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## MCQ (More than One Correct Answer)

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Consider a triangle PQR having sides of lengths p, q and r opposite to the angles P, Q and R, respectively. Then which o...
JEE Advanced 2021 Paper 2 Online
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 a...
JEE Advanced 2020 Paper 1 Offline
In a non-right-angled triangle $$\Delta$$PQR, let p, q, r denote the lengths of the sides opposite to the angles At P, ...
JEE Advanced 2019 Paper 1 Offline
In a triangle $$\Delta$$$$XYZ$$, let $$x, y, z$$ be the lengths of sides opposite to the angles $$X, Y, Z$$ respectivel...
JEE Advanced 2016 Paper 1 Offline
In a triangle $$PQR$$, $$P$$ is the largest angle and $$\cos P = {1 \over 3}$$. Further the incircle of the triangle tou...
JEE Advanced 2013 Paper 2 Offline
In $$\Delta ABC$$, internal angle bisector of $$\angle A$$ meets side $$BC$$ in $$D$$. $$DE \bot AD$$ meets $$AC$$ in $$... IIT-JEE 2006 In a triangle, the lengths of the two larger sides are$$10$$and$$9$$, respectively. If the angles are in$$AP$$. Then... IIT-JEE 1987 There exists a triangle$$ABC$$satisfying the conditions IIT-JEE 1986 ## Numerical More In a triangle ABC, let AB =$$\sqrt {23} $$, BC = 3 and CA = 4. Then the value of$${{\cot A + \cot C} \over {\cot B}}$$... JEE Advanced 2021 Paper 1 Online In a triangle PQR, let a = QR, b = RP, and c = PQ. If |a| = 3, |b| = 4 and$${{a\,.(\,c - \,b)} \over {c\,.\,(a - \,b)}}...
JEE Advanced 2020 Paper 1 Offline
Consider a triangle $$ABC$$ and let $$a, b$$ and $$c$$ denote the lengths of the sides opposit to vertices $$A, B$$ and ...
IIT-JEE 2010 Paper 2 Offline
Let $$ABC$$ and $$ABC'$$ be two non-congruent triangles with sides $$AB=4$$, $$AC=AC'$$$$=$$$$2\sqrt 2$$ and angle $$B ... IIT-JEE 2009 ## MCQ (Single Correct Answer) More In a triangle the sum of two sides is$$x$$and the product of the same sides is$$y$$. If$${x^2} - {c^2} = y$$, where ... JEE Advanced 2014 Paper 2 Offline Let$$PQR$$be a triangle of area$$\Delta $$with$$a=2$$,$$b = {7 \over 2}$$and$$c = {5 \over 2}$$; where$$a, b,$$... IIT-JEE 2012 Paper 2 Offline Let$$ABC$$be a triangle such that$$\angle ACB = {\pi \over 6}$$and let$$a, b$$and$$c$$denote the lengths of the... IIT-JEE 2010 Paper 1 Offline If the angles$$A, B$$and$$C$$of a triangle are in an arithmetic progression and if$$a, b$$and$$c$$denote the len... IIT-JEE 2010 Paper 1 Offline Let$$ABCD$$be a quadrilateral with area$$18$$, with side$$AB$$parallel to the side$$CD$$and$$2AB=CD$$. Let$$AD$... IIT-JEE 2007 One angle of an isosceles $$\Delta$$ is $${120^ \circ }$$ and radius of its incircle $$= \sqrt 3$$. Then the area of ... IIT-JEE 2006 In an equilateral triangle, $$3$$ coins of radii $$1$$ unit each are kept so that they touch each other and also the si... IIT-JEE 2005 In a triangle $$ABC$$, $$a,b,c$$ are the lengths of its sides and $$A,B,C$$ are the angles of triangle $$ABC$$. The corr... IIT-JEE 2005 Screening The sides of a triangle are in the ratio $$1:\sqrt 3 :2$$, then the angles of the triangle are in the ratio IIT-JEE 2004 Screening If the angles of a triangle are in the ratio $$4:1:1$$, then the ratio of the longest side to the perimeter is IIT-JEE 2003 Screening Which of the following pieces of data does NOT uniquely determine an acute-angled triangle $$ABC$$ ($$R$$ being the radi... IIT-JEE 2002 Screening A man from the top of a $$100$$ metres high tower sees a car moving towards the tower at an angle of depression of $${30... IIT-JEE 2001 Screening A pole stands vertically inside a triangular park$$\Delta ABC$$. If the angle of elevation of the top of the pole from ... IIT-JEE 2000 Screening In a triangle$$ABC$$, let$$\angle C = {\pi \over 2}$$. If$$r$$is the inradius and$$R$$is the circumradius of the ... IIT-JEE 2000 Screening In a triangle$$ABC$$,$$2ac\,\sin {1 \over 2}\left( {A - B + C} \right) = $$IIT-JEE 2000 Screening Let$${A_0}{A_1}{A_2}{A_3}{A_4}{A_5}$$be a regular hexagon inscribed in a circle of unit radius. Then the product of th... IIT-JEE 1998 If in a triangle$$PQR$$,$$\sin P,\sin Q,\sin R$$are in$$A.P.,$$then IIT-JEE 1998 In a triangle$$ABC$$,$$\angle B = {\pi \over 3}$$and$$\angle C = {\pi \over 4}$$. Let$$D$$divide$$BC$$internal... IIT-JEE 1995 Screening If the lengths of the sides of triangle are$$3, 5, 7$$then the largest angle of the triangle is IIT-JEE 1994 In a triangle$$ABC$$, angle$$A$$is greater than angle$$B$$. If the measures of angles$$A$$and$$B$$satify the equ... IIT-JEE 1990 From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is$${15^... IIT-JEE 1983 If the bisector of the angle $$P$$ of a triangle $$PQR$$ meets $$QR$$ in $$S$$, then IIT-JEE 1979 ## Subjective More If $${I_n}$$ is the area of $$n$$ sided regular polygon inscribed in a circle of unit radius and $${O_n}$$ be the area o... IIT-JEE 2003 If $$\Delta$$ is the area of a triangle with side lengths $$a, b, c,$$ then show that $$\Delta \le {1 \over 4}\sqrt {... IIT-JEE 2001 Let$$ABC$$be a triangle with incentre$$I$$and inradius$$r$$. Let$$D,E,F$$be the feet of the perpendiculars from ... IIT-JEE 2000 Let$$ABC$$be a triangle having$$O$$and$$I$$as its circumcenter and in centre respectively. If$$R$$and$$r$$are ... IIT-JEE 1999 Prove that a triangle$$ABC$$is equilateral if and only if$$\tan A + \tan B + \tan C = 3\sqrt 3 $$. IIT-JEE 1998 A bird flies in a circle on a horizontal plane. An observer stands at a point on the ground. Suppose$${60^ \circ }$$an... IIT-JEE 1998 Consider the following statements connecting a triangle$$ABC$$(i) The sides$$a, b, c$$and area$$\Delta $$are rati... IIT-JEE 1994 Let$${A_1},{A_2},........,{A_n}$$be the vertices of an$$n$$-sided regular polygon such that$${1 \over {{A_1}{A_2}}} ... IIT-JEE 1994 A tower $$AB$$ leans towards west making an angle $$\alpha$$ with the vertical. The angular elevation of $$B$$, the top... IIT-JEE 1994 An observer at $$O$$ notices that the angle of elevation of the top of a tower is $${30^ \circ }$$. The line joining $$O... IIT-JEE 1993 Three circles touch the one another externally. The tangent at their point of contact meet at a point whose distance fro... IIT-JEE 1992 In a triangle of base a the ratio of the other two sides is$$r\left( { &lt; 1} \right)$$. Show that the altitude of the... IIT-JEE 1991 A man notices two objects in a straight line due west. After walking a distance$$c$$due north he observes that the obj... IIT-JEE 1991 The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine... IIT-JEE 1991 A vertical tower$$PQ$$stands at a point$$P$$. Points$$A$$and$$B$$are located to the South and East of$$P$$respe... IIT-JEE 1990$$ABC$$is a triangular park with$$AB=AC=100m$$. A television tower stands at the midpoint of$$BC$$. The angles o... IIT-JEE 1989 A sign -post in the form of an isosceles triangle$$ABC$$is mounted on a pole of height$$h$$fixed