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Class- X Session- 2022-23 
Subject- Mathematics (Standard) 
Sample Question Paper 
Time Allowed: 3 Hrs.                                                                            Maximum Marks : 80 
General Instructions: 
  
1. This Question Paper has 5 Sections A-E.  
2. Section A  has 20 MCQs carrying 1 mark each   
3. Section B has 5 questions carrying 02 marks each.  
4. Section C has 6 questions carrying 03 marks each.  
5. Section D has 4 questions carrying 05 marks each.  
6. Section E has 3 case based integrated units of assessment (04 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 5 marks, 2 Qs 
of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has 
been provided in the 2marks 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.   
S.NO
. 
 MA
RKS 
1  Let a and b be two positive integers such that a = p
3
q
4 
and b = p
2
q
3
 , where p and q are 
prime numbers. If  HCF(a,b) = p
m
q
n 
 and LCM(a,b) = p
r
q
s
, then (m+n)(r+s)=  
(a) 15 (b) 30 (c) 35 (d) 72 
 
 
1 
2 Let p be a prime number. The quadratic equation having its roots as factors of p is  
(a) x
2
 –px +p=0 (b) x
2
–(p+1)x +p=0 (c) x
2
+(p+1)x +p=0 (d) x
2
 –px+p+1=0 
 
 
1 
3 If a and ß are the zeros of a polynomial f(x) = px
2
 – 2x + 3p and a + ß  = aß, then p is 
 
(a)-2/3 (b) 2/3 (c) 1/3 (d) -1/3 
 
 
1 
4 If the system of equations 3x+y =1 and (2k-1)x +(k-1)y =2k+1 is inconsistent, then k =  
(a) -1 (b) 0 (c) 1 (d) 2 
 
 
1 
5 If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), 
then the coordinates of its fourth vertex S are 
(a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2)   
  
 
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) 3:2 (b) 16:81 (c) 4:9 (d) 2:3 
 
    
 
1 
Page 2


Class- X Session- 2022-23 
Subject- Mathematics (Standard) 
Sample Question Paper 
Time Allowed: 3 Hrs.                                                                            Maximum Marks : 80 
General Instructions: 
  
1. This Question Paper has 5 Sections A-E.  
2. Section A  has 20 MCQs carrying 1 mark each   
3. Section B has 5 questions carrying 02 marks each.  
4. Section C has 6 questions carrying 03 marks each.  
5. Section D has 4 questions carrying 05 marks each.  
6. Section E has 3 case based integrated units of assessment (04 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 5 marks, 2 Qs 
of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has 
been provided in the 2marks 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.   
S.NO
. 
 MA
RKS 
1  Let a and b be two positive integers such that a = p
3
q
4 
and b = p
2
q
3
 , where p and q are 
prime numbers. If  HCF(a,b) = p
m
q
n 
 and LCM(a,b) = p
r
q
s
, then (m+n)(r+s)=  
(a) 15 (b) 30 (c) 35 (d) 72 
 
 
1 
2 Let p be a prime number. The quadratic equation having its roots as factors of p is  
(a) x
2
 –px +p=0 (b) x
2
–(p+1)x +p=0 (c) x
2
+(p+1)x +p=0 (d) x
2
 –px+p+1=0 
 
 
1 
3 If a and ß are the zeros of a polynomial f(x) = px
2
 – 2x + 3p and a + ß  = aß, then p is 
 
(a)-2/3 (b) 2/3 (c) 1/3 (d) -1/3 
 
 
1 
4 If the system of equations 3x+y =1 and (2k-1)x +(k-1)y =2k+1 is inconsistent, then k =  
(a) -1 (b) 0 (c) 1 (d) 2 
 
 
1 
5 If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), 
then the coordinates of its fourth vertex S are 
(a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2)   
  
 
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) 3:2 (b) 16:81 (c) 4:9 (d) 2:3 
 
    
 
1 
7 If x tan 60
°
cos 60
°
= sin60
°
cot 60
°
, then x = 
(a) cos30° 
 
(b) tan30° (c) sin30° 
 
(d) cot30° 
 
 
1 
8 
If sin? + cos? = v2, then tan? + cot ? = 
(a) 1 (b) 2 (c) 3 (d) 4 
 
 
1 
9 In the given figure, DE ? BC, AE = a units, EC =b units, DE =x units and BC = y 
units. Which of the following is true? 
 
