KENDRIYA VIDYALAYA SANGATHAN
MODEL QUESTON PAPER 1
SUBJECT: MATHEMATICS (041) MAX. MARKS : 80
CLASS : X DURATION : 3 HRS
General Instruction:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions. All Questions are compulsory.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Question numbers 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, Question numbers 21-25 are very short answer (VSA) type questions, carrying 02
marks each.
5. In Section C, Question numbers 26-31 are short answer (SA) type questions, carrying 03 marks
each.
6. In Section D, Question numbers 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Question numbers 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. There is no overall choice. However, an internal choice in 2 questions 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. Take 𝜋 = 22/ 7 wherever required if not stated.
10. Use of calculators is not allowed.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. 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
2. If 217 x+131y=913 and 131x+217y = 827 then the value of x+y =
(a) 3 (b) 4 (c) 5 (d) 6
3. The midpoint of a line segment joining two points A(2, 4) and B(-2, -4) is
(a) (-2, 4) (b) (2, -4) (c) (0, 0) (d) (-2, -4)
4. The values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is
(a) 0 only (b) 8 only (c) 0,8 (d) 4
5. A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3 the probability that |x| < 2
is
(a) 1/7 (b) 2/7 (c) 3/7 (d) 5/7
6. If cos θ + cos2 θ = 1, the value of sin2 θ + sin4 θ is :
(a) –1 (b) 0 (c) 1 (d) 2
7. If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:
(a) 2 (b) -2 (c) 1 (d) -1
Page - 1-
, 8. Two dice are thrown simultaneously. The probability that the product of the numbers appearing
on the dice is 7 is
(a) 7/36 (b) 2/36 (c) 0 (d) 1/36
9. The ratio in which the line segment joining the points P(-3, 10) and Q(6, –8) is divided by O(-1, 6)
is:
(a) 1:3 (b) 3:4 (c) 2:7 (d) 2:5
10. Consider the following distribution:
Marks obtained Number of students
More than or equal to 0 63
More than or equal to 10 58
More than or equal to 20 55
More than or equal to 30 51
More than or equal to 40 48
More than or equal to 50 42
the frequency of the class 30-40 is
(a) 4 (b) 48 (c) 51 (d) 3
11. The distance of the point P (2, 3) from the x-axis is
(a) 2 (b) 3 (c) 1 (d) 5
12. A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a
vertical pole to the ground. Find the distance of the pole to the peg in the ground, if the angle
made by the rope with the ground level is 30⁰.
(a) 20√3 m (b)15√3 m (c)10√3 m (d) 20 m
13. A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability
that the drawn card has a number which is a perfect square is :
(a) 1/45 (b) 2/15 (c) 4/45 (d) 1/9
14. In the given figure, PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then ∠OAB is
(a) 30° (b) 60° (c) 90° (d) 15°
15. If the lines 3x + 2ky – 2 = 0 and 2x + 5y + 1 = 0 are parallel, then what is the value of k?
(a) 4/15 (b) 15/4 (c) ⅘ (d) 5/4
16. If a cylinder is covered by two hemispheres shaped lid of equal shape, then the total curved
surface area of the new object will be
(a) 4πrh + 2πr2 (b) 4πrh – 2πr2 (c) 2πrh + 4πr2 (d) 2πrh + 4πr
Page - 2-
MODEL QUESTON PAPER 1
SUBJECT: MATHEMATICS (041) MAX. MARKS : 80
CLASS : X DURATION : 3 HRS
General Instruction:
Read the following instructions carefully and follow them:
1. This question paper contains 38 questions. All Questions are compulsory.
2. This Question Paper is divided into 5 Sections A, B, C, D and E.
3. In Section A, Question numbers 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, Question numbers 21-25 are very short answer (VSA) type questions, carrying 02
marks each.
5. In Section C, Question numbers 26-31 are short answer (SA) type questions, carrying 03 marks
each.
6. In Section D, Question numbers 32-35 are long answer (LA) type questions, carrying 05 marks each.
7. In Section E, Question numbers 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. There is no overall choice. However, an internal choice in 2 questions 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. Take 𝜋 = 22/ 7 wherever required if not stated.
10. Use of calculators is not allowed.
SECTION – A
Questions 1 to 20 carry 1 mark each.
1. 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
2. If 217 x+131y=913 and 131x+217y = 827 then the value of x+y =
(a) 3 (b) 4 (c) 5 (d) 6
3. The midpoint of a line segment joining two points A(2, 4) and B(-2, -4) is
(a) (-2, 4) (b) (2, -4) (c) (0, 0) (d) (-2, -4)
4. The values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is
(a) 0 only (b) 8 only (c) 0,8 (d) 4
5. A number x is chosen at random from the numbers -3, -2, -1, 0, 1, 2, 3 the probability that |x| < 2
is
(a) 1/7 (b) 2/7 (c) 3/7 (d) 5/7
6. If cos θ + cos2 θ = 1, the value of sin2 θ + sin4 θ is :
(a) –1 (b) 0 (c) 1 (d) 2
7. If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:
(a) 2 (b) -2 (c) 1 (d) -1
Page - 1-
, 8. Two dice are thrown simultaneously. The probability that the product of the numbers appearing
on the dice is 7 is
(a) 7/36 (b) 2/36 (c) 0 (d) 1/36
9. The ratio in which the line segment joining the points P(-3, 10) and Q(6, –8) is divided by O(-1, 6)
is:
(a) 1:3 (b) 3:4 (c) 2:7 (d) 2:5
10. Consider the following distribution:
Marks obtained Number of students
More than or equal to 0 63
More than or equal to 10 58
More than or equal to 20 55
More than or equal to 30 51
More than or equal to 40 48
More than or equal to 50 42
the frequency of the class 30-40 is
(a) 4 (b) 48 (c) 51 (d) 3
11. The distance of the point P (2, 3) from the x-axis is
(a) 2 (b) 3 (c) 1 (d) 5
12. A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a
vertical pole to the ground. Find the distance of the pole to the peg in the ground, if the angle
made by the rope with the ground level is 30⁰.
(a) 20√3 m (b)15√3 m (c)10√3 m (d) 20 m
13. A box contains cards numbered 6 to 50. A card is drawn at random from the box. The probability
that the drawn card has a number which is a perfect square is :
(a) 1/45 (b) 2/15 (c) 4/45 (d) 1/9
14. In the given figure, PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then ∠OAB is
(a) 30° (b) 60° (c) 90° (d) 15°
15. If the lines 3x + 2ky – 2 = 0 and 2x + 5y + 1 = 0 are parallel, then what is the value of k?
(a) 4/15 (b) 15/4 (c) ⅘ (d) 5/4
16. If a cylinder is covered by two hemispheres shaped lid of equal shape, then the total curved
surface area of the new object will be
(a) 4πrh + 2πr2 (b) 4πrh – 2πr2 (c) 2πrh + 4πr2 (d) 2πrh + 4πr
Page - 2-
