KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 01 FOR BOARD EXAM 2024
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. 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
2. The solution of the following pair of equation is:
x – 3y = 2, 3x – y = 14
(a) x = 5, y = 1 (b) x = 2, y = 3 (c) x = 1, y = 2 (d) x = 1, y = 4
3. If two positive integers a and b are written as a = x3y2 and b = xy3, where x and y are prime
numbers, then the HCF (a, b) is:
(a) xy (b) xy2 (c) x3y3 (d) x2y2
4. 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
5. 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
6. 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)
(a) 0.785 cm2 (b) 0.98125 cm2 (c) 2.7475 cm2 (d) 3.14 cm2
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1-
, 7. A 1.6 m tall girl stands at distance of 3.2 m from a lamp post and casts shadow of 4.8 m on the
ground, then the height of the lamp post is
(a) 8 m (b) 4 m (c) 6 m (d) 8/3 m
8. A tangent is drawn from a point at a distance of 17 cm of circle (O, r) of radius 8 cm. The length of
tangent is
(a) 5 cm (b) 9 cm (c) 15 cm (d) 23 cm
9. The runs scored by a batsman in 35 different matches are given below:
Runs Scored 0-15 15-30 30-45 45-60 60-75 75-90
Frequency 5 7 4 8 8 3
The lower limit of the median class is
(a) 15 (b) 30 (c) 45 (d) 60
10. If in two triangles, DEF and PQR, ∠ =∠ and ∠ =∠ , then which of the following is not true?
EF DF EF DE DE DF EF DE
(a) (b) (c) (d)
PR PQ RP PQ QR PQ RP QR
11. In the given figure, if AB = 14 cm, then the value of tan B is:
4 14 5 13
(a) (b) (c) (d)
3 3 3 3
12. Two cubes each with 6 cm edge are joined end to end. The surface area of the resulting cuboid is
(a) 180 ² (b) 360 ² (c) 300 ² (d) 260 ²
13. A cone, a hemisphere and cylinder are of the same base and of the same height. The ratio of their
volumes is
(a) 1 : 2 : 3 (b) 2 : 1 : 3 (c) 3 : 1 : 2 (d) 3 : 2 : 1
14. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7 (b) 14 (c) 21 (d) 28
15. If 3 sin θ – cos θ = 0 and 0° < θ < 90°, find the value of θ.
(a) 30° (b) 45° (c) 60° (d) 90°
16. 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
17. 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
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2-
SAMPLE PAPER TEST 01 FOR BOARD EXAM 2024
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. 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
2. The solution of the following pair of equation is:
x – 3y = 2, 3x – y = 14
(a) x = 5, y = 1 (b) x = 2, y = 3 (c) x = 1, y = 2 (d) x = 1, y = 4
3. If two positive integers a and b are written as a = x3y2 and b = xy3, where x and y are prime
numbers, then the HCF (a, b) is:
(a) xy (b) xy2 (c) x3y3 (d) x2y2
4. 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
5. 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
6. 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)
(a) 0.785 cm2 (b) 0.98125 cm2 (c) 2.7475 cm2 (d) 3.14 cm2
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1-
, 7. A 1.6 m tall girl stands at distance of 3.2 m from a lamp post and casts shadow of 4.8 m on the
ground, then the height of the lamp post is
(a) 8 m (b) 4 m (c) 6 m (d) 8/3 m
8. A tangent is drawn from a point at a distance of 17 cm of circle (O, r) of radius 8 cm. The length of
tangent is
(a) 5 cm (b) 9 cm (c) 15 cm (d) 23 cm
9. The runs scored by a batsman in 35 different matches are given below:
Runs Scored 0-15 15-30 30-45 45-60 60-75 75-90
Frequency 5 7 4 8 8 3
The lower limit of the median class is
(a) 15 (b) 30 (c) 45 (d) 60
10. If in two triangles, DEF and PQR, ∠ =∠ and ∠ =∠ , then which of the following is not true?
EF DF EF DE DE DF EF DE
(a) (b) (c) (d)
PR PQ RP PQ QR PQ RP QR
11. In the given figure, if AB = 14 cm, then the value of tan B is:
4 14 5 13
(a) (b) (c) (d)
3 3 3 3
12. Two cubes each with 6 cm edge are joined end to end. The surface area of the resulting cuboid is
(a) 180 ² (b) 360 ² (c) 300 ² (d) 260 ²
13. A cone, a hemisphere and cylinder are of the same base and of the same height. The ratio of their
volumes is
(a) 1 : 2 : 3 (b) 2 : 1 : 3 (c) 3 : 1 : 2 (d) 3 : 2 : 1
14. The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is
(a) 7 (b) 14 (c) 21 (d) 28
15. If 3 sin θ – cos θ = 0 and 0° < θ < 90°, find the value of θ.
(a) 30° (b) 45° (c) 60° (d) 90°
16. 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
17. 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
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2-