 
 
 
(a) x= 
?? +?? ????
  
(b) y= 
????
?? +??   (c) x= 
????
?? +?? (d) 
?? ?? = 
?? ?? 
 
 
1 
10 ABCD is a trapezium with AD ? BC and AD = 4cm. If the diagonals AC and BD 
intersect each other at O such that AO/OC = DO/OB =1/2, then BC = 
(a) 6cm 
 
(b) 7cm (c) 8cm 
 
(d) 9cm 
 
 
1 
11 If two tangents inclined at an angle of 60? are drawn to a circle of radius 3cm, then the 
length of each tangent is equal to 
(a) 
3v3
2
 cm 
(b) 3cm (c) 6cm (d) 3v3cm 
 
 
1 
12 The area of  the circle that can be inscribed in a square of 6cm is 
(a) 36p cm
2 
(b) 18p  cm
2
 (c) 12 p cm
2
 (d) 9p  cm
2
 
 
  
1 
13 The sum of the length, breadth and height of a cuboid is 6v3cm and the length of its 
diagonal is 2v3cm. The total surface area of the cuboid is 
(a) 48 cm
2 
(b) 72 cm
2
 (c) 96 cm
2
 (d) 108 cm
2
 
 
 
1 
14 If the difference of Mode and Median of a data is 24, then the difference of median 
and mean is 
(a) 8 (b) 12 (c) 24 (d) 36 
 
 
1 
15 The number of revolutions made by a circular wheel of radius 0.25m in rolling a 
distance of 11km is 
(a) 2800 (b) 4000 (c) 5500 (d) 7000 
 
 
1 
16 For the following distribution,  
 
Class 0-5 5-10 10-15 15-20 20-25 
Frequency 10 15 12 20 9 
the sum of the lower limits of the median and modal class is 
(a) 15  (b) 25 (c) 30 (d) 35 
 
1 
Page 3


Class- X Session- 2022-23 
Subject- Mathematics (Standard) 
Sample Question Paper 
Time Allowed: 3 Hrs.                                                                            Maximum Marks : 80 
General Instructions: 
  
1. This Question Paper has 5 Sections A-E.  
2. Section A  has 20 MCQs carrying 1 mark each   
3. Section B has 5 questions carrying 02 marks each.  
4. Section C has 6 questions carrying 03 marks each.  
5. Section D has 4 questions carrying 05 marks each.  
6. Section E has 3 case based integrated units of assessment (04 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 5 marks, 2 Qs 
of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has 
been provided in the 2marks 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.   
S.NO
. 
 MA
RKS 
1  Let a and b be two positive integers such that a = p
3
q
4 
and b = p
2
q
3
 , where p and q are 
prime numbers. If  HCF(a,b) = p
m
q
n 
 and LCM(a,b) = p
r
q
s
, then (m+n)(r+s)=  
(a) 15 (b) 30 (c) 35 (d) 72 
 
 
1 
2 Let p be a prime number. The quadratic equation having its roots as factors of p is  
(a) x
2
 –px +p=0 (b) x
2
–(p+1)x +p=0 (c) x
2
+(p+1)x +p=0 (d) x
2
 –px+p+1=0 
 
 
1 
3 If a and ß are the zeros of a polynomial f(x) = px
2
 – 2x + 3p and a + ß  = aß, then p is 
 
(a)-2/3 (b) 2/3 (c) 1/3 (d) -1/3 
 
 
1 
4 If the system of equations 3x+y =1 and (2k-1)x +(k-1)y =2k+1 is inconsistent, then k =  
(a) -1 (b) 0 (c) 1 (d) 2 
 
 
1 
5 If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), 
then the coordinates of its fourth vertex S are 
(a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2)   
  
 
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) 3:2 (b) 16:81 (c) 4:9 (d) 2:3 
 
    
 
1 
7 If x tan 60
°
cos 60
°
= sin60
°
cot 60
°
, then x = 
(a) cos30° 
 
(b) tan30° (c) sin30° 
 
(d) cot30° 
 
 
1 
8 
If sin? + cos? = v2, then tan? + cot ? = 
(a) 1 (b) 2 (c) 3 (d) 4 
 
 
1 
9 In the given figure, DE ? BC, AE = a units, EC =b units, DE =x units and BC = y 
units. Which of the following is true? 
 
