Mathematics Question Paper (Set-3), Class 10 (2016) Class 10 Notes | EduRev

 Page 1


 
 
 
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Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
Mathematics 
Set-3 
Time: 3 hrs          M.M: 90 
 
 
General Instructions : 
(i) All questions are compulsory. 
(ii) The question paper consists of 31 questions divided into four sections – A, B, C and D. 
(iii) Section A contains 4 questions of 1 mark each, Section B contains 6 questions of 2 marks 
each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions 
of 4 marks each. 
(iv) Use of calculated is not permitted. 
 
Section A 
Q1 Find the 9
th
 term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185. 
Q2 Cards marked with number 3, 4, 5, ...., 50 are placed in a box and mixed thoroughly. A 
card is drawn at random form the box. Find the probability that the selected card bears a 
perfect square number. 
Q3 From an external point P, tangents PA and PB are drawn to a circle with centre O. If 
?PAB = 50°, then find ?AOB. 
Q4 In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the 
horizontal and reaches up to a point D of pole. If AD = 2.54 m, find the length of the 
ladder. (use3v=1.73) 
 
Q5 Find the ratio in which y-axis divides the line segment joining the points A(5, –6) and B(–
1, –4).   Also find the coordinates of the point of division. 
Q6 If 
2
   3
3
x and x = = - are roots of the quadratic equation
2
 7 0 ax x b + + = , find the values 
of a and b. 
Q7 The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) 
and R(–3, 6), find the  coordinates of P. 
Q8 In Fig. 2, a circle is inscribed in a ABC ? , such that it touches the sides AB, BC and CA at 
points D, E and F respectively. If the lengths of sides AB, BC and CA and 12 cm, 8 cm and 
10 cm respectively, find the lengths of AD, BE and CF. 
Page 2


 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
Mathematics 
Set-3 
Time: 3 hrs          M.M: 90 
 
 
General Instructions : 
(i) All questions are compulsory. 
(ii) The question paper consists of 31 questions divided into four sections – A, B, C and D. 
(iii) Section A contains 4 questions of 1 mark each, Section B contains 6 questions of 2 marks 
each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions 
of 4 marks each. 
(iv) Use of calculated is not permitted. 
 
Section A 
Q1 Find the 9
th
 term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185. 
Q2 Cards marked with number 3, 4, 5, ...., 50 are placed in a box and mixed thoroughly. A 
card is drawn at random form the box. Find the probability that the selected card bears a 
perfect square number. 
Q3 From an external point P, tangents PA and PB are drawn to a circle with centre O. If 
?PAB = 50°, then find ?AOB. 
Q4 In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the 
horizontal and reaches up to a point D of pole. If AD = 2.54 m, find the length of the 
ladder. (use3v=1.73) 
 
Q5 Find the ratio in which y-axis divides the line segment joining the points A(5, –6) and B(–
1, –4).   Also find the coordinates of the point of division. 
Q6 If 
2
   3
3
x and x = = - are roots of the quadratic equation
2
 7 0 ax x b + + = , find the values 
of a and b. 
Q7 The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) 
and R(–3, 6), find the  coordinates of P. 
Q8 In Fig. 2, a circle is inscribed in a ABC ? , such that it touches the sides AB, BC and CA at 
points D, E and F respectively. If the lengths of sides AB, BC and CA and 12 cm, 8 cm and 
10 cm respectively, find the lengths of AD, BE and CF. 
 
 
 
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Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
 
Q10 In Fig. 3, AP and BP are tangents to a circle with centre O, such that AP = 5 cm and 
  60 . APB ? = ° Find the  length of chord AB. 
 
