1
JEE Advanced 2022 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-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
A
$(0, \sqrt{2})$
B
$(1,2)$
C
$(\sqrt{2}, 3)$
D
$(2 \sqrt{2}, 3 \sqrt{2})$
2
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-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?
A
$$\cos P \ge 1 - {{{p^2}} \over {2qr}}$$
B
$$\cos R \ge \left( {{{q - r} \over {p + q}}} \right)\cos P + \left( {{{p - r} \over {p + q}}} \right)\cos Q$$
C
$${{q + r} \over p} < 2{{\sqrt {\sin q\sin R} } \over {\sin P}}$$
D
If p < q and p < r, then $$\cos Q > {p \over r}$$ and $$\cos R > {p \over q}$$
3
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-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?
A
2Y = X + Z
B
Y = X + Z
C
$$\tan {X \over 2}$$ = $${x \over {y + z}}$$
D
x2 + z2 $$-$$ y2 = xz
4
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-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?
A
Length of OE = $${1 \over 6}$$
B
Length of RS = $${{\sqrt 7 } \over 2}$$
C
Area of $$\Delta$$SOE = $${{\sqrt 3 } \over {12}}$$
D
Radius of incircle of $$\Delta$$PQR = $${{\sqrt 3 } \over {2}}$$($${2 - \sqrt 3 }$$)
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