 
 
 
(a) x= 
?? +?? ????
  
(b) y= 
????
?? +??   (c) x= 
????
?? +?? (d) 
?? ?? = 
?? ?? 
 
 
1 
10 ABCD is a trapezium with AD ? BC and AD = 4cm. If the diagonals AC and BD 
intersect each other at O such that AO/OC = DO/OB =1/2, then BC = 
(a) 6cm 
 
(b) 7cm (c) 8cm 
 
(d) 9cm 
 
 
1 
11 If two tangents inclined at an angle of 60? are drawn to a circle of radius 3cm, then the 
length of each tangent is equal to 
(a) 
3v3
2
 cm 
(b) 3cm (c) 6cm (d) 3v3cm 
 
 
1 
12 The area of  the circle that can be inscribed in a square of 6cm is 
(a) 36p cm
2 
(b) 18p  cm
2
 (c) 12 p cm
2
 (d) 9p  cm
2
 
 
  
1 
13 The sum of the length, breadth and height of a cuboid is 6v3cm and the length of its 
diagonal is 2v3cm. The total surface area of the cuboid is 
(a) 48 cm
2 
(b) 72 cm
2
 (c) 96 cm
2
 (d) 108 cm
2
 
 
 
1 
14 If the difference of Mode and Median of a data is 24, then the difference of median 
and mean is 
(a) 8 (b) 12 (c) 24 (d) 36 
 
 
1 
15 The number of revolutions made by a circular wheel of radius 0.25m in rolling a 
distance of 11km is 
(a) 2800 (b) 4000 (c) 5500 (d) 7000 
 
 
1 
16 For the following distribution,  
 
Class 0-5 5-10 10-15 15-20 20-25 
Frequency 10 15 12 20 9 
the sum of the lower limits of the median and modal class is 
(a) 15  (b) 25 (c) 30 (d) 35 
 
1 
17 Two dice are rolled simultaneously. What is the probability that 6 will come up at least 
once? 
 
(a)1/6 (b) 7/36 (c) 11/36 (d) 13/36 
 
 
1 
18 
If 5 tanß =4, then 
 5 ???????? -2 cos ?? 5 sin ?? +2 cos ?? = 
 
(a) 1/3 (b) 2/5 (c) 3/5 (d) 6 
 
 
1 
 
 
 
 
 
19 
 
 
 
 
 
 
 
 
 
 
 
DIRECTION: In the question number 19 and 20, a statement of assertion (A) is 
followed by a statement of Reason (R).  
Choose the correct option 
 
Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then 
their LCM is 340 
 
Statement R( Reason) : HCF is always a factor of LCM 
 
(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 and 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 
 
Statement A (Assertion): If the co-ordinates of the mid-points of the sides AB and AC 
of  ?ABC are D(3,5) and E(-3,-3) respectively, then BC = 20 units 
 
Statement R( Reason) : The line joining the mid points of two sides of a triangle is 
parallel to the third side and equal to half of it. 
 
(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 and 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 
 
 
Page 4


Class- X Session- 2022-23 
Subject- Mathematics (Standard) 
Sample Question Paper 
Time Allowed: 3 Hrs.                                                                            Maximum Marks : 80 
General Instructions: 
  
1. This Question Paper has 5 Sections A-E.  
2. Section A  has 20 MCQs carrying 1 mark each   
3. Section B has 5 questions carrying 02 marks each.  
4. Section C has 6 questions carrying 03 marks each.  
5. Section D has 4 questions carrying 05 marks each.  
6. Section E has 3 case based integrated units of assessment (04 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 5 marks, 2 Qs 
of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has 
been provided in the 2marks 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.   
S.NO
. 
 MA
RKS 
1  Let a and b be two positive integers such that a = p
3
q
4 
and b = p
2
q
3
 , where p and q are 
prime numbers. If  HCF(a,b) = p
m
q
n 
 and LCM(a,b) = p
r
q
s
, then (m+n)(r+s)=  
(a) 15 (b) 30 (c) 35 (d) 72 
 
