Class 10 Mathematics (Standard) Term I: CBSE (Official) Sample Question Paper (2021-22) | Mathematics (Maths) Class 10 PDF Download

 Page 1


Sample Question Paper 
Class – X Session -2021-22 
TERM 1 
Subject- Mathematics (Standard) 041  
Time Allowed: 90 minutes                                                                                  Maximum Marks: 40 
General Instructions: 
1. The question paper contains three parts A, B and C 
2. Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
4 Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions. 
5. There is no negative marking.  
 
 SECTION A  
 
 Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
 
 
Q No 
 
Marks 
1 The ratio of LCM and HCF of the least composite and the least prime numbers is 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
 
 
1 
 
2 The value of k for which the lines 5x+7y=3 and 15x + 21y = k coincide is 
(a) 9 (b) 5 (c) 7 (d) 18 
 
1 
 
 
3 A girl walks 200m towards East and then 150m towards North. The distance of the girl 
from the starting point is   
(a)350m (b) 250m (c) 300m (d) 225 
 
 
1 
 
 
 
4 The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the 
altitude of the rhombus is 
(a) 12cm (b) 12.8cm (c) 19 cm` (d) 19.2cm 
 
 
1 
 
 
 
5 Two fair coins are tossed. What is the probability of getting at the most one head? 
(a) ¾ (b) ¼ (c) ½ (d) 3/8  
 
 
1 
 
6 ?ABC~?PQR. If AM and PN are altitudes of ?ABC and ?PQR respectively and AB
2 
: 
PQ
2
 = 4 : 9, then AM:PN = 
(a) 16:81 (b) 4:9 (c) 3:2  (d) 2:3 
 
 
1 
 
 
7 If  2sin
2
ß – cos
2
ß = 2, then ß is 
(a) 0? 
 
(b) 90? (c) 45? 
 
(d) 30? 
 
 
1 
 
 
8 Prime factors of the denominator of a rational number with  the decimal expansion 
44.123 are  
(a) 2,3 (b) 2,3,5 (c) 2,5 (d) 3,5 
 
 
1 
 
9 The lines x = a and y = b, are 
(a) intersecting  (b) parallel  (c) overlapping  (d) (None of these)  
 
 
1 
 
 
10 The distance of point A(-5, 6) from the origin is 
(a) 11 units 
 
(b) 61 units (c) v11 units 
 
(d) v61 units 
 
 
1 
 
 
11 If a² = 23/25, then a is 
(a) rational (b) irrational (c) whole number (d) integer 
 
 
 
1 
 
Page 2


Sample Question Paper 
Class – X Session -2021-22 
TERM 1 
Subject- Mathematics (Standard) 041  
Time Allowed: 90 minutes                                                                                  Maximum Marks: 40 
General Instructions: 
1. The question paper contains three parts A, B and C 
2. Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
4 Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions. 
5. There is no negative marking.  
 
 SECTION A  
 
 Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
 
 
Q No 
 
Marks 
1 The ratio of LCM and HCF of the least composite and the least prime numbers is 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
 
 
1 
 
2 The value of k for which the lines 5x+7y=3 and 15x + 21y = k coincide is 
(a) 9 (b) 5 (c) 7 (d) 18 
 
1 
 
 
3 A girl walks 200m towards East and then 150m towards North. The distance of the girl 
from the starting point is   
(a)350m (b) 250m (c) 300m (d) 225 
 
 
1 
 
 
 
4 The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the 
altitude of the rhombus is 
(a) 12cm (b) 12.8cm (c) 19 cm` (d) 19.2cm 
 
 
1 
 
 
 
5 Two fair coins are tossed. What is the probability of getting at the most one head? 
(a) ¾ (b) ¼ (c) ½ (d) 3/8  
 
 
1 
 
6 ?ABC~?PQR. If AM and PN are altitudes of ?ABC and ?PQR respectively and AB
2 
: 
PQ
2
 = 4 : 9, then AM:PN = 
(a) 16:81 (b) 4:9 (c) 3:2  (d) 2:3 
 
 
1 
 
 
7 If  2sin
2
ß – cos
2
ß = 2, then ß is 
(a) 0? 
 
(b) 90? (c) 45? 
 