Q10 How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero? 
Q11 A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread 
evenly all around it in the shape of a circular ring of width 3 m to form an embankment. 
Find the height of the embankment. 
Q12 If  the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the 
sum of first n terms of the A.P. 
Q13 The angles of depression of the top and bottom of a 50 m high building from the top of a 
tower are 45° and  60° respectively. Find the height of the tower and the horizontal 
distance between the tower and the building. 
( )
 3 1.73 use =
 
Q14 In Fig. 4, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square 
as diameter. Find the area of the shaded region. (
22
 
7
usep = ) 
 
Q15 In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base 
of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 
3.5 cm. Find the total surface area of the bock. (
22
 
7
usep = ) 
 
Page 3


 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
Mathematics 
Set-3 
Time: 3 hrs          M.M: 90 
 
 
General Instructions : 
(i) All questions are compulsory. 
(ii) The question paper consists of 31 questions divided into four sections – A, B, C and D. 
(iii) Section A contains 4 questions of 1 mark each, Section B contains 6 questions of 2 marks 
each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions 
of 4 marks each. 
(iv) Use of calculated is not permitted. 
 
Section A 
Q1 Find the 9
th
 term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185. 
Q2 Cards marked with number 3, 4, 5, ...., 50 are placed in a box and mixed thoroughly. A 
card is drawn at random form the box. Find the probability that the selected card bears a 
perfect square number. 
Q3 From an external point P, tangents PA and PB are drawn to a circle with centre O. If 
?PAB = 50°, then find ?AOB. 
Q4 In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the 
horizontal and reaches up to a point D of pole. If AD = 2.54 m, find the length of the 
ladder. (use3v=1.73) 
 
Q5 Find the ratio in which y-axis divides the line segment joining the points A(5, –6) and B(–
1, –4).   Also find the coordinates of the point of division. 
Q6 If 
2
   3
3
x and x = = - are roots of the quadratic equation
2
 7 0 ax x b + + = , find the values 
of a and b. 
Q7 The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) 
and R(–3, 6), find the  coordinates of P. 
Q8 In Fig. 2, a circle is inscribed in a ABC ? , such that it touches the sides AB, BC and CA at 
points D, E and F respectively. If the lengths of sides AB, BC and CA and 12 cm, 8 cm and 
10 cm respectively, find the lengths of AD, BE and CF. 
 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
 
Q10 In Fig. 3, AP and BP are tangents to a circle with centre O, such that AP = 5 cm and 
  60 . APB ? = ° Find the  length of chord AB. 
 
Q10 How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero? 
Q11 A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread 
evenly all around it in the shape of a circular ring of width 3 m to form an embankment. 
Find the height of the embankment. 
Q12 If  the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the 
sum of first n terms of the A.P. 
Q13 The angles of depression of the top and bottom of a 50 m high building from the top of a 
tower are 45° and  60° respectively. Find the height of the tower and the horizontal 
distance between the tower and the building. 
( )
 3 1.73 use =
 
Q14 In Fig. 4, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square 
as diameter. Find the area of the shaded region. (
22
 
7
usep = ) 
 
Q15 In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base 
of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 
3.5 cm. Find the total surface area of the bock. (
22
 
7
usep = ) 
 
 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
Q16 In Fig. 6, ABC is a triangle coordinates of whose vertex A are (0, -1). D and E respectively 
are the mid-points of the sides AB and AC and their coordinates are (1, 0) and (0, 1) 
respectively. If F is the mid-point of BC, find the areas of   D . ABC and EF ? ?
 
 
Q17 In Fig. 7, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre O and 
radius OP while arc PBQ is a semi-circle drawn on PQ ad diameter with centre M. If OP = 
PQ = 10 cm show that area of shaded region is 
2
25 3
6
cm
p ? ?
? ?
? ?
- 
 
Q18 A box consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major 
defects. Ramesh, a shopkeeper will buy only those shirts which are good but 'Kewal' 
another shopkeeper will not buy shirts with major defects. A shirt is taken out of the box 
at random. What is the probability that 
(i) Ramesh will buy the selected shirt? 
(ii) 'Kewal' will buy the selected shirt? 
Q19 Solve the following quadratic equation for x: 
2
1 0 
a a b
x x
a b a
? +
+ + +
? ?
? ?
=
+
?
 
Q20 A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base 
diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the 
toy. 
22
 
7
usep =
 
Q21 A passenger, while boarding the plane, slipped form the stairs and got hurt. The pilot 
took the passenger in the emergency clinic at the airport for treatment. Due to this, the 
plane got delayed by half an hour. To reach the destination 1500 km away in time, so 
that the passengers could catch the connecting flight, the speed of the plane was 
increased by 250 km/hour than the usual speed. Find the usual speed of the plane. 
 
