1

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..........................

Answer

1
2

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 = .................................

Answer

2
3

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) = (..........,....................).

Answer

- 4, 7
4

IIT-JEE 1982

Fill in the Blanks
The coeffcient of $${x^{99}}$$ in the polynomial (x -1) (x - 2)...(x - 100) is ..............

Answer

- 5050

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