JEE Advanced 2022 Paper 2 Online | Properties of Triangle Question 1 | Mathematics

JEE Advanced 2022 Paper 2 Online

MCQ (More than One Correct Answer)

-2

Let $P Q R S$ be a quadrilateral in a plane, where

$Q R=1, \angle P Q R=\angle Q R S=70^{\circ}, \angle P Q S=15^{\circ}$ and $\angle P R S=40^{\circ}$.

If $\angle R P S=\theta^{\circ}, P Q=\alpha$ and $P S=\beta$, then the interval(s) that contain(s) the value of

$4 \alpha \beta \sin \theta^{\circ}$ is/are

$(0, \sqrt{2})$

$(1,2)$

$(\sqrt{2}, 3)$

$(2 \sqrt{2}, 3 \sqrt{2})$

JEE Advanced 2021 Paper 2 Online

MCQ (More than One Correct Answer)

-2

Consider a triangle PQR having sides of lengths p, q and r opposite to the angles P, Q and R, respectively. Then which of the following statements is (are) TRUE?

$$\cos P \ge 1 - {{{p^2}} \over {2qr}}$$

$$\cos R \ge \left( {{{q - r} \over {p + q}}} \right)\cos P + \left( {{{p - r} \over {p + q}}} \right)\cos Q$$

$${{q + r} \over p} < 2{{\sqrt {\sin q\sin R} } \over {\sin P}}$$

If p < q and p < r, then $$\cos Q > {p \over r}$$ and $$\cos R > {p \over q}$$

JEE Advanced 2020 Paper 1 Offline

MCQ (More than One Correct Answer)

-2

Let x, y and z be positive real numbers. Suppose x, y and z are the lengths of the sides of a triangle opposite to its angles X, Y, and Z, respectively. If

$$\tan {X \over 2} + \tan {Z \over 2} = {{2y} \over {x + y + z}}$$, then which of the following statements is/are TRUE?

2Y = X + Z

Y = X + Z

$$\tan {X \over 2}$$ = $${x \over {y + z}}$$

x² + z² $$-$$ y² = xz

JEE Advanced 2019 Paper 1 Offline

MCQ (More than One Correct Answer)

-1

In a non-right-angled triangle $$\Delta $$PQR, let p, q, r denote the lengths of the sides opposite to the angles At P, Q, R respectively. The median from R meets the side PQ at S, the perpendicular from P meets the side QR at E, and RS and PE intersect at O. If p = $${\sqrt 3 }$$, q = 1, and the radius of the circumcircle of the $$\Delta $$PQR equals 1, then which of the following options is/are correct?

Length of OE = $${1 \over 6}$$

Length of RS = $${{\sqrt 7 } \over 2}$$

Area of $$\Delta $$SOE = $${{\sqrt 3 } \over {12}}$$

Radius of incircle of $$\Delta $$PQR = $${{\sqrt 3 } \over {2}}$$($${2 - \sqrt 3 }$$)