What value is depicted in this question? 
Q22 In Fig. 8, O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and 
OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB, where 
TP and TQ are two tangents to the circle. 
Page 4


 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
Mathematics 
Set-3 
Time: 3 hrs          M.M: 90 
 
 
General Instructions : 
(i) All questions are compulsory. 
(ii) The question paper consists of 31 questions divided into four sections – A, B, C and D. 
(iii) Section A contains 4 questions of 1 mark each, Section B contains 6 questions of 2 marks 
each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions 
of 4 marks each. 
(iv) Use of calculated is not permitted. 
 
Section A 
Q1 Find the 9
th
 term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185. 
Q2 Cards marked with number 3, 4, 5, ...., 50 are placed in a box and mixed thoroughly. A 
card is drawn at random form the box. Find the probability that the selected card bears a 
perfect square number. 
Q3 From an external point P, tangents PA and PB are drawn to a circle with centre O. If 
?PAB = 50°, then find ?AOB. 
Q4 In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the 
horizontal and reaches up to a point D of pole. If AD = 2.54 m, find the length of the 
ladder. (use3v=1.73) 
 
Q5 Find the ratio in which y-axis divides the line segment joining the points A(5, –6) and B(–
1, –4).   Also find the coordinates of the point of division. 
Q6 If 
2
   3
3
x and x = = - are roots of the quadratic equation
2
 7 0 ax x b + + = , find the values 
of a and b. 
Q7 The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) 
and R(–3, 6), find the  coordinates of P. 
Q8 In Fig. 2, a circle is inscribed in a ABC ? , such that it touches the sides AB, BC and CA at 
points D, E and F respectively. If the lengths of sides AB, BC and CA and 12 cm, 8 cm and 
10 cm respectively, find the lengths of AD, BE and CF. 
 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
 
Q10 In Fig. 3, AP and BP are tangents to a circle with centre O, such that AP = 5 cm and 
  60 . APB ? = ° Find the  length of chord AB. 
 
Q10 How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero? 
Q11 A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread 
evenly all around it in the shape of a circular ring of width 3 m to form an embankment. 
Find the height of the embankment. 
Q12 If  the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the 
sum of first n terms of the A.P. 
Q13 The angles of depression of the top and bottom of a 50 m high building from the top of a 
tower are 45° and  60° respectively. Find the height of the tower and the horizontal 
distance between the tower and the building. 
( )
 3 1.73 use =
 
Q14 In Fig. 4, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square 
as diameter. Find the area of the shaded region. (
22
 
7
usep = ) 
 
Q15 In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base 
of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 
3.5 cm. Find the total surface area of the bock. (
22
 
7
usep = ) 
 
 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
Q16 In Fig. 6, ABC is a triangle coordinates of whose vertex A are (0, -1). D and E respectively 
are the mid-points of the sides AB and AC and their coordinates are (1, 0) and (0, 1) 
respectively. If F is the mid-point of BC, find the areas of   D . ABC and EF ? ?
 
 
Q17 In Fig. 7, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre O and 
radius OP while arc PBQ is a semi-circle drawn on PQ ad diameter with centre M. If OP = 
PQ = 10 cm show that area of shaded region is 
2
25 3
6
cm
p ? ?
? ?
? ?
- 
 
Q18 A box consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major 
defects. Ramesh, a shopkeeper will buy only those shirts which are good but 'Kewal' 
another shopkeeper will not buy shirts with major defects. A shirt is taken out of the box 
at random. What is the probability that 
(i) Ramesh will buy the selected shirt? 
(ii) 'Kewal' will buy the selected shirt? 
Q19 Solve the following quadratic equation for x: 
2
1 0 
a a b
x x
a b a
? +
+ + +
? ?
? ?
=
+
?
 
Q20 A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base 
diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the 
toy. 
22
 
7
usep =
 
Q21 A passenger, while boarding the plane, slipped form the stairs and got hurt. The pilot 
took the passenger in the emergency clinic at the airport for treatment. Due to this, the 
plane got delayed by half an hour. To reach the destination 1500 km away in time, so 
that the passengers could catch the connecting flight, the speed of the plane was 
increased by 250 km/hour than the usual speed. Find the usual speed of the plane. 
 