(d) 30? 
 
 
1 
 
 
8 Prime factors of the denominator of a rational number with  the decimal expansion 
44.123 are  
(a) 2,3 (b) 2,3,5 (c) 2,5 (d) 3,5 
 
 
1 
 
9 The lines x = a and y = b, are 
(a) intersecting  (b) parallel  (c) overlapping  (d) (None of these)  
 
 
1 
 
 
10 The distance of point A(-5, 6) from the origin is 
(a) 11 units 
 
(b) 61 units (c) v11 units 
 
(d) v61 units 
 
 
1 
 
 
11 If a² = 23/25, then a is 
(a) rational (b) irrational (c) whole number (d) integer 
 
 
 
1 
 
12 If LCM(x, 18) =36 and HCF(x, 18) =2, then x is 
(a) 2 (b) 3 (c) 4 (d) 5 
 
 
1 
 
 
13 
In ?ABC right angled at B, if tan A= v3, then cos A cos C- sin A sin C = 
(a) -1 (b) 0 (c) 1 
(d) v3/2 
 
 
1 
 
14 If the angles of ?ABC are in ratio 1:1:2, respectively (the largest angle being      angle 
C), then the value of 
sec A
cosec B
 –  
tan A
cot B
  is 
(a) 0 (b) 1/2 (c) 1 
(d) v3/2 
 
 
1 
 
 
 
15 The number of revolutions made by a circular wheel of radius  0.7m  in rolling a distance 
of 176m is 
(a) 22 (b) 24 (c) 75 (d) 40  
 
 
1 
 
16 ?ABC is such that AB=3 cm, BC= 2cm, CA= 2.5 cm. If ?ABC ~ ?DEF and           EF = 
4cm, then perimeter of ?DEF is 
(a) 7.5 cm (b) 15 cm (c) 22.5 cm (d) 30 cm 
 
 
1 
 
17 In the figure, if DE? BC, AD = 3cm, BD = 4cm and BC= 14 cm, then DE equals 
 
 
(a) 7cm (b) 6cm (c) 4cm (d) 3cm 
 
 
1 
 
 
18 
If 4 tanß = 3, then 
 4 ???????? -3 cos ?? 4 sin ?? +3 cos ?? = 
(a) 0 (b) 1/3 (c) 2/3 (d) ¾ 
 
 
1 
 
 
19 One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation 
can be 
a) 10x+14y +4 = 0 b) –10x –14y+ 4 = 0 c) –10x+14y + 4 = 0 (d) 10x – 14y = –4 
 
 
1 
 
 
 
20 A letter of English alphabets is chosen at random. What is the probability that it is a letter 
of the word ‘MATHEMATICS’? 
(a) 4/13 (b) 9/26 (c) 5/13 (d) 11/26 
 
 
1 
 
 SECTION B 
 
 
 Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted  
QN 
 
MARKS 
21 If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs 
of such numbers are 
(a) 2 (b) 3 (c) 4 (d) 5 
 
 
1 
22 Given below is the graph representing two linear equations by lines AB and CD 
respectively. What is the area of the triangle formed by these two lines and the line x=0?  
 
1 
Page 3


Sample Question Paper 
Class – X Session -2021-22 
TERM 1 
Subject- Mathematics (Standard) 041  
Time Allowed: 90 minutes                                                                                  Maximum Marks: 40 
General Instructions: 
1. The question paper contains three parts A, B and C 
2. Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
4 Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions. 
5. There is no negative marking.  
 
