KENDRIYA VIDYALAYA JYOTIPURAM JAMMU REGION
HALF YEARLY EXAMINATION 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.
OA OC
1. In the figure, if = , then
OD OB
which pair of angles are equal? [1]
(a) ∠A = ∠C, ∠B = ∠D (b) ∠A = ∠B, ∠C = ∠D
(c) ∠C = ∠B, ∠A = ∠D (d) None of these
2. If tan θ = 1, then the value of sec θ + cosec θ is:
(a) 3√2 (b) 4√2 (c) 2√2 (d) √2
3. If the area of circle is numerically equal to twice its circumference, then the diameter of the
circle is
(a) 4 units (b) 6 units (c) 8 units (d) 12 units
4. In the given figure, if TP and TQ are tangents to a circle with centre O, so that ∠POQ = 110°,
then ∠PTQ is
(a) 110° (b) 90° (c) 80° (d) 70°
, 5. The value of ‘a’, if HCF (a, 18) = 2 and LCM (a, 18) = 36, is: (1)
(a) 2 (b) 5 (c) 7 (d) 4
6. If r = 3 is a root of quadratic equation kr2 – kr – 3 = 0, then the value of k is:
(a) 1/2 (b) 3 (c) 1/3 (d) 1/4
7. 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
8. If the angle of elevation of the top of a tower from a point of observation at a distance of 100 m
from its base is 45°, then the height of the tower is:
(a) 160 m (b) 100 m (c) 200 m (d) 150 m
9. When 2120 is expressed as the product of its prime factors we get
(a) 2 × 5³ × 53 (b) 2³ × 5 × 53 (c) 5 × 7² × 31 (d) 5² × 7 × 33
10. If p and q are the zeroes of the quadratic polynomial f(x) = 2x2 – 7x + 3, find the value of p + q –
pq is
(a) 1 (b) 2 (c) 3 (d) None of these
11. If the angle between two radii of a circle is 140°, then the angle between the tangents at the ends of
the radii is
(a) 90° (b) 50° (c) 70° (d) 40°
12. Points A(3, 1), B(5, 1), C(a, b) and D(4, 3) are vertices of a parallelogram ABCD. The values of a
and b are respectively
(a) a = 6, b = 3 (b) a = 2, b = 1 (c) a = 4, b = 2 (d) None of these
13. If sec A = 15/7 and A + B = 90°, find the value of cosec B.
(a) 8/7 (b) 12/7 (c) 7/15 (d) 15/7
14. 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
15. What is the positive real root of 64x2 – 1 = 0?
(a) 1/8 (b) 1/4 (c) 1/2 (d) 1/6
16. In ∆ABC and ∆DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are
(a) congruent but not similar (b) similar but not congruent
(c) neither congruent nor similar (d) congruent as well as similar
17. The LCM of smallest two-digit composite number and smallest composite number is:
(a) 12 (b) 4 (c) 20 (d) 44
18. 2 sin A – 3cos A
If cosec A = 13/12, then the value of
4 sin A – 9 cos A
(a) 4 (b) 5 (c) 6 (d) 3
HALF YEARLY EXAMINATION 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.
OA OC
1. In the figure, if = , then
OD OB
which pair of angles are equal? [1]
(a) ∠A = ∠C, ∠B = ∠D (b) ∠A = ∠B, ∠C = ∠D
(c) ∠C = ∠B, ∠A = ∠D (d) None of these
2. If tan θ = 1, then the value of sec θ + cosec θ is:
(a) 3√2 (b) 4√2 (c) 2√2 (d) √2
3. If the area of circle is numerically equal to twice its circumference, then the diameter of the
circle is
(a) 4 units (b) 6 units (c) 8 units (d) 12 units
4. In the given figure, if TP and TQ are tangents to a circle with centre O, so that ∠POQ = 110°,
then ∠PTQ is
(a) 110° (b) 90° (c) 80° (d) 70°
, 5. The value of ‘a’, if HCF (a, 18) = 2 and LCM (a, 18) = 36, is: (1)
(a) 2 (b) 5 (c) 7 (d) 4
6. If r = 3 is a root of quadratic equation kr2 – kr – 3 = 0, then the value of k is:
(a) 1/2 (b) 3 (c) 1/3 (d) 1/4
7. 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
8. If the angle of elevation of the top of a tower from a point of observation at a distance of 100 m
from its base is 45°, then the height of the tower is:
(a) 160 m (b) 100 m (c) 200 m (d) 150 m
9. When 2120 is expressed as the product of its prime factors we get
(a) 2 × 5³ × 53 (b) 2³ × 5 × 53 (c) 5 × 7² × 31 (d) 5² × 7 × 33
10. If p and q are the zeroes of the quadratic polynomial f(x) = 2x2 – 7x + 3, find the value of p + q –
pq is
(a) 1 (b) 2 (c) 3 (d) None of these
11. If the angle between two radii of a circle is 140°, then the angle between the tangents at the ends of
the radii is
(a) 90° (b) 50° (c) 70° (d) 40°
12. Points A(3, 1), B(5, 1), C(a, b) and D(4, 3) are vertices of a parallelogram ABCD. The values of a
and b are respectively
(a) a = 6, b = 3 (b) a = 2, b = 1 (c) a = 4, b = 2 (d) None of these
13. If sec A = 15/7 and A + B = 90°, find the value of cosec B.
(a) 8/7 (b) 12/7 (c) 7/15 (d) 15/7
14. 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
15. What is the positive real root of 64x2 – 1 = 0?
(a) 1/8 (b) 1/4 (c) 1/2 (d) 1/6
16. In ∆ABC and ∆DEF, ∠B = ∠E, ∠F = ∠C and AB = 3DE. Then, the two triangles are
(a) congruent but not similar (b) similar but not congruent
(c) neither congruent nor similar (d) congruent as well as similar
17. The LCM of smallest two-digit composite number and smallest composite number is:
(a) 12 (b) 4 (c) 20 (d) 44
18. 2 sin A – 3cos A
If cosec A = 13/12, then the value of
4 sin A – 9 cos A
(a) 4 (b) 5 (c) 6 (d) 3
