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Test: 35 Year JEE Previous Year Questions: Properties of Triangle


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14 Questions MCQ Test Maths 35 Years JEE Main & Advanced Past year Papers | Test: 35 Year JEE Previous Year Questions: Properties of Triangle

Test: 35 Year JEE Previous Year Questions: Properties of Triangle for JEE 2022 is part of Maths 35 Years JEE Main & Advanced Past year Papers preparation. The Test: 35 Year JEE Previous Year Questions: Properties of Triangle questions and answers have been prepared according to the JEE exam syllabus.The Test: 35 Year JEE Previous Year Questions: Properties of Triangle MCQs are made for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: 35 Year JEE Previous Year Questions: Properties of Triangle below.
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Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 1

The sides of a triangle are 3x+4y, 4x+3y and 5x+5y where x, y > 0 then the triangle is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 1

Let a = 3x + 4y, b = 4x + 3y and c = 5x + 5y as x, y > 0, c = 5x + 5y is the largest side
∴ C is the largest angle . Now

∴ C is obtuse angle Þ DABC is obtuse angled

Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 2

In a triangle with sides a, b, c, r1 > r2 > r3 (which are the exradii) then

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 2

Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 3

The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of  side a , is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 3



Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 4

In a triangle ABC, medians AD and BE are drawn. If AD = 4,   then the area of the Δ ABC is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 4



[∴ Median of a D divides it into two Δ's of equal area.]

Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 5

If  in a ΔABC   then the sides a, b and c

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 5

a[cos C +1] + c[cos A +1] = 3b
(a + c) + (a cos C + c cos B) = 3b
a + c + b = 3b or a + c = 2b or a,b,c arein A.P.

Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 6

The sides of a triangle are sin α, cos α and  Then the greatest angle of the triangle is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 6

Let a = sin a,b = cosa and 

Clearly a and b < 1 but c > 1 as sina > 0 and cosa > 0
∴ c is the greatest side and greatest angle is C


∴ C = 120°

Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 7

A person stan ding on t he bank of a river obser ves that  the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 meters away from the tree the angle of elevation becomes 30°. The breadth of the river is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 7


From the figure

Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 8

In a triangle ABC, let  If r is the inradius and R is the circumradius of the triangle ABC, then 2 (r + R) equals

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 8


⇒ c= 2R     (∵ ∠C = 90°)

     (∵ ∠C = 90°)

⇒ 2r +c = a+b ⇒ 2r +2 R = a+b (using c = 2R)

Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 9

If in a ΔABC , the altitudes from the vertices A, B, C on opposite sides are in H.P, then sin A, sin B, sin C are in

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 9



⇒ a, b, c are in A.P.
⇒ KsinA, K sin B, K sin C are in AP
⇒ sinA, sinB, sinC are in A.P.

Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 10

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60° at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30°.
The height of the tower is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 10

In the Δ AOB, ∠ AOB = 60°, and ∠ OBA = ∠ OAB (since OA = OB = AB radius of same circle). ∴ D AOB is a equilateral triangle. Let the height of tower is h m. Given distance between two points A & B lie on boundary of circular park, subtends an angle of 60° at the foot of the tower is AB i.e. AB = a. A tower OC stands at the centre of a circular park. Angle of elevation of the top of the tower from A and B is 30°

Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 11

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60°. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45°. Then the height of the pole is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 11



Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 12

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 12

If O is centre of polygon and AB is one of the side, then by figure

n = 3, 4, 6 respectively.

Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 13

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45° . It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30° . Then the speed (in m/s) of the bird is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 13

Let the speed be y m/sec.
Let AC be the vertical pole of height 20 m.
Let O be the point on the ground such that ∠AOC = 45° Let OC = x



Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 14

If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30°, 45° and 60° respectively, then the ratio, AB : BC, is :

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Properties of Triangle - Question 14

∵ PB bisects ÐAPC, therefore AB : BC = PA : PC

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