 
1 
2 Let p be a prime number. The quadratic equation having its roots as factors of p is  
(a) x
2
 –px +p=0 (b) x
2
–(p+1)x +p=0 (c) x
2
+(p+1)x +p=0 (d) x
2
 –px+p+1=0 
 
 
1 
3 If a and ß are the zeros of a polynomial f(x) = px
2
 – 2x + 3p and a + ß  = aß, then p is 
 
(a)-2/3 (b) 2/3 (c) 1/3 (d) -1/3 
 
 
1 
4 If the system of equations 3x+y =1 and (2k-1)x +(k-1)y =2k+1 is inconsistent, then k =  
(a) -1 (b) 0 (c) 1 (d) 2 
 
 
1 
5 If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), 
then the coordinates of its fourth vertex S are 
(a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2)   
  
 
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) 3:2 (b) 16:81 (c) 4:9 (d) 2:3 
 
    
 
1 
7 If x tan 60
°
cos 60
°
= sin60
°
cot 60
°
, then x = 
(a) cos30° 
 
(b) tan30° (c) sin30° 
 
(d) cot30° 
 
 
1 
8 
If sin? + cos? = v2, then tan? + cot ? = 
(a) 1 (b) 2 (c) 3 (d) 4 
 
 
1 
9 In the given figure, DE ? BC, AE = a units, EC =b units, DE =x units and BC = y 
units. Which of the following is true? 
 
 
 
 
(a) x= 
?? +?? ????
  
(b) y= 
????
?? +??   (c) x= 
????
?? +?? (d) 
?? ?? = 
?? ?? 
 
 
1 
10 ABCD is a trapezium with AD ? BC and AD = 4cm. If the diagonals AC and BD 
intersect each other at O such that AO/OC = DO/OB =1/2, then BC = 
(a) 6cm 
 
(b) 7cm (c) 8cm 
 
(d) 9cm 
 
 
1 
11 If two tangents inclined at an angle of 60? are drawn to a circle of radius 3cm, then the 
length of each tangent is equal to 
(a) 
3v3
2
 cm 
(b) 3cm (c) 6cm (d) 3v3cm 
 
 
1 
12 The area of  the circle that can be inscribed in a square of 6cm is 
(a) 36p cm
2 
(b) 18p  cm
2
 (c) 12 p cm
2
 (d) 9p  cm
2
 
 
  
1 
13 The sum of the length, breadth and height of a cuboid is 6v3cm and the length of its 
diagonal is 2v3cm. The total surface area of the cuboid is 
(a) 48 cm
2 
(b) 72 cm
2
 (c) 96 cm
2
 (d) 108 cm
2
 
 
 
1 
14 If the difference of Mode and Median of a data is 24, then the difference of median 
and mean is 
(a) 8 (b) 12 (c) 24 (d) 36 
 
 
1 
15 The number of revolutions made by a circular wheel of radius 0.25m in rolling a 
distance of 11km is 
(a) 2800 (b) 4000 (c) 5500 (d) 7000 
 
 
1 
16 For the following distribution,  
 
Class 0-5 5-10 10-15 15-20 20-25 
Frequency 10 15 12 20 9 
the sum of the lower limits of the median and modal class is 
(a) 15  (b) 25 (c) 30 (d) 35 
 
1 
17 Two dice are rolled simultaneously. What is the probability that 6 will come up at least 
once? 
 
