IIT-JEE 2001 Screening | Trigonometric Functions & Equations Question 39 | Mathematics

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IIT-JEE 2001 Screening

MCQ (Single Correct Answer)

-0.5

If $$\alpha + \beta = \pi /2$$ and $$\beta + \gamma = \alpha ,$$ then $$\tan \,\alpha \,$$ equals

$$2\left( {\tan \beta + \tan \gamma } \right)$$

$$\,\tan \beta + \tan \gamma $$

$$\tan \beta + 2\tan \gamma $$

$$2\tan \beta + \tan \gamma $$

IIT-JEE 2000 Screening

MCQ (Single Correct Answer)

-0.5

Let $$f\left( \theta \right) = \sin \theta \left( {\sin \theta + \sin 3\theta } \right)$$. Then $$f\left( \theta \right)$$ is

$$ \ge 0\,\,$$ only when $$\theta \ge 0$$

$$ \le 0$$ for all real $$\theta $$

$$ \ge 0$$ for all real $$\theta $$

$$ \le 0$$ only when $$\theta \le 0$$

IIT-JEE 1999

MCQ (Single Correct Answer)

-0.5

In a triangle $$PQR,\angle R = \pi /2$$. If $$\,\,\tan \left( {P/2} \right)$$ and $$\tan \left( {Q/2} \right)$$ are the roots of the equation $$a{x^2} + bx + c = 0\left( {a \ne 0} \right)$$ then.

$$a + b = c$$

$$a + c = b$$

$$b + c = a$$

$$b = c$$

IIT-JEE 1998

MCQ (Single Correct Answer)

-0.5

Which of the following number(s) is /are rational?

$$\sin {\mkern 1mu} {15^ \circ }$$

$$\cos {\mkern 1mu} {15^ \circ }$$

$$\sin {\mkern 1mu} {15^ \circ }{\mkern 1mu} \cos {\mkern 1mu} {15^ \circ }$$

$$\sin {\mkern 1mu} {15^ \circ }{\mkern 1mu} \cos {\mkern 1mu} {75^ \circ }$$

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