Page 1
Class - X Session 2022-23
Subject - Mathematics (Basic)
Sample Question Paper
Time Allowed: 3 Hours Maximum Marks: 80
General Instructions:
1. This Question Paper has 5 Sections A, B, C, D, and E.
2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.
4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.
5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each.
6. Section E has 3 Case Based integrated units of assessment (4 marks each) with sub-parts of
the values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 2 marks, 2 Qs of 3 marks
and 2 Questions of 5 marks has been provided. An internal choice has been provided in the 2
marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
Section A consists of 20 questions of 1 mark each.
SN Ma
rks
1 If two positive integers p and q can be expressed as p = ab
2
and q = a
3
b; a, b being prime
numbers, then LCM (p, q) is
(a) ab (b) a
2
b
2
(c) a
3
b
2
(d) a
3
b
3
1
2 What is the greatest possible speed at which a man can walk 52 km and 91 km in an exact
number of hours?
(a) 17 km/hours (b) 7 km/hours
(c) 13 km/hours (d) 26 km/hours
1
3 If one zero of the quadratic polynomial x
2
+ 3x + k is 2, then the value of k is
(a) 10 (b) -10 (c) 5 (d) –5
1
4
Graphically, the pair of equations given by
6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are
(a) intersecting at exactly one point. (b) parallel.
(c) coincident. (d) intersecting at exactly two points.
1
Page 2
Class - X Session 2022-23
Subject - Mathematics (Basic)
Sample Question Paper
Time Allowed: 3 Hours Maximum Marks: 80
General Instructions:
1. This Question Paper has 5 Sections A, B, C, D, and E.
2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.
4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.
5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each.
6. Section E has 3 Case Based integrated units of assessment (4 marks each) with sub-parts of
the values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 2 marks, 2 Qs of 3 marks
and 2 Questions of 5 marks has been provided. An internal choice has been provided in the 2
marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
Section A consists of 20 questions of 1 mark each.
SN Ma
rks
1 If two positive integers p and q can be expressed as p = ab
2
and q = a
3
b; a, b being prime
numbers, then LCM (p, q) is
(a) ab (b) a
2
b
2
(c) a
3
b
2
(d) a
3
b
3
1
2 What is the greatest possible speed at which a man can walk 52 km and 91 km in an exact
number of hours?
(a) 17 km/hours (b) 7 km/hours
(c) 13 km/hours (d) 26 km/hours
1
3 If one zero of the quadratic polynomial x
2
+ 3x + k is 2, then the value of k is
(a) 10 (b) -10 (c) 5 (d) –5
1
4
Graphically, the pair of equations given by
6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are
(a) intersecting at exactly one point. (b) parallel.
(c) coincident. (d) intersecting at exactly two points.
1
5 If the quadratic equation x
2
+ 4x + k = 0 has real and equal roots, then
(a) k < 4 (b) k > 4 (c) k = 4 (d) k = 4
1
6 The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5 units (b) 12 units (c) 11 units (d) (7 + v5) units
1
7
If in triangles ABC and DEF,
AB
DE
=
BC
FD
, then they will be similar, when
(a) ?B = ?E (b) ?A = ?D (c) ?B = ?D (d) ?A = ?F
1
8 In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?.
(a) 1 : 5 (b) 5 : 1 (c) 1 : 1 (d) 1 : 2
1
9 In the figure, if PA and PB are tangents to the circle
with centre O such that ?APB = 50°, then ?OAB is
equal to
(a) 25° (b) 30° (c) 40° (d) 50°
1
10
If sin A =
1
2
, then the value of sec A is :
(a)
2
v3
(b)
1
v3
(c) v3
(d) 1
1
11
v3 cos
2
A + v3 sin
2
A is equal to
(a) 1
(b)
1
v3
(c) v3
(d) 0
1
12
The value of cos1° . cos2° . cos3° . cos4°. . . . . . . . . . . .. cos90° is
(a) 1 (b) 0 (c) – 1 (d) 2
1
13 If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
(a) 22 : 7 (b) 14 : 11 (c) 7 : 22 (d) 11: 14
1
14 If the radii of two circles are in the ratio of 4 : 3, then their areas are in the ratio of :
(a) 4 : 3 (b) 8 : 3 (c) 16 : 9 (d) 9 : 16
1
15 The total surface area of a solid hemisphere of radius 7 cm is :
(a) 447p cm
2
(b) 239p cm
2
(c) 174p cm
2
(d) 147p cm
2
1
Page 3
Class - X Session 2022-23
Subject - Mathematics (Basic)
Sample Question Paper
Time Allowed: 3 Hours Maximum Marks: 80
General Instructions:
1. This Question Paper has 5 Sections A, B, C, D, and E.
2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.