What value is depicted in this question? 
Q22 In Fig. 8, O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and 
OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB, where 
TP and TQ are two tangents to the circle. 
 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
 
Q23 A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of 
elevation of the bird is 45°. The bird flies away horizontally in such a way that it 
remained at a constant height from the ground. After 2 seconds, the angle of elevation of 
the bird from the same point is 30°. Find the speed of flying of the bird. 
( )
 3 1.732 . Take = 
Q24 A game of chance consists of spinning an arrow on a circular board, divided into 8 equal 
parts, which comes to rest pointing at one of the numbers 1, 2, 3, ..., 8 (Fig. 9), which are 
equally likely outcomes. What is the probability that the arrow will point at (i) an odd 
number (ii) a number greater than 3 (iii) a number less than 9. 
 
 
Q25 Prove that the area of a triangle with vertices (t, t -2), (t + 2, t + 2) and (t + 3, t) is 
independent of t. 
Q26 A bucket open at the top is in the form of a frustum of a cone with a capacity of
3
12308.8 cm . The radii of the top and bottom circular ends are 20 cm and 12 cm, 
respectively. Find the height of the bucket and the area of metal sheet used in making the 
bucket. ( ) 3.14 use p =
 
Q27 An elastic belt is placed around the rim of a pulley of radius 5 cm. (Fig. 10) From one 
point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley 
until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact 
with the pulley. Also find the shaded area. 
( )
 3.14  3 1.73 use and p = =
 
 
Q28 The sum of three numbers in A.P. is 12 and sum of their cubes is 288. Find the numbers. 
Q29 Prove that the lengths of tangents drawn from an external point to a circle are equal. 
Page 5


 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
Mathematics 
Set-3 
Time: 3 hrs          M.M: 90 
 
 
General Instructions : 
(i) All questions are compulsory. 
(ii) The question paper consists of 31 questions divided into four sections – A, B, C and D. 
(iii) Section A contains 4 questions of 1 mark each, Section B contains 6 questions of 2 marks 
each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions 
of 4 marks each. 
(iv) Use of calculated is not permitted. 
 
Section A 
Q1 Find the 9
th
 term from the end (towards the first term) of the A.P. 5, 9, 13, ...., 185. 
Q2 Cards marked with number 3, 4, 5, ...., 50 are placed in a box and mixed thoroughly. A 
card is drawn at random form the box. Find the probability that the selected card bears a 
perfect square number. 
Q3 From an external point P, tangents PA and PB are drawn to a circle with centre O. If 
?PAB = 50°, then find ?AOB. 
Q4 In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the 
horizontal and reaches up to a point D of pole. If AD = 2.54 m, find the length of the 
ladder. (use3v=1.73) 
 
Q5 Find the ratio in which y-axis divides the line segment joining the points A(5, –6) and B(–
1, –4).   Also find the coordinates of the point of division. 
Q6 If 
2
   3
3
x and x = = - are roots of the quadratic equation
2
 7 0 ax x b + + = , find the values 
of a and b. 
Q7 The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, –5) 
and R(–3, 6), find the  coordinates of P. 
Q8 In Fig. 2, a circle is inscribed in a ABC ? , such that it touches the sides AB, BC and CA at 
points D, E and F respectively. If the lengths of sides AB, BC and CA and 12 cm, 8 cm and 
10 cm respectively, find the lengths of AD, BE and CF. 
 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
 
Q10 In Fig. 3, AP and BP are tangents to a circle with centre O, such that AP = 5 cm and 
  60 . APB ? = ° Find the  length of chord AB. 
 
