PM SHRI KENDRIYA VIDYALAYA GACHIBOWLI,GPRA CAMPUS, HYD-32
SAMPLE PAPER TEST 04 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. In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular
to each other. If PA = 5 cm, then length of AB is equal to
(a) 5 cm (b) 5√2 cm (c) 2√5 cm (d) 10 cm
2. XOYZ is a rectangle with vertices X(–3, 0), O(0, 0), Y(0, 4) and Z(x, y). The length of its each
diagonal is
(a) 5 units (b) √5 units (c) x² + y² units (d) 4 units
3. Which term of the A.P. –29, –26, –23, ..., 61 is 16?
(a) 11th (b) 16th (c) 10th (d) 31st
4. If the length of an arc of a circle subtending an angle 60° at its centre is 22 cm, then the radius of
the circle is :
(a) √21 cm (b) 21 cm (c) √42 cm (d) 42 cm
5. If x = 5 is a solution of the quadratic equation 2x2 + (k – 1)x + 10 = 0, then the value of k is :
(a) 11 (b) – 11 (c) 13 (d) – 13
6. The pair of equations x = 2a and y = 3b (a, b ≠ 0) graphically represents straight lines which are :
(a) coincident (b) parallel (c) intersecting at (2a, 3b) (d) intersecting at (3b, 2a)
7. The point on x-axis which is equidistant from the points (5, – 3) and (4, 2) is :
(a) (4.5, 0) (b) (7, 0) (c) (0.5, 0) (d) (– 7, 0)
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 -
, 8. The 7th term from the end of the A.P. : – 8, – 5, – 2, ..., 49 is :
(a) 67 (b) 13 (c) 31 (d) 10
9. After an examination, a teacher wants to know the marks obtained by maximum number of the
students in her class. She requires to calculate ................. of marks.
(a) median (b) mode (c) mean (d) range
10. Two positive integers m and n are expressed as m = p5q2 and n = p3q4, where p and q are prime
numbers. The LCM of m and n is :
(a) p8q6 (b) p3q2 (c) p5q4 (d) p5q2 + p3q4
1
11. The value of sin 2 2 is :
1 tan
(a) 0 (b) 2 (c) 1 (d) – 1
12. All queens, jacks and aces are removed from a pack of 52 playing cards. The remaining cards are
well-shuffled and one card is picked up at random from it. The probability of that card to be a
king is :
(a) 1/10 (b) 1/13 (c) 3/10 (d) 3/13
1 1
13. If α and β are zeroes of the polynomial 5x² + 3x – 7, the value of is
(a) −3/7 (b) 3/5 (c) 3/7 (d) −5/7
14. The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. PQ/AB
is equal to
(a) 7/8 (b) 6/7 (c) 7/6 (d) 8/7
15. In the given figure, if M and N are points on the sides OP and OS respectively of ∆OPS, such that
MN || PS, then the length of OP is :
(a) 6.8 cm (b) 17 cm (c) 15.3 cm (d) 9.6 cm
16. In the given figure, PA and PB are two tangents drawn to the circle with centre O and radius 5
cm. If ∠APB = 60°, then the length of PA is :
(a) 5/√3 cm (b) 5√3 cm (c) 10/√3 cm (d) 10 cm
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2 -
SAMPLE PAPER TEST 04 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. In the given figure, tangents PA and PB to the circle centred at O, from point P are perpendicular
to each other. If PA = 5 cm, then length of AB is equal to
(a) 5 cm (b) 5√2 cm (c) 2√5 cm (d) 10 cm
2. XOYZ is a rectangle with vertices X(–3, 0), O(0, 0), Y(0, 4) and Z(x, y). The length of its each
diagonal is
(a) 5 units (b) √5 units (c) x² + y² units (d) 4 units
3. Which term of the A.P. –29, –26, –23, ..., 61 is 16?
(a) 11th (b) 16th (c) 10th (d) 31st
4. If the length of an arc of a circle subtending an angle 60° at its centre is 22 cm, then the radius of
the circle is :
(a) √21 cm (b) 21 cm (c) √42 cm (d) 42 cm
5. If x = 5 is a solution of the quadratic equation 2x2 + (k – 1)x + 10 = 0, then the value of k is :
(a) 11 (b) – 11 (c) 13 (d) – 13
6. The pair of equations x = 2a and y = 3b (a, b ≠ 0) graphically represents straight lines which are :
(a) coincident (b) parallel (c) intersecting at (2a, 3b) (d) intersecting at (3b, 2a)
7. The point on x-axis which is equidistant from the points (5, – 3) and (4, 2) is :
(a) (4.5, 0) (b) (7, 0) (c) (0.5, 0) (d) (– 7, 0)
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 -
, 8. The 7th term from the end of the A.P. : – 8, – 5, – 2, ..., 49 is :
(a) 67 (b) 13 (c) 31 (d) 10
9. After an examination, a teacher wants to know the marks obtained by maximum number of the
students in her class. She requires to calculate ................. of marks.
(a) median (b) mode (c) mean (d) range
10. Two positive integers m and n are expressed as m = p5q2 and n = p3q4, where p and q are prime
numbers. The LCM of m and n is :
(a) p8q6 (b) p3q2 (c) p5q4 (d) p5q2 + p3q4
1
11. The value of sin 2 2 is :
1 tan
(a) 0 (b) 2 (c) 1 (d) – 1
12. All queens, jacks and aces are removed from a pack of 52 playing cards. The remaining cards are
well-shuffled and one card is picked up at random from it. The probability of that card to be a
king is :
(a) 1/10 (b) 1/13 (c) 3/10 (d) 3/13
1 1
13. If α and β are zeroes of the polynomial 5x² + 3x – 7, the value of is
(a) −3/7 (b) 3/5 (c) 3/7 (d) −5/7
14. The perimeters of two similar triangles ABC and PQR are 56 cm and 48 cm respectively. PQ/AB
is equal to
(a) 7/8 (b) 6/7 (c) 7/6 (d) 8/7
15. In the given figure, if M and N are points on the sides OP and OS respectively of ∆OPS, such that
MN || PS, then the length of OP is :
(a) 6.8 cm (b) 17 cm (c) 15.3 cm (d) 9.6 cm
16. In the given figure, PA and PB are two tangents drawn to the circle with centre O and radius 5
cm. If ∠APB = 60°, then the length of PA is :
(a) 5/√3 cm (b) 5√3 cm (c) 10/√3 cm (d) 10 cm
Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2 -
