Properties of Triangles Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. The angles of elevation of the top of a tower (A) from the top (B) and
bottom (D) at a building of height a are 30°  and 45° respectively. If the
tower and the building stand at the same level, then the height of the
tower is
(a)
(b)
(c)
(d)
2. If the angle A of a triangle ABC is given by the equation 
, then sin A  and tan A are the roots of the equation
(a) (b)
(c)
(d)
Page 2


PART-I (Single Correct MCQs)
1. The angles of elevation of the top of a tower (A) from the top (B) and
bottom (D) at a building of height a are 30°  and 45° respectively. If the
tower and the building stand at the same level, then the height of the
tower is
(a)
(b)
(c)
(d)
2. If the angle A of a triangle ABC is given by the equation 
, then sin A  and tan A are the roots of the equation
(a) (b)
(c)
(d)
3. A balloon is observed simultaneously from three points A, B and C on a
straight road directly under it. The angular elevation at B is twice and at
C is thrice that of A. If the distance between A and B is 200 metres and
the distance between B and C is 100 metres, then the height of balloon
is given by
(a) 50 metres
(b)
(c)
(d) None of these
4. A, B, C are the angles of a triangle, then 
(a) 1
(b) 2
(c) 3
(d) 4
5. The base of a cliff is circular. From the extremities of a diameter of the
base the angles of elevation of the top of the cliff are 30° and 60°. If the
height of the cliff be 500 metres, then the diameter of the base of the
cliff is
(a)
(b)
(c)
(d)
6. If in a ?ABC, 2b
2
 = a
2
 + c
2
, then  is equal to
(a)
Page 3


PART-I (Single Correct MCQs)
1. The angles of elevation of the top of a tower (A) from the top (B) and
bottom (D) at a building of height a are 30°  and 45° respectively. If the
tower and the building stand at the same level, then the height of the
tower is
(a)
(b)
(c)
(d)
2. If the angle A of a triangle ABC is given by the equation 
, then sin A  and tan A are the roots of the equation
(a) (b)
(c)
(d)
3. A balloon is observed simultaneously from three points A, B and C on a
straight road directly under it. The angular elevation at B is twice and at
C is thrice that of A. If the distance between A and B is 200 metres and
the distance between B and C is 100 metres, then the height of balloon
is given by
(a) 50 metres
(b)
(c)
(d) None of these
4. A, B, C are the angles of a triangle, then 
(a) 1
(b) 2
(c) 3
(d) 4
5. The base of a cliff is circular. From the extremities of a diameter of the
base the angles of elevation of the top of the cliff are 30° and 60°. If the
height of the cliff be 500 metres, then the diameter of the base of the
cliff is
(a)
(b)
(c)
(d)
6. If in a ?ABC, 2b
2
 = a
2
 + c
2
, then  is equal to
(a)
(b)
(c)
(d)
7. Two men are on the opposite side of a tower. They measure the angle of
elevation of the top of the tower 45° and 30° respectively. If the height
of the tower is 40 m, find the distance between the men.
(a) 40  m
(b) m
(c) 68.280  m
(d) 109.28  m
8. A vertical pole consists of two parts, the lower part being one third of
the whole. At a point in the horizontal plane through the base of the
pole and distance 20 meters from it, the upper part of the pole subtends
an angle whose tangent is . The possible heights of the pole are
(a) 20 m and  m
(b) 20 m and 60 m
(c) 16 m and 48 m
(d) None of these
9. In an equilateral triangle, the inradius, circumradius and one of the ex-
radii are in the ratio
(a) 2 : 3 : 5
(b) 1 : 2 : 3
(c) 3 : 7 : 9
Page 4