 SECTION A  
 
 Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
 
 
Q No 
 
Marks 
1 The ratio of LCM and HCF of the least composite and the least prime numbers is 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
 
 
1 
 
2 The value of k for which the lines 5x+7y=3 and 15x + 21y = k coincide is 
(a) 9 (b) 5 (c) 7 (d) 18 
 
1 
 
 
3 A girl walks 200m towards East and then 150m towards North. The distance of the girl 
from the starting point is   
(a)350m (b) 250m (c) 300m (d) 225 
 
 
1 
 
 
 
4 The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the 
altitude of the rhombus is 
(a) 12cm (b) 12.8cm (c) 19 cm` (d) 19.2cm 
 
 
1 
 
 
 
5 Two fair coins are tossed. What is the probability of getting at the most one head? 
(a) ¾ (b) ¼ (c) ½ (d) 3/8  
 
 
1 
 
6 ?ABC~?PQR. If AM and PN are altitudes of ?ABC and ?PQR respectively and AB
2 
: 
PQ
2
 = 4 : 9, then AM:PN = 
(a) 16:81 (b) 4:9 (c) 3:2  (d) 2:3 
 
 
1 
 
 
7 If  2sin
2
ß – cos
2
ß = 2, then ß is 
(a) 0? 
 
(b) 90? (c) 45? 
 
(d) 30? 
 
 
1 
 
 
8 Prime factors of the denominator of a rational number with  the decimal expansion 
44.123 are  
(a) 2,3 (b) 2,3,5 (c) 2,5 (d) 3,5 
 
 
1 
 
9 The lines x = a and y = b, are 
(a) intersecting  (b) parallel  (c) overlapping  (d) (None of these)  
 
 
1 
 
 
10 The distance of point A(-5, 6) from the origin is 
(a) 11 units 
 
(b) 61 units (c) v11 units 
 
(d) v61 units 
 
 
1 
 
 
11 If a² = 23/25, then a is 
(a) rational (b) irrational (c) whole number (d) integer 
 
 
 
1 
 
12 If LCM(x, 18) =36 and HCF(x, 18) =2, then x is 
(a) 2 (b) 3 (c) 4 (d) 5 
 
 
1 
 
 
13 
In ?ABC right angled at B, if tan A= v3, then cos A cos C- sin A sin C = 
(a) -1 (b) 0 (c) 1 
(d) v3/2 
 
 
1 
 
14 If the angles of ?ABC are in ratio 1:1:2, respectively (the largest angle being      angle 
C), then the value of 
sec A
cosec B
 –  
tan A
cot B
  is 
(a) 0 (b) 1/2 (c) 1 
(d) v3/2 
 
 
1 
 
 
 
15 The number of revolutions made by a circular wheel of radius  0.7m  in rolling a distance 
of 176m is 
(a) 22 (b) 24 (c) 75 (d) 40  
 
 
1 
 
16 ?ABC is such that AB=3 cm, BC= 2cm, CA= 2.5 cm. If ?ABC ~ ?DEF and           EF = 
4cm, then perimeter of ?DEF is 
(a) 7.5 cm (b) 15 cm (c) 22.5 cm (d) 30 cm 
 
 
1 
 
17 In the figure, if DE? BC, AD = 3cm, BD = 4cm and BC= 14 cm, then DE equals 
 
 
(a) 7cm (b) 6cm (c) 4cm (d) 3cm 
 
 
1 
 
 
18 
If 4 tanß = 3, then 
 4 ???????? -3 cos ?? 4 sin ?? +3 cos ?? = 
(a) 0 (b) 1/3 (c) 2/3 (d) ¾ 
 
 
1 
 
 
19 One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation 
can be 
a) 10x+14y +4 = 0 b) –10x –14y+ 4 = 0 c) –10x+14y + 4 = 0 (d) 10x – 14y = –4 
 
 
1 
 
 
 
20 A letter of English alphabets is chosen at random. What is the probability that it is a letter 
of the word ‘MATHEMATICS’? 
(a) 4/13 (b) 9/26 (c) 5/13 (d) 11/26 
 
 
1 
 
 SECTION B 
 
 
 Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted  
QN 
 
MARKS 
21 If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs 
of such numbers are 
(a) 2 (b) 3 (c) 4 (d) 5 
 
 
1 
22 Given below is the graph representing two linear equations by lines AB and CD 
respectively. What is the area of the triangle formed by these two lines and the line x=0?  
 