(a)1/6 (b) 7/36 (c) 11/36 (d) 13/36 
 
 
1 
18 
If 5 tanß =4, then 
 5 ???????? -2 cos ?? 5 sin ?? +2 cos ?? = 
 
(a) 1/3 (b) 2/5 (c) 3/5 (d) 6 
 
 
1 
 
 
 
 
 
19 
 
 
 
 
 
 
 
 
 
 
 
DIRECTION: In the question number 19 and 20, a statement of assertion (A) is 
followed by a statement of Reason (R).  
Choose the correct option 
 
Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then 
their LCM is 340 
 
Statement R( Reason) : HCF is always a factor of LCM 
 
(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 and 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 
 
Statement A (Assertion): If the co-ordinates of the mid-points of the sides AB and AC 
of  ?ABC are D(3,5) and E(-3,-3) respectively, then BC = 20 units 
 
Statement R( Reason) : The line joining the mid points of two sides of a triangle is 
parallel to the third side and equal to half of it. 
 
(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 and 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.   
S.No.  Marks 
21 If 49x+51y= 499, 51 x+49 y= 501, then find the value of x and y  
 
2 
22 
In the given figure below, 
AD
AE
=
AC
BD
 and ?1 = ?2.  Show that ? BAE ~ ?CAD .        
                                     
                                                                    
2 
23 In the given figure, O is the centre of circle. Find ?AQB , given that PA and PB are 
tangents to the circle and ?APB = 75°. 
 
 
2 
24 
The length of the minute hand of a clock is 6cm. Find the area swept by it when it moves 
from 7:05 p.m. to 7:40 p.m.  
 
OR 
In the given figure, arcs have been drawn of radius 7cm each with vertices A, B, C 
and D of quadrilateral ABCD as centres. Find the area of the shaded region.                               
                                               
2 
Page 5


Class- X Session- 2022-23 
Subject- Mathematics (Standard) 
Sample Question Paper 
Time Allowed: 3 Hrs.                                                                            Maximum Marks : 80 
General Instructions: 
  
1. This Question Paper has 5 Sections A-E.  
2. Section A  has 20 MCQs carrying 1 mark each   
3. Section B has 5 questions carrying 02 marks each.  
4. Section C has 6 questions carrying 03 marks each.  
5. Section D has 4 questions carrying 05 marks each.  
6. Section E has 3 case based integrated units of assessment (04 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 5 marks, 2 Qs 
of 3 marks and 2 Questions of 2 marks has been provided. An internal choice has 
been provided in the 2marks 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.   
S.NO
. 
 MA
RKS 
1  Let a and b be two positive integers such that a = p
3
q
4 
and b = p
2
q
3
 , where p and q are 
prime numbers. If  HCF(a,b) = p
m
q
n 
 and LCM(a,b) = p
r
q
s
, then (m+n)(r+s)=  
(a) 15 (b) 30 (c) 35 (d) 72 
 
 
1 
2 Let p be a prime number. The quadratic equation having its roots as factors of p is  
(a) x
2
 –px +p=0 (b) x
2
–(p+1)x +p=0 (c) x
2
+(p+1)x +p=0 (d) x
2
 –px+p+1=0 
 
 
1 
3 If a and ß are the zeros of a polynomial f(x) = px
2
 – 2x + 3p and a + ß  = aß, then p is 
 
(a)-2/3 (b) 2/3 (c) 1/3 (d) -1/3 
 
 
1 
4 If the system of equations 3x+y =1 and (2k-1)x +(k-1)y =2k+1 is inconsistent, then k =  
(a) -1 (b) 0 (c) 1 (d) 2 
 
 
1 
5 If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), 
then the coordinates of its fourth vertex S are 
(a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2)   
  
 
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) 3:2 (b) 16:81 (c) 4:9 (d) 2:3 
 
    
 
1 
7 If x tan 60
°
cos 60
°
= sin60
°
cot 60
°
, then x = 
(a) cos30° 
 
(b) tan30° (c) sin30° 
 
(d) cot30° 
 
 
1 
8 
If sin? + cos? = v2, then tan? + cot ? = 
(a) 1 (b) 2 (c) 3 (d) 4 
 
 
1 
9 In the given figure, DE ? BC, AE = a units, EC =b units, DE =x units and BC = y 
units. Which of the following is true? 
 
 
 
 
(a) x= 
?? +?? ????
  
(b) y= 
????
?? +??   (c) x= 
????
?? +?? (d) 
?? ?? = 
?? ?? 
 
