SAMPLE QUESTION PAPER
Class X Session 2024-25
MATHEMATICS STANDARD (Code No.041)
TIME: 3 hours MAX.MARKS: 80
General Instructions:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19
and 20 are Assertion- Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks
each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with
sub parts of the values of 1, 1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2
Questions of Section C and 2 Questions of Section D has been provided. An internal choice has
been provided in all the 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take π =22/7 wherever required if not stated.
11. Use of calculators is not allowed.
Section A
Section A consists of 20 questions of 1 mark each.
1. The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30), 1
(4,-20) and (6,0). The zeroes of the polynomial are
A) - 6,0 B) 4, 6 C) - 30,-20 D) - 6,6
2. The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is 1
inconsistent, is
A) -10 B) -5 C) 5 D) 7
3. Which of the following statements is not true? 1
A) A number of secants can be drawn at any point on the circle.
B) Only one tangent can be drawn at any point on a circle.
C) A chord is a line segment joining two points on the circle
D) From a point inside a circle only two tangents can be drawn.
4. If nth term of an A.P. is 7n-4 then the common difference of the A.P. is 1
A) 7 B) 7n C) - 4 D) 4
,5. The radius of the base of a right circular cone and the radius of a sphere are each 5 cm 1
in length. If the volume of the cone is equal to the volume of the sphere then the height
of the cone is
A) 5 cm B) 20 cm C) 10 cm D) 4 cm
6. 5 4 𝑠𝑖𝑛𝜃 + 𝑐𝑜𝑠𝜃 1
If tan𝜃 = then is equal to
2 4 𝑠𝑖𝑛𝜃 − 𝑐𝑜𝑠𝜃
11 3 9
A) B) C) D) 4
9 2 11
7. In the given figure, a tangent has been drawn at a point P on the circle centred at O. 1
Q
O
T P
If ∠ TPQ= 110𝑂 then ∠POQ is equal to
A) 110𝑂 B) 70𝑂 C) 140𝑂 D)55𝑂
8. 5 5 1
A quadratic polynomial having zeroes - √ and √ is
2 2
A) 𝑥 2 − 5√2 x +1 B) 8𝑥 2 - 20 C) 15𝑥 2 - 6 D) 𝑥 2 - 2√5 x -1
9. Consider the frequency distribution of 45 observations. 1
Class 0-10 10-20 20-30 30-40 40-50
Frequency 5 9 15 10 6
The upper limit of median class is
A) 20 B) 10 C) 30 D) 40
10. O is the point of intersection of two chords AB and CD of a circle. 1
B
D O
A C
If ∠𝐵𝑂𝐶 = 80𝑂 and OA = OD then 𝛥𝑂𝐷𝐴 𝑎𝑛𝑑 𝛥𝑂𝐵𝐶 are
A) equilateral and similar B) isosceles and similar
C) isosceles but not similar D) not similar
, 11. The roots of the quadratic equation 𝑥 2 +x-1 = 0 are 1
A) Irrational and distinct B) not real
C ) rational and distinct D) real and equal
12. If 𝜃 = 30𝑜 then the value of 3tan𝜃 is 1
1 3
A)1 B) C) (D) not defined
√3 √3
13. 396 1
The volume of a solid hemisphere is 𝑐𝑚 3.The total surface area of the solid
7
hemisphere (in sq.cm) is
396 594 549 604
A) B) C) D)
7 7 7 7
14. In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is 1
drawn at random. The probability that drawn ball is white in colour is
1 3 11 5
𝐴) B) C) D)
6 8 24 8
15. The point on the x- axis nearest to the point (-4,-5) is 1
A) (0, 0) B) (-4, 0) C ) (-5, 0) D) (√41, 0)
16. Which of the following gives the middle most observation of the data? 1
A) Median B) Mean C) Range D) Mode
17. A point on the x-axis divides the line segment joining the points A(2, -3) and B(5, 6) in 1
the ratio 1:2. The point is
7 3
A) (4, 0) B) ( , ) C) (3, 0) D) (0,3)
2 2
18. A card is drawn from a well shuffled deck of playing cards. The probability of getting red 1
face card is
3 1 3 3
𝐴) B) C) D)
13 2 52 26
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
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.
19. Assertion (A): HCF of any two consecutive even natural numbers is always 2. 1
Reason (R): Even natural numbers are divisible by 2.
20. Assertion (A): If the radius of sector of a circle is reduced to its half and angle is 1
doubled then the perimeter of the sector remains the same.
Class X Session 2024-25
MATHEMATICS STANDARD (Code No.041)
TIME: 3 hours MAX.MARKS: 80
General Instructions:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Questions no. 1-18 are multiple choice questions (MCQs) and questions no. 19
and 20 are Assertion- Reason based questions of 1 mark each.
4. In Section B, Questions no. 21-25 are very short answer (VSA) type questions, carrying 02 marks
each.
