1
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
Two poles, AB of length a metres and CD of length a + b (b $$\ne$$ a) metres are erected at the same horizontal level with bases at B and D. If BD = x and tan$$\angle$$ACB = $${1 \over 2}$$, then :
A
x2 + 2(a + 2b)x $$-$$ b(a + b) = 0
B
x2 + 2(a + 2b)x + a(a + b) = 0
C
x2 $$-$$ 2ax + b(a + b) = 0
D
x2 $$-$$ 2ax + a(a + b) = 0
2
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
Let $${{\sin A} \over {\sin B}} = {{\sin (A - C)} \over {\sin (C - B)}}$$, where A, B, C are angles of triangle ABC. If the lengths of the sides opposite these angles are a, b, c respectively, then :
A
b2 $$-$$ a2 = a2 + c2
B
b2, c2, a2 are in A.P.
C
c2, a2, b2 are in A.P.
D
a2, b2, c2 are in A.P.
3
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
A 10 inches long pencil AB with mid point C and a small eraser P are placed on the horizontal top of a table such that PC = $$\sqrt 5$$ inches and $$\angle$$PCB = tan-1(2). The acute angle through which the pencil must be rotated about C so that the perpendicular distance between eraser and pencil becomes exactly 1 inch is : A
$${\tan ^{ - 1}}\left( {{3 \over 4}} \right)$$
B
tan$$-$$1(1)
C
$${\tan ^{ - 1}}\left( {{4 \over 3}} \right)$$
D
$${\tan ^{ - 1}}\left( {{1 \over 2}} \right)$$
4
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
A spherical gas balloon of radius 16 meter subtends an angle 60$$^\circ$$ at the eye of the observer A while the angle of elevation of its center from the eye of A is 75$$^\circ$$. Then the height (in meter) of the top most point of the balloon from the level of the observer's eye is :
A
$$8(2 + 2\sqrt 3 + \sqrt 2 )$$
B
$$8(\sqrt 6 + \sqrt 2 + 2)$$
C
$$8(\sqrt 2 + 2 + \sqrt 3 )$$
D
$$8(\sqrt 6 - \sqrt 2 + 2)$$
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