} \right)!} \over {{2^{2n}}{{\left( {n!} \right)}^2}}} \le {1 \over {{{\left( {3n + 1} \right)}^{1/2}}}}$$ for all positive integers $$n$$.
2
IIT-JEE 1987
Subjective
+3
-0
Solve for x the following equation:

$${\log _{(2x + 3)}}(6{x^2} + 23x + 21) = 4 - {\log _{(3x + 7)}}(4{x^2} + 12x + 9)\,$$

3
IIT-JEE 1987
Fill in the Blanks
+2
-0
The area of the triangle formed by the tangents from the point (4, 3) to the circle $${x^2} + {y^2} = 9$$ and the line joining their points of contact is...................
4
IIT-JEE 1987
Subjective
+3
-0
Let a given line $$L_1$$ intersects the x and y axes at P and Q, respectively. Let another line $$L_2$$, perpendicular to $$L_1$$, cut the x and y axes at R and S, respectively. Show that the locus of the point of intersection of the lines PS and QR is a circle passing through the origin.
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