to the ground. The ... IIT-JEE 1988 If in a triangle$$ABC$$,$$\cos A\cos B + \sin A\sin B\sin C = 1,$$Show that$$a:b:c = 1:1:\sqrt 2 $$IIT-JEE 1986 In a triangle$$ABC$$, the median to the side$$BC$$is of length$$${1 \over {\sqrt {11 - 6\sqrt 3 } }}$$and it divi... IIT-JEE 1985 A ladder rests against a wall at an angle$$\alpha $$to the horizintal. Its foot is pulled away from the wall through a... IIT-JEE 1985 With usual notation, if in a triangle$$ABC$$;$${{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}$$... IIT-JEE 1984 For a triangle$$ABC$$it is given that$$\cos A + \cos B + \cos C = {3 \over 2}$$. Prove that the triangle is equilater... IIT-JEE 1984 The ex-radii$${r_1},{r_2},{r_3}$$of$$\Delta ABC$$are H.P. Show that its sides$$a, b, c$$are in A.P. IIT-JEE 1983 A vertical pole stands at a point$$Q$$on a horizontal ground.$$A$$and$$B$$are points on the ground,$$d$$meters a... IIT-JEE 1982 Let the angles$$A, B, C$$of a triangle$$ABC$$be in A.P. and let$$b:c = \sqrt 3 :\sqrt 2 $$. Find the angle$$A$$. IIT-JEE 1981 (i)$$PQ$$is a vertical tower.$$P$$is the foot and$$Q$$is the top of the tower.$$A, B, C$$are three points in the... IIT-JEE 1980$$ABC$$is a triangle with$$AB=AC$$.$$D$$is any point on the side$$BC$$.$$E$$and$$F$$are points on the side$$AB...
IIT-JEE 1980
$$ABC$$ is a triangle. $$D$$ is the middle point of $$BC$$. If $$AD$$ is perpendicular to $$AC$$, then prove that $$\c... IIT-JEE 1980 (a) If a circle is inscribed in a right angled triangle$$ABC$$with the right angle at$$B$$, show that the diameter of... IIT-JEE 1979 (a) A balloon is observed simultaneously from three points$$A, B$$and$$C$$on a straight road directly beneath it. Th... IIT-JEE 1979 A triangle$$ABC$$has sides$$AB=AC=5$$cm and$$BC=6$$cm Triangle$$A'B'C'$$is the reflection of the triangle$$ABC\$...
IIT-JEE 1978

## Fill in the Blanks

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In a triangle $$ABC$$, $$a:b:c=4:5:6$$. The ratio of the radius of the circumcircle to that of the incircle is ............
IIT-JEE 1996
A circle is inscribed in an equilateral triangle of side $$a$$. The area of any square inscribed in this circle is .......
IIT-JEE 1994
In a triangle $$ABC$$, $$AD$$ is the altitude from $$A$$. Given $$b&gt;c$$, $$\angle C = {23^ \circ }$$ and $$AD = {{abc... IIT-JEE 1994 If in a triangle$$ABC$$,$${{2\cos A} \over a} + {{\cos B} \over b} + {{2\cos C} \over c} = {a \over {bc}} + {b \over {...
IIT-JEE 1993
If the angles of a triangle are $${30^ \circ }$$ and $${45^ \circ }$$ and the included side is $$\left( {\sqrt 3 + 1} \... IIT-JEE 1988 A polygon of nine sides, each of length$$2$$, is inscribed in a circle. The radius of the circle is ................. IIT-JEE 1987 In a triangle$$ABC$$, if cot$$A$$, cot$$B$$, cot$$C$$are in A.P., then$${a^2},{b^2},{c^2}$$, are in ................. IIT-JEE 1985 The set of all real numbers$$a$$such that$${a^2} + 2a,2a + 3$$and$${a^2} + 3a + 8$$are the sides of a triangle is ... IIT-JEE 1985 In a$$\Delta ABC,\,\angle A = {90^ \circ }$$and$$AD$$is an altitude. Complete the relation$${{BD} \over {BA}} = {{A...
IIT-JEE 1980
$$ABC$$ is a triangle with $$\angle B$$ greater than $$\angle C.\,D$$ and $$E$$ are points on $$BC$$ such that $$AD$$ is...
IIT-JEE 1980
$$ABC$$ is a triangle, $$P$$ is a point on $$AB$$, and $$Q$$ is point on $$AC$$ such that $$\angle AQP = \angle ABC$$. C...
IIT-JEE 1980

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