 
1 
10 ABCD is a trapezium with AD ? BC and AD = 4cm. If the diagonals AC and BD 
intersect each other at O such that AO/OC = DO/OB =1/2, then BC = 
(a) 6cm 
 
(b) 7cm (c) 8cm 
 
(d) 9cm 
 
 
1 
11 If two tangents inclined at an angle of 60? are drawn to a circle of radius 3cm, then the 
length of each tangent is equal to 
(a) 
3v3
2
 cm 
(b) 3cm (c) 6cm (d) 3v3cm 
 
 
1 
12 The area of  the circle that can be inscribed in a square of 6cm is 
(a) 36p cm
2 
(b) 18p  cm
2
 (c) 12 p cm
2
 (d) 9p  cm
2
 
 
  
1 
13 The sum of the length, breadth and height of a cuboid is 6v3cm and the length of its 
diagonal is 2v3cm. The total surface area of the cuboid is 
(a) 48 cm
2 
(b) 72 cm
2
 (c) 96 cm
2
 (d) 108 cm
2
 
 
 
1 
14 If the difference of Mode and Median of a data is 24, then the difference of median 
and mean is 
(a) 8 (b) 12 (c) 24 (d) 36 
 
 
1 
15 The number of revolutions made by a circular wheel of radius 0.25m in rolling a 
distance of 11km is 
(a) 2800 (b) 4000 (c) 5500 (d) 7000 
 
 
1 
16 For the following distribution,  
 
Class 0-5 5-10 10-15 15-20 20-25 
Frequency 10 15 12 20 9 
the sum of the lower limits of the median and modal class is 
(a) 15  (b) 25 (c) 30 (d) 35 
 
1 
17 Two dice are rolled simultaneously. What is the probability that 6 will come up at least 
once? 
 
(a)1/6 (b) 7/36 (c) 11/36 (d) 13/36 
 
 
1 
18 
If 5 tanß =4, then 
 5 ???????? -2 cos ?? 5 sin ?? +2 cos ?? = 
 
(a) 1/3 (b) 2/5 (c) 3/5 (d) 6 
 
 
1 
 
 
 
 
 
19 
 
 
 
 
 
 
 
 
 
 
 
DIRECTION: In the question number 19 and 20, a statement of assertion (A) is 
followed by a statement of Reason (R).  
Choose the correct option 
 
Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then 
their LCM is 340 
 
Statement R( Reason) : HCF is always a factor of LCM 
 
(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 and 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 
 
Statement A (Assertion): If the co-ordinates of the mid-points of the sides AB and AC 
of  ?ABC are D(3,5) and E(-3,-3) respectively, then BC = 20 units 
 
Statement R( Reason) : The line joining the mid points of two sides of a triangle is 
parallel to the third side and equal to half of it. 
 
(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 and 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.   
S.No.  Marks 
21 If 49x+51y= 499, 51 x+49 y= 501, then find the value of x and y  
 
2 
22 
In the given figure below, 
AD
AE
=
AC
BD
 and ?1 = ?2.  Show that ? BAE ~ ?CAD .        
                                     
                                                                    
2 
23 In the given figure, O is the centre of circle. Find ?AQB , given that PA and PB are 
tangents to the circle and ?APB = 75°. 
 
 
2 
24 
The length of the minute hand of a clock is 6cm. Find the area swept by it when it moves 
from 7:05 p.m. to 7:40 p.m.  
 
OR 
In the given figure, arcs have been drawn of radius 7cm each with vertices A, B, C 
and D of quadrilateral ABCD as centres. Find the area of the shaded region.                               
                                               
2 
 
25 If sin(A+B) =1 and cos(A-B)= v3/2, 0°< A+B = 90° and A> B, then find the 
measures of angles A and B. 
 
OR 
 
Find an acute angle ? when 
cos? - sin ?
cos?+sin ?
 = 
1-v3
1+v3
  
  
2 
 
 SECTION C 
 
 
 Section C consists of 6 questions of 3 marks each.   
S.No  Marks 
26 
Given that v3 is irrational , prove that 5 + 2v3 is irrational. 
 
3 
27 If the zeroes of the polynomial x
2
 +px +q are double in value to the zeroes of the 
polynomial 2x
2
 -5x -3, then find the values of p and q. 
 
