1
IIT-JEE 1997
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+2
-0
Let $$p$$ and $$q$$ be roots of the equation $${x^2} - 2x + A = 0$$ and let $$r$$ and $$s$$ be the roots of the equation $${x^2} - 18x + B = 0.$$ If $$p < q < r < s$$ are in arithmetic progression, then $$A = \,..........$$ and $$B = \,..........$$
2
IIT-JEE 1996
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+1
-0
For any odd integer $$n$$ $$\ge 1,\,\,{n^3} - {\left( {n - 1} \right)^3} + .... + {\left( { - 1} \right)^{n - 1}}\,{1^3} = ........$$
3
IIT-JEE 1992
Fill in the Blanks
+2
-0
Let the harmonic mean and geometric mean of two positive numbers be the ratio 4 : 5. Then the two number are in the ratio .........
4
IIT-JEE 1988
Fill in the Blanks
+2
-0
The sum of the first n terms of the series $${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + .........$$ is
$$n\,\,{\left( {n + 1} \right)^2}/2,$$ when $$n$$ is even. When $$n$$ is odd, the sum is .............
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