1 
 
  
(a) 3sq. units (b) 4sq. units (c) 6sq. units (d) 8sq. units  
 
 
23 If tan a + cot a = 2, then tan
20
a + cot
20
a = 
(a) 0 (b) 2 (c) 20 (d) 2
20
 
 
 
1 
24 If 217x + 131y = 913, 131x + 217y = 827, then x + y is 
(a) 5 (b) 6 (c) 7 (d) 8 
 
 
1 
25 The LCM of two prime numbers p and q (p > q) is 221. Find the value of 3p – q. 
(a) 4 (b) 28 (c) 38 (d) 48 
 
  
1 
26 A card is drawn from a well shuffled deck of cards. What is the probability that the 
card drawn is neither a king nor a queen? 
(a) 11/13 (b) 12/13 (c) 11/26 (d) 11/52  
 
 
1 
27 Two fair dice are rolled simultaneously. The  probability that 5 will come up at least 
once is 
(a) 5/36 (b) 11/36 (c) 12/36 (d) 23/36 
 
 
1 
28 If 1+ sin
2
a = 3 sina cosa, then values of cot a are  
(a) -1, 1 (b) 0,1 (c)1, 2 (d) -1,-1 
 
 
1 
29 The vertices of a parallelogram in order are A(1,2), B(4, y),  C(x, 6) and D(3,5). Then    
(x, y) is 
(a) (6, 3) (b) (3, 6) (c) (5, 6) (d) (1, 4) 
 
1 
30 In the given figure, ?ACB = ?CDA, AC = 8cm, AD = 3cm, then BD is 
 
(a) 22/3 cm (b) 26/3 cm (c) 55/3 cm (d) 64/3 cm 
 
 
1 
31 The equation of the perpendicular bisector of line segment joining points A(4,5) and     
B(-2,3) is 
(a) 2x – y +7=0 (b) 3x +2 y – 7=0 (c) 3x – y – 7 =0 (d) 3x + y – 7=0 
 
 
1 
Page 4


Sample Question Paper 
Class – X Session -2021-22 
TERM 1 
Subject- Mathematics (Standard) 041  
Time Allowed: 90 minutes                                                                                  Maximum Marks: 40 
General Instructions: 
1. The question paper contains three parts A, B and C 
2. Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
4 Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions. 
5. There is no negative marking.  
 
 SECTION A  
 
 Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
 
 
Q No 
 
Marks 
1 The ratio of LCM and HCF of the least composite and the least prime numbers is 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
 
 
1 
 
2 The value of k for which the lines 5x+7y=3 and 15x + 21y = k coincide is 
(a) 9 (b) 5 (c) 7 (d) 18 
 
1 
 
 
3 A girl walks 200m towards East and then 150m towards North. The distance of the girl 
from the starting point is   
(a)350m (b) 250m (c) 300m (d) 225 
 
 
1 
 
 
 
4 The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the 
altitude of the rhombus is 
(a) 12cm (b) 12.8cm (c) 19 cm` (d) 19.2cm 
 
 
1 
 
 
 
5 Two fair coins are tossed. What is the probability of getting at the most one head? 
(a) ¾ (b) ¼ (c) ½ (d) 3/8  
 
 
1 
 
6 ?ABC~?PQR. If AM and PN are altitudes of ?ABC and ?PQR respectively and AB
2 
: 
PQ
2
 = 4 : 9, then AM:PN = 
(a) 16:81 (b) 4:9 (c) 3:2  (d) 2:3 
 
 
1 
 
 
7 If  2sin
2
ß – cos
2
ß = 2, then ß is 
(a) 0? 
 
(b) 90? (c) 45? 
 
(d) 30? 
 
