Class 10 Mathematics (Basic): CBSE (Official) Sample Question Paper (2022-23) | Mathematics (Maths) Class 10 PDF Download

 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