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1

### IIT-JEE 2006

Subjective
Let $$a$$ and $$b$$ be the roots of the equation $${x^2} - 10cx - 11d = 0$$ and those $${x^2} - 10ax - 11b = 0$$ are $$c$$, $$d$$ then the value of $$a + b + c + d,$$ when $$a \ne b \ne c \ne d,$$ is

$$1210$$
2

### IIT-JEE 2004

Subjective
If $$a,\,b,c$$ are positive real numbers. Then prove that $${\left( {a + 1} \right)^7}{\left( {b + 1} \right)^7}{\left( {c + 1} \right)^7} > {7^7}\,{a^4}{b^4}{c^4}$$\$

Solve it.
3

### IIT-JEE 2003

Subjective
If $${x^2} + \left( {a - b} \right)x + \left( {1 - a - b} \right) = 0$$ where $$a,\,b\, \in \,R$$ then find the values of a for which equation has unequal real roots for all values of $$b$$.

$$a > 1$$
4

### IIT-JEE 2001

Subjective
Let $$a,\,b,\,c$$ be real numbers with $$a \ne 0$$ and let $$\alpha ,\,\beta$$ be the roots of the equation $$a{x^2} + bx + c = 0$$. Express the roots of $${a^3}{x^2} + abcx + {c^3} = 0$$ in terms of $$\alpha ,\,\beta \,$$.

$${\alpha ^2}\beta ,\,\,\alpha {\beta ^2}$$

### Joint Entrance Examination

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NEET

Class 12