PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 08 FOR BOARD EXAM 2025
SUBJECT: MATHEMATICS MAX. MARKS : 80
CLASS : X DURATION : 3 HRS
General Instruction:
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 π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have
(a) a unique solution (b) exactly two solutions
(c) Infinitely many solutions (d) no solution
2. If p and q are positive integers such that p = a3b2 and q = a2b, where ‘a’ and ‘b’ are prime numbers,
then the LCM ( p, q) is …..
(a) ab (b) a2b2 (c) a3b2 (d) a3b3
3. The ratio in which x-axis divides the join of (2, -3) and (5, 6) is:
(a) 1: 2 (b) 3 : 4 (c) 1: 3 (d) 1: 5
4. Find the value of k for which the equation x2 + k(2x + k − 1)+ 2 = 0 has real and equal roots.
(a) 2 (b) 3 (c) 4 (d) 5
5. In a formula racing competition, the time taken by two racing cars A and B to complete 1 round of
the track is 30 minutes and p minutes respectively. If the cars meet again at the starting point for the
first time after 90 minutes and the HCF (30, p) = 15, then the value of p is
(a)45 minutes (b)60 minutes (c)75 minutes (d)180 minutes
6. For the following distribution:
Marks Below Below Below Below Below Below
10 20 30 40 50 60
No. of Students 3 12 27 57 75 80
the modal class is
(a) 10 – 20 (b) 20 – 30 (c) 30 – 40 (d) 50 – 60
7. A medicine-capsule is in the shape of a cylinder of radius 0.25 cm with two hemispheres stuck to
each of its ends. The length of the entire capsule is 2 cm. What is the total surface area of the
capsule? (Take π as 3.14)
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1-
, (a) 0.785 cm2 (b) 0.98125 cm2 (c) 2.7475 cm2 (d) 3.14 cm2
8. In ABC, DE || AB, If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to
(a) 7.5 cm (b) 3 cm (c) 4.5 cm (d) 6 cm
9. The 11th and 13th terms of an AP are 35 and 41 respectively, its common difference is
(a) 38 (b) 32 (c) 6 (d) 3
10. If is an acute angle and tan + cot = 2, then the value of sin3 + cos3 is
1 2
(a) 1 (b) (c) (d) 2
2 2
11. Volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is
(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9
12. The area of the square that can be inscribed in a circle of radius 8 cm is
(a) 256 cm² (b) 128 cm² (c) 64√2 cm² (d) 64 cm²
13. Two dice are thrown at the same time and the product of numbers appearing on them is noted. The
probability that the product is a prime number is
(a) 1/3 (b) 1/6 (c) 1/5 (d) 5/6
14. In ΔABC right angled at B, if cotC = √3 , then then cosAsinC + sinAcosC =
(a) –1 (b) 0 (c) 1 (d) √
15. In the below figure, the pair of tangents AP and AQ drawn from an external point A to a circle with
centre O are perpendicular to each other and length of each tangent is 5 cm. Then radius of the
circle is
(a) 10 cm (b) 7.5 cm (c) 5 cm (d) 2.5 cm
16. A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with
water. If the sphere is completely submerged, then the water level rises (in cm) by
(a) 3 (b) 4 (c) 5 (d) 6
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2-
SAMPLE PAPER TEST 08 FOR BOARD EXAM 2025
SUBJECT: MATHEMATICS MAX. MARKS : 80
CLASS : X DURATION : 3 HRS
General Instruction:
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 π =22/7 wherever required if not stated.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. The pair of equations x + 2y + 5 = 0 and –3x – 6y + 1 = 0 have
(a) a unique solution (b) exactly two solutions
(c) Infinitely many solutions (d) no solution
2. If p and q are positive integers such that p = a3b2 and q = a2b, where ‘a’ and ‘b’ are prime numbers,
then the LCM ( p, q) is …..
(a) ab (b) a2b2 (c) a3b2 (d) a3b3
3. The ratio in which x-axis divides the join of (2, -3) and (5, 6) is:
(a) 1: 2 (b) 3 : 4 (c) 1: 3 (d) 1: 5
4. Find the value of k for which the equation x2 + k(2x + k − 1)+ 2 = 0 has real and equal roots.
(a) 2 (b) 3 (c) 4 (d) 5
5. In a formula racing competition, the time taken by two racing cars A and B to complete 1 round of
the track is 30 minutes and p minutes respectively. If the cars meet again at the starting point for the
first time after 90 minutes and the HCF (30, p) = 15, then the value of p is
(a)45 minutes (b)60 minutes (c)75 minutes (d)180 minutes
6. For the following distribution:
Marks Below Below Below Below Below Below
10 20 30 40 50 60
No. of Students 3 12 27 57 75 80
the modal class is
(a) 10 – 20 (b) 20 – 30 (c) 30 – 40 (d) 50 – 60
7. A medicine-capsule is in the shape of a cylinder of radius 0.25 cm with two hemispheres stuck to
each of its ends. The length of the entire capsule is 2 cm. What is the total surface area of the
capsule? (Take π as 3.14)
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1-
, (a) 0.785 cm2 (b) 0.98125 cm2 (c) 2.7475 cm2 (d) 3.14 cm2
8. In ABC, DE || AB, If CD = 3 cm, EC = 4 cm, BE = 6 cm, then DA is equal to
(a) 7.5 cm (b) 3 cm (c) 4.5 cm (d) 6 cm
9. The 11th and 13th terms of an AP are 35 and 41 respectively, its common difference is
(a) 38 (b) 32 (c) 6 (d) 3
10. If is an acute angle and tan + cot = 2, then the value of sin3 + cos3 is
1 2
(a) 1 (b) (c) (d) 2
2 2
11. Volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is
(a) 3 : 4 (b) 4 : 3 (c) 9 : 16 (d) 16 : 9
12. The area of the square that can be inscribed in a circle of radius 8 cm is
(a) 256 cm² (b) 128 cm² (c) 64√2 cm² (d) 64 cm²
13. Two dice are thrown at the same time and the product of numbers appearing on them is noted. The
probability that the product is a prime number is
(a) 1/3 (b) 1/6 (c) 1/5 (d) 5/6
14. In ΔABC right angled at B, if cotC = √3 , then then cosAsinC + sinAcosC =
(a) –1 (b) 0 (c) 1 (d) √
15. In the below figure, the pair of tangents AP and AQ drawn from an external point A to a circle with
centre O are perpendicular to each other and length of each tangent is 5 cm. Then radius of the
circle is
(a) 10 cm (b) 7.5 cm (c) 5 cm (d) 2.5 cm
16. A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with
water. If the sphere is completely submerged, then the water level rises (in cm) by
(a) 3 (b) 4 (c) 5 (d) 6
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2-