5. In Section C, Questions no. 26-31 are short answer (SA) type questions, carrying 03 marks each.
6. In Section D, Questions no. 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Questions no. 36-38 are case study based questions carrying 4 marks each with
sub parts of the values of 1, 1 and 2 marks each respectively.
8. All Questions are compulsory. However, an internal choice in 2 Question of Section B, 2
Questions of Section C and 2 Questions of Section D has been provided. An internal choice has
been provided in all the 2 marks questions of Section E.
9. Draw neat and clean figures wherever required.
10. Take π =22/7 wherever required if not stated.
11. Use of calculators is not allowed.
Section A
Section A consists of 20 questions of 1 mark each.
1. The graph of a quadratic polynomial p(x) passes through the points (-6,0), (0, -30), 1
(4,-20) and (6,0). The zeroes of the polynomial are
A) - 6,0 B) 4, 6 C) - 30,-20 D) - 6,6
2. The value of k for which the system of equations 3x-ky= 7 and 6x+ 10y =3 is 1
inconsistent, is
A) -10 B) -5 C) 5 D) 7
3. Which of the following statements is not true? 1
A) A number of secants can be drawn at any point on the circle.
B) Only one tangent can be drawn at any point on a circle.
C) A chord is a line segment joining two points on the circle
D) From a point inside a circle only two tangents can be drawn.
4. If nth term of an A.P. is 7n-4 then the common difference of the A.P. is 1
A) 7 B) 7n C) - 4 D) 4
,5. The radius of the base of a right circular cone and the radius of a sphere are each 5 cm 1
in length. If the volume of the cone is equal to the volume of the sphere then the height
of the cone is
A) 5 cm B) 20 cm C) 10 cm D) 4 cm
6. 5 4 𝑠𝑖𝑛𝜃 + 𝑐𝑜𝑠𝜃 1
If tan𝜃 = then is equal to
2 4 𝑠𝑖𝑛𝜃 − 𝑐𝑜𝑠𝜃
11 3 9
A) B) C) D) 4
9 2 11
7. In the given figure, a tangent has been drawn at a point P on the circle centred at O. 1
Q
O
T P
If ∠ TPQ= 110𝑂 then ∠POQ is equal to
A) 110𝑂 B) 70𝑂 C) 140𝑂 D)55𝑂
8. 5 5 1
A quadratic polynomial having zeroes - √ and √ is
2 2
A) 𝑥 2 − 5√2 x +1 B) 8𝑥 2 - 20 C) 15𝑥 2 - 6 D) 𝑥 2 - 2√5 x -1
9. Consider the frequency distribution of 45 observations. 1
Class 0-10 10-20 20-30 30-40 40-50
Frequency 5 9 15 10 6
The upper limit of median class is
A) 20 B) 10 C) 30 D) 40
10. O is the point of intersection of two chords AB and CD of a circle. 1
B
D O
A C
If ∠𝐵𝑂𝐶 = 80𝑂 and OA = OD then 𝛥𝑂𝐷𝐴 𝑎𝑛𝑑 𝛥𝑂𝐵𝐶 are
A) equilateral and similar B) isosceles and similar
C) isosceles but not similar D) not similar
, 11. The roots of the quadratic equation 𝑥 2 +x-1 = 0 are 1
A) Irrational and distinct B) not real
C ) rational and distinct D) real and equal
12. If 𝜃 = 30𝑜 then the value of 3tan𝜃 is 1
1 3
A)1 B) C) (D) not defined
√3 √3
13. 396 1
The volume of a solid hemisphere is 𝑐𝑚 3.The total surface area of the solid
7
hemisphere (in sq.cm) is
396 594 549 604
A) B) C) D)
7 7 7 7
14. In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is 1
drawn at random. The probability that drawn ball is white in colour is
1 3 11 5
𝐴) B) C) D)
6 8 24 8
15. The point on the x- axis nearest to the point (-4,-5) is 1
A) (0, 0) B) (-4, 0) C ) (-5, 0) D) (√41, 0)
16. Which of the following gives the middle most observation of the data? 1
A) Median B) Mean C) Range D) Mode
17. A point on the x-axis divides the line segment joining the points A(2, -3) and B(5, 6) in 1
the ratio 1:2. The point is
7 3
A) (4, 0) B) ( , ) C) (3, 0) D) (0,3)
2 2
18. A card is drawn from a well shuffled deck of playing cards. The probability of getting red 1
face card is
3 1 3 3
𝐴) B) C) D)
13 2 52 26
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
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.
19. Assertion (A): HCF of any two consecutive even natural numbers is always 2. 1
Reason (R): Even natural numbers are divisible by 2.
20. Assertion (A): If the radius of sector of a circle is reduced to its half and angle is 1
doubled then the perimeter of the sector remains the same.