Q10 How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero? 
Q11 A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread 
evenly all around it in the shape of a circular ring of width 3 m to form an embankment. 
Find the height of the embankment. 
Q12 If  the sum of first 7 terms of an A.P. is 49 and that of its first 17 terms is 289, find the 
sum of first n terms of the A.P. 
Q13 The angles of depression of the top and bottom of a 50 m high building from the top of a 
tower are 45° and  60° respectively. Find the height of the tower and the horizontal 
distance between the tower and the building. 
( )
 3 1.73 use =
 
Q14 In Fig. 4, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square 
as diameter. Find the area of the shaded region. (
22
 
7
usep = ) 
 
Q15 In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base 
of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 
3.5 cm. Find the total surface area of the bock. (
22
 
7
usep = ) 
 
 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
Q16 In Fig. 6, ABC is a triangle coordinates of whose vertex A are (0, -1). D and E respectively 
are the mid-points of the sides AB and AC and their coordinates are (1, 0) and (0, 1) 
respectively. If F is the mid-point of BC, find the areas of   D . ABC and EF ? ?
 
 
Q17 In Fig. 7, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre O and 
radius OP while arc PBQ is a semi-circle drawn on PQ ad diameter with centre M. If OP = 
PQ = 10 cm show that area of shaded region is 
2
25 3
6
cm
p ? ?
? ?
? ?
- 
 
Q18 A box consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major 
defects. Ramesh, a shopkeeper will buy only those shirts which are good but 'Kewal' 
another shopkeeper will not buy shirts with major defects. A shirt is taken out of the box 
at random. What is the probability that 
(i) Ramesh will buy the selected shirt? 
(ii) 'Kewal' will buy the selected shirt? 
Q19 Solve the following quadratic equation for x: 
2
1 0 
a a b
x x
a b a
? +
+ + +
? ?
? ?
=
+
?
 
Q20 A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base 
diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the 
toy. 
22
 
7
usep =
 
Q21 A passenger, while boarding the plane, slipped form the stairs and got hurt. The pilot 
took the passenger in the emergency clinic at the airport for treatment. Due to this, the 
plane got delayed by half an hour. To reach the destination 1500 km away in time, so 
that the passengers could catch the connecting flight, the speed of the plane was 
increased by 250 km/hour than the usual speed. Find the usual speed of the plane. 
 
What value is depicted in this question? 
Q22 In Fig. 8, O is the centre of a circle of radius 5 cm. T is a point such that OT = 13 cm and 
OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB, where 
TP and TQ are two tangents to the circle. 
 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
 
Q23 A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of 
elevation of the bird is 45°. The bird flies away horizontally in such a way that it 
remained at a constant height from the ground. After 2 seconds, the angle of elevation of 
the bird from the same point is 30°. Find the speed of flying of the bird. 
( )
 3 1.732 . Take = 
Q24 A game of chance consists of spinning an arrow on a circular board, divided into 8 equal 
parts, which comes to rest pointing at one of the numbers 1, 2, 3, ..., 8 (Fig. 9), which are 
equally likely outcomes. What is the probability that the arrow will point at (i) an odd 
number (ii) a number greater than 3 (iii) a number less than 9. 
 
 
Q25 Prove that the area of a triangle with vertices (t, t -2), (t + 2, t + 2) and (t + 3, t) is 
independent of t. 
Q26 A bucket open at the top is in the form of a frustum of a cone with a capacity of
3
12308.8 cm . The radii of the top and bottom circular ends are 20 cm and 12 cm, 
respectively. Find the height of the bucket and the area of metal sheet used in making the 
bucket. ( ) 3.14 use p =
 
Q27 An elastic belt is placed around the rim of a pulley of radius 5 cm. (Fig. 10) From one 
point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley 
until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact 
with the pulley. Also find the shaded area. 
( )
 3.14  3 1.73 use and p = =
 
 
Q28 The sum of three numbers in A.P. is 12 and sum of their cubes is 288. Find the numbers. 
Q29 Prove that the lengths of tangents drawn from an external point to a circle are equal. 
 
 
 
Material downloaded from http://myCBSEguide.com and http://onlineteachers.co.in 
Portal for CBSE Notes, Test Papers, Sample Papers, Tips and Tricks 
Q30 The time taken by a person to cover 150 km was 
1
2
2
hours more than the time taken in 
the return journey. If he returned at a speed of 10 km/hour more than the speed while 
going, find the speed per hour in each direction. 
Q31 Draw a triangle ABC with BC = 7 cm, ?B = 45° and ?A = 105°. Then construct a triangle 
whose sides are times the corresponding sides of ?ABC.