4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.
5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each.
6. Section E has 3 Case Based integrated units of assessment (4 marks each) with sub-parts of
the values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 2 marks, 2 Qs of 3 marks
and 2 Questions of 5 marks has been provided. An internal choice has been provided in the 2
marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
Section A consists of 20 questions of 1 mark each.
SN Ma
rks
1 If two positive integers p and q can be expressed as p = ab
2
and q = a
3
b; a, b being prime
numbers, then LCM (p, q) is
(a) ab (b) a
2
b
2
(c) a
3
b
2
(d) a
3
b
3
1
2 What is the greatest possible speed at which a man can walk 52 km and 91 km in an exact
number of hours?
(a) 17 km/hours (b) 7 km/hours
(c) 13 km/hours (d) 26 km/hours
1
3 If one zero of the quadratic polynomial x
2
+ 3x + k is 2, then the value of k is
(a) 10 (b) -10 (c) 5 (d) –5
1
4
Graphically, the pair of equations given by
6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are
(a) intersecting at exactly one point. (b) parallel.
(c) coincident. (d) intersecting at exactly two points.
1
5 If the quadratic equation x
2
+ 4x + k = 0 has real and equal roots, then
(a) k < 4 (b) k > 4 (c) k = 4 (d) k = 4
1
6 The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5 units (b) 12 units (c) 11 units (d) (7 + v5) units
1
7
If in triangles ABC and DEF,
AB
DE
=
BC
FD
, then they will be similar, when
(a) ?B = ?E (b) ?A = ?D (c) ?B = ?D (d) ?A = ?F
1
8 In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?.
(a) 1 : 5 (b) 5 : 1 (c) 1 : 1 (d) 1 : 2
1
9 In the figure, if PA and PB are tangents to the circle
with centre O such that ?APB = 50°, then ?OAB is
equal to
(a) 25° (b) 30° (c) 40° (d) 50°
1
10
If sin A =
1
2
, then the value of sec A is :
(a)
2
v3
(b)
1
v3
(c) v3
(d) 1
1
11
v3 cos
2
A + v3 sin
2
A is equal to
(a) 1
(b)
1
v3
(c) v3
(d) 0
1
12
The value of cos1° . cos2° . cos3° . cos4°. . . . . . . . . . . .. cos90° is
(a) 1 (b) 0 (c) – 1 (d) 2
1
13 If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
(a) 22 : 7 (b) 14 : 11 (c) 7 : 22 (d) 11: 14
1
14 If the radii of two circles are in the ratio of 4 : 3, then their areas are in the ratio of :
(a) 4 : 3 (b) 8 : 3 (c) 16 : 9 (d) 9 : 16
1
15 The total surface area of a solid hemisphere of radius 7 cm is :
(a) 447p cm
2
(b) 239p cm
2
(c) 174p cm
2
(d) 147p cm
2
1
16
For the following distribution :
Class 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25
Frequency 10 15 12 20 9
the upper limit of the modal class is
(a) 10 (b) 15 (c) 20 (d) 25
1
17 If the mean of the following distribution is 2.6, then the value of y is
Variable (x) 1 2 3 4 5
Frequency 4 5 y 1 2
(a) 3 (b) 8 (c) 13 (d) 24
1
18
A card is selected at random from a well shuffled deck of 52 cards. The probability of its
being a red face card is
(a)
3
26
(b)
3
13
(c)
2
13
(d)
1
2
1
Direction for questions 19 & 20: In question numbers 19 and 20, a statement of
Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
19
Assertion: If HCF of 510 and 92 is 2, then the LCM of 510 & 92 is 32460
Reason: as HCF(a,b) x LCM(a,b) = a x b
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation
of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct
explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
1
20
Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally
divided by x axis is 1:2.
Reason (R): as formula for the internal division is (
?? ?? 2
+ ?? ?? 1
?? + ??
,
?? ?? 2
+ ?? ?? 1
?? + ??