PART-I (Single Correct MCQs)
1. The angles of elevation of the top of a tower (A) from the top (B) and
bottom (D) at a building of height a are 30°  and 45° respectively. If the
tower and the building stand at the same level, then the height of the
tower is
(a)
(b)
(c)
(d)
2. If the angle A of a triangle ABC is given by the equation 
, then sin A  and tan A are the roots of the equation
(a) (b)
(c)
(d)
3. A balloon is observed simultaneously from three points A, B and C on a
straight road directly under it. The angular elevation at B is twice and at
C is thrice that of A. If the distance between A and B is 200 metres and
the distance between B and C is 100 metres, then the height of balloon
is given by
(a) 50 metres
(b)
(c)
(d) None of these
4. A, B, C are the angles of a triangle, then 
(a) 1
(b) 2
(c) 3
(d) 4
5. The base of a cliff is circular. From the extremities of a diameter of the
base the angles of elevation of the top of the cliff are 30° and 60°. If the
height of the cliff be 500 metres, then the diameter of the base of the
cliff is
(a)
(b)
(c)
(d)
6. If in a ?ABC, 2b
2
 = a
2
 + c
2
, then  is equal to
(a)
(b)
(c)
(d)
7. Two men are on the opposite side of a tower. They measure the angle of
elevation of the top of the tower 45° and 30° respectively. If the height
of the tower is 40 m, find the distance between the men.
(a) 40  m
(b) m
(c) 68.280  m
(d) 109.28  m
8. A vertical pole consists of two parts, the lower part being one third of
the whole. At a point in the horizontal plane through the base of the
pole and distance 20 meters from it, the upper part of the pole subtends
an angle whose tangent is . The possible heights of the pole are
(a) 20 m and  m
(b) 20 m and 60 m
(c) 16 m and 48 m
(d) None of these
9. In an equilateral triangle, the inradius, circumradius and one of the ex-
radii are in the ratio
(a) 2 : 3 : 5
(b) 1 : 2 : 3
(c) 3 : 7 : 9
(d) 3 : 7 : 9
10. The shadow of a tower is found to be 60 metre shorter when the sun’s
altitude changes from 30° to 60°. The height of the tower from the
ground is approximately equal to
(a) 62 m
(b) 301 m
(c) 101 m
(d) 52  m
11. In any triangle ABC, if , then
(a) a = b = c
(b) c = a
(c) a = b
(d) b = c
12. In a , if angle C is obtuse, then
(a) tan A tan B < 1
(b)
(c)
(d) None of these
13. In a ,  and . If D divides BC internally in
ratio 1 : 3, then 
(a)
(b) 1/3
(c)
(d)
14. Each side of an equilateral triangle subtends an angle of 60° at the top
of a tower h m high located at the centre of the triangle. If a is the
Page 5


PART-I (Single Correct MCQs)
1. The angles of elevation of the top of a tower (A) from the top (B) and
bottom (D) at a building of height a are 30°  and 45° respectively. If the
tower and the building stand at the same level, then the height of the
tower is
(a)
(b)
(c)
(d)
2. If the angle A of a triangle ABC is given by the equation 
, then sin A  and tan A are the roots of the equation
(a) (b)
(c)
(d)
3. A balloon is observed simultaneously from three points A, B and C on a
straight road directly under it. The angular elevation at B is twice and at
C is thrice that of A. If the distance between A and B is 200 metres and
the distance between B and C is 100 metres, then the height of balloon
is given by
(a) 50 metres
(b)
(c)
(d) None of these
4. A, B, C are the angles of a triangle, then 
(a) 1
(b) 2
(c) 3
(d) 4
5. The base of a cliff is circular. From the extremities of a diameter of the
base the angles of elevation of the top of the cliff are 30° and 60°. If the
height of the cliff be 500 metres, then the diameter of the base of the
cliff is
(a)
(b)
(c)
(d)
6. If in a ?ABC, 2b
2
 = a
2
 + c
2
, then  is equal to
(a)
(b)
(c)
(d)
7. Two men are on the opposite side of a tower. They measure the angle of
elevation of the top of the tower 45° and 30° respectively. If the height
of the tower is 40 m, find the distance between the men.
(a) 40  m
(b) m
(c) 68.280  m
(d) 109.28  m
8. A vertical pole consists of two parts, the lower part being one third of
the whole. At a point in the horizontal plane through the base of the
pole and distance 20 meters from it, the upper part of the pole subtends
an angle whose tangent is . The possible heights of the pole are
(a) 20 m and  m
(b) 20 m and 60 m
(c) 16 m and 48 m
(d) None of these
9. In an equilateral triangle, the inradius, circumradius and one of the ex-
radii are in the ratio
(a) 2 : 3 : 5
(b) 1 : 2 : 3
(c) 3 : 7 : 9
(d) 3 : 7 : 9
10. The shadow of a tower is found to be 60 metre shorter when the sun’s
altitude changes from 30° to 60°. The height of the tower from the
ground is approximately equal to
(a) 62 m
(b) 301 m
(c) 101 m
(d) 52  m
11. In any triangle ABC, if , then
(a) a = b = c
(b) c = a
(c) a = b
(d) b = c
12. In a , if angle C is obtuse, then
(a) tan A tan B < 1
(b)
(c)
(d) None of these
13. In a ,  and . If D divides BC internally in
ratio 1 : 3, then 
(a)
(b) 1/3
(c)
(d)
14. Each side of an equilateral triangle subtends an angle of 60° at the top
of a tower h m high located at the centre of the triangle. If a is the
length of each of side of the triangle, then
(a)
(b)
(c)
(d)
15. An aeroplane flying horizontally 1 km above the ground is observed at
an elevation of 60° and after 10 s the elevation is observed to be 30°.
The uniform speed of the aeroplane in kilometre per hour is
(a)
(b) 240
(c)
(d) 480
16. The length of the shadow of a pole inclined at 10° to the vertical
towards the sun is 2.05 metres, when the elevation of the sun is 38°.
The length of the pole is
(a)
(b)
(c)
(d) None of these
17. If A, B, C are acute positive angles such that A + B+ C = p and cot A
cot B cot C = K , then
(a)