1

### IIT-JEE 1986

Fill in the Blanks
The solution of equation $${\log _7}\,{\log _5}\,\left( {\sqrt {x + 5} + \sqrt x } \right) = 0$$ is ........................

4
2

### IIT-JEE 1986

Fill in the Blanks
If the quadratic equations $${x^2} + ax + b = 0$$ and $${x^2} + bx + a = 0$$ $$(a \ne b)$$ have a common root, then the numerical value of a + b is..........................

1
3

### IIT-JEE 1984

Fill in the Blanks
If the product of the roots of the equation $$\,{x^2} - 3\,k\,x + 2\,{e^{2lnk}} - 1 = 0\,\,\,\,is\,7$$, then the roots are real for k = .................................

2
4

### IIT-JEE 1982

Fill in the Blanks
If $$2 + i\sqrt 3$$ is root of the equation $${x^2} + px + q = 0$$, where p and q are real, then (p, q) = (..........,....................).

- 4, 7

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