)
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation
of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct
explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
1
Section B
Section B consists of 5 questions of 2 marks each.
Page 4
Class - X Session 2022-23
Subject - Mathematics (Basic)
Sample Question Paper
Time Allowed: 3 Hours Maximum Marks: 80
General Instructions:
1. This Question Paper has 5 Sections A, B, C, D, and E.
2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.
4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.
5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each.
6. Section E has 3 Case Based integrated units of assessment (4 marks each) with sub-parts of
the values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 2 marks, 2 Qs of 3 marks
and 2 Questions of 5 marks has been provided. An internal choice has been provided in the 2
marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
Section A consists of 20 questions of 1 mark each.
SN Ma
rks
1 If two positive integers p and q can be expressed as p = ab
2
and q = a
3
b; a, b being prime
numbers, then LCM (p, q) is
(a) ab (b) a
2
b
2
(c) a
3
b
2
(d) a
3
b
3
1
2 What is the greatest possible speed at which a man can walk 52 km and 91 km in an exact
number of hours?
(a) 17 km/hours (b) 7 km/hours
(c) 13 km/hours (d) 26 km/hours
1
3 If one zero of the quadratic polynomial x
2
+ 3x + k is 2, then the value of k is
(a) 10 (b) -10 (c) 5 (d) –5
1
4
Graphically, the pair of equations given by
6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are
(a) intersecting at exactly one point. (b) parallel.
(c) coincident. (d) intersecting at exactly two points.
1
5 If the quadratic equation x
2
+ 4x + k = 0 has real and equal roots, then
(a) k < 4 (b) k > 4 (c) k = 4 (d) k = 4
1
6 The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5 units (b) 12 units (c) 11 units (d) (7 + v5) units
1
7
If in triangles ABC and DEF,
AB
DE
=
BC
FD
, then they will be similar, when
(a) ?B = ?E (b) ?A = ?D (c) ?B = ?D (d) ?A = ?F
1
8 In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?.
(a) 1 : 5 (b) 5 : 1 (c) 1 : 1 (d) 1 : 2
1
9 In the figure, if PA and PB are tangents to the circle
with centre O such that ?APB = 50°, then ?OAB is
equal to
(a) 25° (b) 30° (c) 40° (d) 50°
1
10
If sin A =
1
2
, then the value of sec A is :
(a)
2
v3
(b)
1
v3
(c) v3
(d) 1
1
11
v3 cos
2
A + v3 sin
2
A is equal to
(a) 1
(b)
1
v3
(c) v3
(d) 0
1
12
The value of cos1° . cos2° . cos3° . cos4°. . . . . . . . . . . .. cos90° is
(a) 1 (b) 0 (c) – 1 (d) 2
1
13 If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
(a) 22 : 7 (b) 14 : 11 (c) 7 : 22 (d) 11: 14
1
14 If the radii of two circles are in the ratio of 4 : 3, then their areas are in the ratio of :
(a) 4 : 3 (b) 8 : 3 (c) 16 : 9 (d) 9 : 16
1
15 The total surface area of a solid hemisphere of radius 7 cm is :
(a) 447p cm
2
(b) 239p cm
2
(c) 174p cm
2
(d) 147p cm
2
1
16
For the following distribution :
Class 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25
Frequency 10 15 12 20 9
the upper limit of the modal class is
(a) 10 (b) 15 (c) 20 (d) 25
1
17 If the mean of the following distribution is 2.6, then the value of y is
Variable (x) 1 2 3 4 5
Frequency 4 5 y 1 2
(a) 3 (b) 8 (c) 13 (d) 24
1
18
A card is selected at random from a well shuffled deck of 52 cards. The probability of its
being a red face card is
(a)
3
26
(b)
3
13
(c)
2
13
(d)
1
2
1
Direction for questions 19 & 20: In question numbers 19 and 20, a statement of
Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
19
Assertion: If HCF of 510 and 92 is 2, then the LCM of 510 & 92 is 32460
Reason: as HCF(a,b) x LCM(a,b) = a x b
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation
of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct
explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
1
20
Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally
divided by x axis is 1:2.
Reason (R): as formula for the internal division is (
?? ?? 2
+ ?? ?? 1
?? + ??
,
?? ?? 2
+ ?? ?? 1
?? + ??
)
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation
of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct
explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
1
Section B
Section B consists of 5 questions of 2 marks each.