 
1 
 
 
8 Prime factors of the denominator of a rational number with  the decimal expansion 
44.123 are  
(a) 2,3 (b) 2,3,5 (c) 2,5 (d) 3,5 
 
 
1 
 
9 The lines x = a and y = b, are 
(a) intersecting  (b) parallel  (c) overlapping  (d) (None of these)  
 
 
1 
 
 
10 The distance of point A(-5, 6) from the origin is 
(a) 11 units 
 
(b) 61 units (c) v11 units 
 
(d) v61 units 
 
 
1 
 
 
11 If a² = 23/25, then a is 
(a) rational (b) irrational (c) whole number (d) integer 
 
 
 
1 
 
12 If LCM(x, 18) =36 and HCF(x, 18) =2, then x is 
(a) 2 (b) 3 (c) 4 (d) 5 
 
 
1 
 
 
13 
In ?ABC right angled at B, if tan A= v3, then cos A cos C- sin A sin C = 
(a) -1 (b) 0 (c) 1 
(d) v3/2 
 
 
1 
 
14 If the angles of ?ABC are in ratio 1:1:2, respectively (the largest angle being      angle 
C), then the value of 
sec A
cosec B
 –  
tan A
cot B
  is 
(a) 0 (b) 1/2 (c) 1 
(d) v3/2 
 
 
1 
 
 
 
15 The number of revolutions made by a circular wheel of radius  0.7m  in rolling a distance 
of 176m is 
(a) 22 (b) 24 (c) 75 (d) 40  
 
 
1 
 
16 ?ABC is such that AB=3 cm, BC= 2cm, CA= 2.5 cm. If ?ABC ~ ?DEF and           EF = 
4cm, then perimeter of ?DEF is 
(a) 7.5 cm (b) 15 cm (c) 22.5 cm (d) 30 cm 
 
 
1 
 
17 In the figure, if DE? BC, AD = 3cm, BD = 4cm and BC= 14 cm, then DE equals 
 
 
(a) 7cm (b) 6cm (c) 4cm (d) 3cm 
 
 
1 
 
 
18 
If 4 tanß = 3, then 
 4 ???????? -3 cos ?? 4 sin ?? +3 cos ?? = 
(a) 0 (b) 1/3 (c) 2/3 (d) ¾ 
 
 
1 
 
 
19 One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation 
can be 
a) 10x+14y +4 = 0 b) –10x –14y+ 4 = 0 c) –10x+14y + 4 = 0 (d) 10x – 14y = –4 
 
 
1 
 
 
 
20 A letter of English alphabets is chosen at random. What is the probability that it is a letter 
of the word ‘MATHEMATICS’? 
(a) 4/13 (b) 9/26 (c) 5/13 (d) 11/26 
 
 
1 
 
 SECTION B 
 
 
 Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted  
QN 
 
MARKS 
21 If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs 
of such numbers are 
(a) 2 (b) 3 (c) 4 (d) 5 
 
 
1 
22 Given below is the graph representing two linear equations by lines AB and CD 
respectively. What is the area of the triangle formed by these two lines and the line x=0?  
 
1 
 
  
(a) 3sq. units (b) 4sq. units (c) 6sq. units (d) 8sq. units  
 
 
23 If tan a + cot a = 2, then tan
20
a + cot
20
a = 
(a) 0 (b) 2 (c) 20 (d) 2
20
 
 
 
1 
24 If 217x + 131y = 913, 131x + 217y = 827, then x + y is 
(a) 5 (b) 6 (c) 7 (d) 8 
 
 
1 
25 The LCM of two prime numbers p and q (p > q) is 221. Find the value of 3p – q. 
(a) 4 (b) 28 (c) 38 (d) 48 
 
  
1 
26 A card is drawn from a well shuffled deck of cards. What is the probability that the 
card drawn is neither a king nor a queen? 
(a) 11/13 (b) 12/13 (c) 11/26 (d) 11/52  
 
 
1 
27 Two fair dice are rolled simultaneously. The  probability that 5 will come up at least 
once is 
(a) 5/36 (b) 11/36 (c) 12/36 (d) 23/36 
 
 
1 
28 If 1+ sin
2
a = 3 sina cosa, then values of cot a are  
(a) -1, 1 (b) 0,1 (c)1, 2 (d) -1,-1 
 
 
1 
29 The vertices of a parallelogram in order are A(1,2), B(4, y),  C(x, 6) and D(3,5). Then    
(x, y) is 
(a) (6, 3) (b) (3, 6) (c) (5, 6) (d) (1, 4) 
 
