IIT-JEE 2006 | Quadratic Equation and Inequalities Question 27 | Mathematics

IIT-JEE 2006

MCQ (Single Correct Answer)

-1

Let $$a, b, c$$ be the sides of a triangle. No two of them are equal and $$\lambda \in R$$. If the roots of the equation $$x^{2}+2(a+b+c) x+3 \lambda(a b+b c+c a)=0$$ are real, then,

$$\lambda<\frac{4}{3}$$

$$\lambda>\frac{5}{3}$$

$$\lambda \in\left(\frac{1}{3}, \frac{5}{3}\right)$$

$$\lambda \in\left(\frac{4}{3}, \frac{5}{3}\right)$$

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-0.5

If one root is square of the other root of the equation $${x^2} + px + q = 0$$, then the realation between $$p$$ and $$q$$ is

$${p^3} - q\left( {3p - 1} \right) + {q^2} = 0$$

$${p^3} - q\left( {3p + 1} \right) + {q^2} = 0$$

$${p^3} + q\left( {3p - 1} \right) + {q^2} = 0$$

$${p^3} + q\left( {3p + 1} \right) + {q^2} = 0$$

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

-0.5

For all $$'x',{x^2} + 2ax + 10 - 3a > 0,$$ then the interval in which '$$a$$' lies is

$$a < - 5$$

$$ - 5 < a < 2$$

$$a > 5$$

$$2 < a < 5$$

IIT-JEE 2003 Screening

MCQ (Single Correct Answer)

-0.5

If $$\,\alpha \in \left( {0,{\pi \over 2}} \right)\,\,then\,\,\sqrt {{x^2} + x} + {{{{\tan }^2}\alpha } \over {\sqrt {{x^2} + x} }}$$ is always greater than or equal to

$$2\,\tan \alpha \,$$

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

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