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1

### IIT-JEE 1996

Fill in the Blanks
For any odd integer $$n$$ $$\ge 1,\,\,{n^3} - {\left( {n - 1} \right)^3} + .... + {\left( { - 1} \right)^{n - 1}}\,{1^3} = ........$$

$${1 \over 4}{\left( {n + 1} \right)^2}\left( {2n - 1} \right)$$
2

### IIT-JEE 1992

Fill in the Blanks
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 : 1 or 1 : 4
3

### IIT-JEE 1988

Fill in the Blanks
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 .............

$${{{n^2}\left( {n + 1} \right)} \over 2}$$
4

### IIT-JEE 1986

Fill in the Blanks
The solution of the equation $$lo{g_7}$$ $$lo{g_5}$$ $$\left( {\sqrt {x + 5} + \sqrt x } \right) = 0$$ is .............

4

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12