1 
30 In the given figure, ?ACB = ?CDA, AC = 8cm, AD = 3cm, then BD is 
 
(a) 22/3 cm (b) 26/3 cm (c) 55/3 cm (d) 64/3 cm 
 
 
1 
31 The equation of the perpendicular bisector of line segment joining points A(4,5) and     
B(-2,3) is 
(a) 2x – y +7=0 (b) 3x +2 y – 7=0 (c) 3x – y – 7 =0 (d) 3x + y – 7=0 
 
 
1 
32 
In the given figure, D is the mid-point of BC, then the value of  
cot ?? °
cot ?? °
 is  
 
(a) 2 (b) 1/2 (c) 1/3 (d) 1/4 
 
 
1 
33 The smallest number by which 1/13 should be multiplied so that its decimal expansion 
terminates after two decimal places is 
(a) 13/100 (b) 13/10 (c) 10/13 (d) 100/13 
 
 
1 
34 Sides AB and BE of a right triangle, right angled at B are of lengths 16 cm and 8 cm 
respectively. The length of the side of largest square FDGB that can be inscribed in the 
triangle  ABE is 
 
 
(a) 32/3cm (b) 16/3cm (c)8/3cm (d) 4/3cm 
 
 
1 
35 Point P divides the line segment joining R(-1, 3) and S(9,8) in ratio k:1. If P lies on the 
line x – y +2=0, then value of k is 
(a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4 
 
 
1 
36 In the figure given below, ABCD is a square of side 14 cm with E, F, G and H as the mid 
points of sides AB, BC, CD and DA respectively. The area of the shaded portion is 
 
 
 
(a) 44cm² (b) 49 cm² (c) 98 cm² (d) 49p/2 cm² 
 
1 
37 Given below is the picture of the Olympic rings made by taking five congruent circles 
of radius 1cm each, intersecting in such a way that the chord formed by joining the 
point of intersection of two circles is also of length 1cm. Total area of all  the dotted 
regions assuming the thickness of the rings to be negligible is 
 
1 
Page 5


Sample Question Paper 
Class – X Session -2021-22 
TERM 1 
Subject- Mathematics (Standard) 041  
Time Allowed: 90 minutes                                                                                  Maximum Marks: 40 
General Instructions: 
1. The question paper contains three parts A, B and C 
2. Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
4 Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions. 
5. There is no negative marking.  
 
 SECTION A  
 
 Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted 
 
 
Q No 
 
Marks 
1 The ratio of LCM and HCF of the least composite and the least prime numbers is 
(a) 1:2 (b) 2:1 (c) 1:1 (d) 1:3 
 
 
1 
 
2 The value of k for which the lines 5x+7y=3 and 15x + 21y = k coincide is 
(a) 9 (b) 5 (c) 7 (d) 18 
 
1 
 
 
3 A girl walks 200m towards East and then 150m towards North. The distance of the girl 
from the starting point is   
(a)350m (b) 250m (c) 300m (d) 225 
 
 
1 
 
 
 
4 The lengths of the diagonals of a rhombus are 24cm and 32cm, then the length of the 
altitude of the rhombus is 
(a) 12cm (b) 12.8cm (c) 19 cm` (d) 19.2cm 
 
 
1 
 
 
 
5 Two fair coins are tossed. What is the probability of getting at the most one head? 
(a) ¾ (b) ¼ (c) ½ (d) 3/8  
 
 
1 
 
6 ?ABC~?PQR. If AM and PN are altitudes of ?ABC and ?PQR respectively and AB
2 
: 
PQ
2
 = 4 : 9, then AM:PN = 
(a) 16:81 (b) 4:9 (c) 3:2  (d) 2:3 
 
 
1 
 
 
7 If  2sin
2
ß – cos
2
ß = 2, then ß is 
(a) 0? 
 
(b) 90? (c) 45? 
 
(d) 30? 
 