3 
28 
A train covered a certain distance at a uniform speed. If the train would have been 6 km/h 
faster, it would have taken 4 hours less than the scheduled time. And, if the train were 
slower by 6 km/hr ; it would have taken 6 hours more than the scheduled time. Find the 
length of the journey. 
 
OR 
Anuj had some chocolates, and he divided them into two lots A and B. He sold the first 
lot at the rate of ?2 for 3 chocolates and the second lot at the rate of ?1 per chocolate, and 
got a total of ?400. If he had sold the first lot at the rate of  ?1 per chocolate, and the 
second lot at the rate of ?4 for 5 chocolates, his total collection would have been ?460. 
Find the total number of chocolates he had. 
 
3 
29 Prove the following that- 
 
   tan
3
?     +     cot
3
?     =  sec? cosec? – 2 sin? cos? 
1+ tan
2
?        1+ cot
2
? 
 
3 
30 Prove that a parallelogram circumscribing a circle is a rhombus 
 
OR 
 
3 
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FAQs on Class 10 Mathematics: CBSE Sample Question Paper (2022-23) (Standard) - 1 - CBSE Sample Papers For Class 10

1. What is the format of the CBSE Sample Question Paper for Class 10 Mathematics?
Ans. The CBSE Sample Question Paper for Class 10 Mathematics follows the standard format prescribed by the CBSE board. It includes a variety of questions such as multiple choice questions, short answer type questions, and long answer type questions. The paper is divided into different sections, each focusing on specific topics or concepts. The total marks and time duration for the examination are also mentioned in the question paper.
2. How can I access the CBSE Sample Question Paper for Class 10 Mathematics (Standard)?
Ans. The CBSE Sample Question Paper for Class 10 Mathematics (Standard) can be accessed through various sources. The official website of CBSE (Central Board of Secondary Education) provides these sample papers for free download. Additionally, many educational websites and online platforms also offer these sample papers in PDF format. Students can search for the specific year's sample paper and download it for practice.
3. Are the CBSE Sample Question Papers for Class 10 Mathematics (Standard) helpful for exam preparation?
Ans. Yes, the CBSE Sample Question Papers for Class 10 Mathematics (Standard) are extremely helpful for exam preparation. These sample papers are designed by subject experts based on the latest CBSE curriculum and exam pattern. By solving these papers, students can get familiar with the question paper format, marking scheme, and the level of difficulty. It helps them assess their preparation level and identify areas where they need improvement. Regular practice with these sample papers can boost confidence and enhance problem-solving skills.
4. Can I expect similar questions from the CBSE Sample Question Paper in the actual Class 10 Mathematics exam?
Ans. While the CBSE Sample Question Paper for Class 10 Mathematics (Standard) provides a good idea about the type of questions that can be asked in the exam, it is important to note that the actual exam may have variations. The sample papers are intended to give students a comprehensive understanding of the concepts and practice different types of questions. However, the specific questions in the actual exam may differ in terms of wording, numerical values, or the way they are presented. Hence, it is advisable to thoroughly study the entire syllabus and not rely solely on the sample papers.
5. Are there any specific tips to effectively utilize the CBSE Sample Question Papers for Class 10 Mathematics (Standard)?
Ans. Yes, here are some tips to effectively utilize the CBSE Sample Question Papers for Class 10 Mathematics (Standard): 1. Start by understanding the pattern: Familiarize yourself with the question paper pattern, marking scheme, and time duration mentioned in the sample paper. 2. Solve the sample papers under exam-like conditions: Set a timer and solve the sample papers within the given time limit. This will help you improve your speed and time management skills. 3. Analyze your mistakes: After solving the sample papers, carefully analyze your mistakes and the areas where you face difficulty. Focus on improving those areas through targeted practice. 4. Practice regularly: Use the sample papers as a regular practice resource. Solve them at least once a week to reinforce your understanding of concepts and improve problem-solving abilities. 5. Seek help when needed: If you encounter any doubts or difficulties while solving the sample papers, do not hesitate to seek help from your teachers, classmates, or online platforms. Clarifying your doubts will enhance your understanding and prepare you better for the actual exam.
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