21 For what values of k will the following pair of linear equations have infinitely many
solutions?
kx + 3y – (k – 3) = 0
12x + ky – k = 0
2
22 In the figure, altitudes AD and CE of ? ABC intersect
each other at the point P. Show that:
(i) ?ABD ~ ?CBE
(ii) ?PDC ~ ?BEC
[OR]
In the figure, DE || AC and DF || AE. Prove that
BF
FE
=
BE
EC
2
23 Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger
circle which touches the smaller circle.
2
24
If cot? =
7
8
, evaluate
(1 + sin ?) (1- sin ?)
(1 + cos ?) (1- cos ?)
2
25 Find the perimeter of a quadrant of a circle of radius 14 cm.
[OR]
Find the diameter of a circle whose area is equal to the sum of the areas of the two circles
of radii 24 cm and 7 cm.
2
Section C
Section C consists of 6 questions of 3 marks each.
26
Prove that v5 is an irrational number.
3
27 Find the zeroes of the quadratic polynomial 6x
2
– 3 – 7x and verify the relationship
between the zeroes and the coefficients.
3
28 A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two
days, and an additional charge for each day thereafter. Latika paid Rs 22 for a book kept
for six days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges
and the charge for each extra day.
[OR]
Places A and B are 100 km apart on a highway. One car starts from A and another from B
at the same time. If the cars travel in the same direction at different speeds, they meet in 5
3
Page 5
Class - X Session 2022-23
Subject - Mathematics (Basic)
Sample Question Paper
Time Allowed: 3 Hours Maximum Marks: 80
General Instructions:
1. This Question Paper has 5 Sections A, B, C, D, and E.
2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.
4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.
5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each.
6. Section E has 3 Case Based integrated units of assessment (4 marks each) with sub-parts of
the values of 1, 1 and 2 marks each respectively.
7. All Questions are compulsory. However, an internal choice in 2 Qs of 2 marks, 2 Qs of 3 marks
and 2 Questions of 5 marks has been provided. An internal choice has been provided in the 2
marks questions of Section E.
8. Draw neat figures wherever required. Take p =22/7 wherever required if not stated.
Section A
Section A consists of 20 questions of 1 mark each.
SN Ma
rks
1 If two positive integers p and q can be expressed as p = ab
2
and q = a
3
b; a, b being prime
numbers, then LCM (p, q) is
(a) ab (b) a
2
b
2
(c) a
3
b
2
(d) a
3
b
3
1
2 What is the greatest possible speed at which a man can walk 52 km and 91 km in an exact
number of hours?
(a) 17 km/hours (b) 7 km/hours
(c) 13 km/hours (d) 26 km/hours
1
3 If one zero of the quadratic polynomial x
2
+ 3x + k is 2, then the value of k is
(a) 10 (b) -10 (c) 5 (d) –5
1
4
Graphically, the pair of equations given by
6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are
(a) intersecting at exactly one point. (b) parallel.
(c) coincident. (d) intersecting at exactly two points.