 
1 
 
 
8 Prime factors of the denominator of a rational number with  the decimal expansion 
44.123 are  
(a) 2,3 (b) 2,3,5 (c) 2,5 (d) 3,5 
 
 
1 
 
9 The lines x = a and y = b, are 
(a) intersecting  (b) parallel  (c) overlapping  (d) (None of these)  
 
 
1 
 
 
10 The distance of point A(-5, 6) from the origin is 
(a) 11 units 
 
(b) 61 units (c) v11 units 
 
(d) v61 units 
 
 
1 
 
 
11 If a² = 23/25, then a is 
(a) rational (b) irrational (c) whole number (d) integer 
 
 
 
1 
 
12 If LCM(x, 18) =36 and HCF(x, 18) =2, then x is 
(a) 2 (b) 3 (c) 4 (d) 5 
 
 
1 
 
 
13 
In ?ABC right angled at B, if tan A= v3, then cos A cos C- sin A sin C = 
(a) -1 (b) 0 (c) 1 
(d) v3/2 
 
 
1 
 
14 If the angles of ?ABC are in ratio 1:1:2, respectively (the largest angle being      angle 
C), then the value of 
sec A
cosec B
 –  
tan A
cot B
  is 
(a) 0 (b) 1/2 (c) 1 
(d) v3/2 
 
 
1 
 
 
 
15 The number of revolutions made by a circular wheel of radius  0.7m  in rolling a distance 
of 176m is 
(a) 22 (b) 24 (c) 75 (d) 40  
 
 
1 
 
16 ?ABC is such that AB=3 cm, BC= 2cm, CA= 2.5 cm. If ?ABC ~ ?DEF and           EF = 
4cm, then perimeter of ?DEF is 
(a) 7.5 cm (b) 15 cm (c) 22.5 cm (d) 30 cm 
 
 
1 
 
17 In the figure, if DE? BC, AD = 3cm, BD = 4cm and BC= 14 cm, then DE equals 
 
 
(a) 7cm (b) 6cm (c) 4cm (d) 3cm 
 
 
1 
 
 
18 
If 4 tanß = 3, then 
 4 ???????? -3 cos ?? 4 sin ?? +3 cos ?? = 
(a) 0 (b) 1/3 (c) 2/3 (d) ¾ 
 
 
1 
 
 
19 One equation of a pair of dependent linear equations is –5x + 7y = 2. The second equation 
can be 
a) 10x+14y +4 = 0 b) –10x –14y+ 4 = 0 c) –10x+14y + 4 = 0 (d) 10x – 14y = –4 
 
 
1 
 
 
 
20 A letter of English alphabets is chosen at random. What is the probability that it is a letter 
of the word ‘MATHEMATICS’? 
(a) 4/13 (b) 9/26 (c) 5/13 (d) 11/26 
 
 
1 
 
 SECTION B 
 
 
 Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted  
QN 
 
MARKS 
21 If sum of two numbers is 1215 and their HCF is 81, then the possible number of pairs 
of such numbers are 
(a) 2 (b) 3 (c) 4 (d) 5 
 
 
1 
22 Given below is the graph representing two linear equations by lines AB and CD 
respectively. What is the area of the triangle formed by these two lines and the line x=0?  
 
1 
 
  
(a) 3sq. units (b) 4sq. units (c) 6sq. units (d) 8sq. units  
 
 
23 If tan a + cot a = 2, then tan
20
a + cot
20
a = 
(a) 0 (b) 2 (c) 20 (d) 2
20
 
 
 
1 
24 If 217x + 131y = 913, 131x + 217y = 827, then x + y is 
(a) 5 (b) 6 (c) 7 (d) 8 
 
 
1 
25 The LCM of two prime numbers p and q (p > q) is 221. Find the value of 3p – q. 
(a) 4 (b) 28 (c) 38 (d) 48 
 
  
1 
26 A card is drawn from a well shuffled deck of cards. What is the probability that the 
card drawn is neither a king nor a queen? 
(a) 11/13 (b) 12/13 (c) 11/26 (d) 11/52  
 
 
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27 Two fair dice are rolled simultaneously. The  probability that 5 will come up at least 
once is 
(a) 5/36 (b) 11/36 (c) 12/36 (d) 23/36 
 
 
1 
28 If 1+ sin
2
a = 3 sina cosa, then values of cot a are  
(a) -1, 1 (b) 0,1 (c)1, 2 (d) -1,-1 
 
 
1 
29 The vertices of a parallelogram in order are A(1,2), B(4, y),  C(x, 6) and D(3,5). Then    
(x, y) is 
(a) (6, 3) (b) (3, 6) (c) (5, 6) (d) (1, 4) 
 
1 
30 In the given figure, ?ACB = ?CDA, AC = 8cm, AD = 3cm, then BD is 
 
(a) 22/3 cm (b) 26/3 cm (c) 55/3 cm (d) 64/3 cm 
 
 
1 
31 The equation of the perpendicular bisector of line segment joining points A(4,5) and     
B(-2,3) is 
(a) 2x – y +7=0 (b) 3x +2 y – 7=0 (c) 3x – y – 7 =0 (d) 3x + y – 7=0 
 
 
1 
32 
In the given figure, D is the mid-point of BC, then the value of  
cot ?? °
cot ?? °
 is  
 
(a) 2 (b) 1/2 (c) 1/3 (d) 1/4 
 
 
1 
33 The smallest number by which 1/13 should be multiplied so that its decimal expansion 
terminates after two decimal places is 
(a) 13/100 (b) 13/10 (c) 10/13 (d) 100/13 
 
 
1 
34 Sides AB and BE of a right triangle, right angled at B are of lengths 16 cm and 8 cm 
respectively. The length of the side of largest square FDGB that can be inscribed in the 
triangle  ABE is 
 
 
(a) 32/3cm (b) 16/3cm (c)8/3cm (d) 4/3cm 
 
 
1 
35 Point P divides the line segment joining R(-1, 3) and S(9,8) in ratio k:1. If P lies on the 
line x – y +2=0, then value of k is 
(a) 2/3 (b) 1/2 (c) 1/3 (d) 1/4 
 
 
1 
36 In the figure given below, ABCD is a square of side 14 cm with E, F, G and H as the mid 
points of sides AB, BC, CD and DA respectively. The area of the shaded portion is 
 
 
 
(a) 44cm² (b) 49 cm² (c) 98 cm² (d) 49p/2 cm² 
 
1 
37 Given below is the picture of the Olympic rings made by taking five congruent circles 
of radius 1cm each, intersecting in such a way that the chord formed by joining the 
point of intersection of two circles is also of length 1cm. Total area of all  the dotted 
regions assuming the thickness of the rings to be negligible is 
 
1 
 
(a) 4(p/12-v3/4) cm² (b) (p/6 - v3/4) cm² (c) 4(p/6 - v3/4) cm² (d) 8(p/6 - v3/4) cm² 
 
 
38 If 2 and  ½ are the zeros of px
2
+5x+r, then 
(a) p = r = 2 (b) p = r = - 2 (c) p  = 2, r= -2 (d) p = -2, r= 2 
 
 
1 
39 The circumference of a circle is 100 cm. The side of a square inscribed in the circle is 
(a) 50v2 cm (b) 100/p cm (c)  50v2/p cm (d) 100v2/p cm 
 
 
1 
40 The number of solutions of 3
x+y 
= 243 and  243
x-y 
= 3 is 
(a) 0 (b) 1 (c) 2 (d) infinite 
 
 
1 
 SECTION C 
 
 
 Case study based questions: 
Section C consists of 10 questions of 1 mark each. Any 8 questions are to be 
attempted. 
 
 
 Q41-Q45 are based on Case Study -1 
 
Case Study -1 
 
 
41 What is the value of k? 
(a) 0     
(b) - 48      
(c) 48   
(d) 48/-16 
1 
42 At what time will she touch the water in the pool? 
(a) 30 seconds         
(b) 2 seconds                    
(c) 1.5 seconds               
(d) 0.5 seconds 
1 
The figure given alongside shows the path of a 
diver, when she takes a jump from the diving 
board. Clearly it is a parabola.  
Annie was standing on a diving board, 48 feet 
above the water level. She took a dive into the 
pool. Her height (in feet) above the water level at 
any time‘t’ in seconds is given by the polynomial 
h(t) such that 
                 h(t) = -16t² + 8t + k.