1
5 If the quadratic equation x
2
+ 4x + k = 0 has real and equal roots, then
(a) k < 4 (b) k > 4 (c) k = 4 (d) k = 4
1
6 The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5 units (b) 12 units (c) 11 units (d) (7 + v5) units
1
7
If in triangles ABC and DEF,
AB
DE
=
BC
FD
, then they will be similar, when
(a) ?B = ?E (b) ?A = ?D (c) ?B = ?D (d) ?A = ?F
1
8 In which ratio the y-axis divides the line segment joining the points (5, – 6) and (–1, – 4)?.
(a) 1 : 5 (b) 5 : 1 (c) 1 : 1 (d) 1 : 2
1
9 In the figure, if PA and PB are tangents to the circle
with centre O such that ?APB = 50°, then ?OAB is
equal to
(a) 25° (b) 30° (c) 40° (d) 50°
1
10
If sin A =
1
2
, then the value of sec A is :
(a)
2
v3
(b)
1
v3
(c) v3
(d) 1
1
11
v3 cos
2
A + v3 sin
2
A is equal to
(a) 1
(b)
1
v3
(c) v3
(d) 0
1
12
The value of cos1° . cos2° . cos3° . cos4°. . . . . . . . . . . .. cos90° is
(a) 1 (b) 0 (c) – 1 (d) 2
1
13 If the perimeter of a circle is equal to that of a square, then the ratio of their areas is
(a) 22 : 7 (b) 14 : 11 (c) 7 : 22 (d) 11: 14
1
14 If the radii of two circles are in the ratio of 4 : 3, then their areas are in the ratio of :
(a) 4 : 3 (b) 8 : 3 (c) 16 : 9 (d) 9 : 16
1
15 The total surface area of a solid hemisphere of radius 7 cm is :
(a) 447p cm
2
(b) 239p cm
2
(c) 174p cm
2
(d) 147p cm
2
1
16
For the following distribution :
Class 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25
Frequency 10 15 12 20 9
the upper limit of the modal class is
(a) 10 (b) 15 (c) 20 (d) 25
1
17 If the mean of the following distribution is 2.6, then the value of y is
Variable (x) 1 2 3 4 5
Frequency 4 5 y 1 2
(a) 3 (b) 8 (c) 13 (d) 24
1
18
A card is selected at random from a well shuffled deck of 52 cards. The probability of its
being a red face card is
(a)
3
26
(b)
3
13
(c)
2
13
(d)
1
2
1
Direction for questions 19 & 20: In question numbers 19 and 20, a statement of
Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
19
Assertion: If HCF of 510 and 92 is 2, then the LCM of 510 & 92 is 32460
Reason: as HCF(a,b) x LCM(a,b) = a x b
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation
of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct
explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
1
20
Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally
divided by x axis is 1:2.
Reason (R): as formula for the internal division is (
?? ?? 2
+ ?? ?? 1
?? + ??
,
?? ?? 2
+ ?? ?? 1
?? + ??
)
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation
of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct
explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.
1
Section B
Section B consists of 5 questions of 2 marks each.
21 For what values of k will the following pair of linear equations have infinitely many
solutions?
kx + 3y – (k – 3) = 0
12x + ky – k = 0
2
22 In the figure, altitudes AD and CE of ? ABC intersect
each other at the point P. Show that:
(i) ?ABD ~ ?CBE
(ii) ?PDC ~ ?BEC
[OR]
In the figure, DE || AC and DF || AE. Prove that
BF
FE
=
BE
EC
2
23 Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger
circle which touches the smaller circle.
2
24
If cot? =
7
8
, evaluate
(1 + sin ?) (1- sin ?)
(1 + cos ?) (1- cos ?)
2
25 Find the perimeter of a quadrant of a circle of radius 14 cm.
[OR]
Find the diameter of a circle whose area is equal to the sum of the areas of the two circles
of radii 24 cm and 7 cm.
2
Section C
Section C consists of 6 questions of 3 marks each.
26
Prove that v5 is an irrational number.
3
27 Find the zeroes of the quadratic polynomial 6x
2
– 3 – 7x and verify the relationship
between the zeroes and the coefficients.
3
28 A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two
days, and an additional charge for each day thereafter. Latika paid Rs 22 for a book kept
for six days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges
and the charge for each extra day.
[OR]
Places A and B are 100 km apart on a highway. One car starts from A and another from B
at the same time. If the cars travel in the same direction at different speeds, they meet in 5
3
hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the
two cars?
29 In the figure, PQ is a chord of length 8 cm of a circle of
radius 5 cm. The tangents at P and Q intersect at a point
T. Find the length TP.
3
30 Prove that
tan?
1 - cot?
+
cot?
1 - tan?
= 1 + sec?cosec?
[OR]
If sin ? + cos ? = v3, then prove that tan ? + cot ? = 1
3
31
Two dice are thrown at the same time. What is the probability that the sum of the two
numbers appearing on the top of the dice is
(i) 8?
(ii) 13?
(iii) less than or equal to 12?
3
Section D
Section D consists of 4 questions of 5 marks each.
32 An express train takes 1 hour less than a passenger train to travel 132 km between
Mysore and Bangalore (without taking into consideration the time they stop at intermediate
stations). If the average speed of the express train is 11km/h more than that of the
passenger train, find the average speed of the two trains.
[OR]
A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km
upstream than to return downstream to the same spot. Find the speed of the stream.
5
33 Prove that If a line is drawn parallel to one side of a
triangle to intersect the other two sides in distinct
points, the other two sides are divided in the same
ratio. In the figure, find EC if
AD
DB
=
AE
EC
using the above
theorem.
5
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