Class- X Session- 2022-23
Subject- Mathematics (Standard)
Sample Question Paper
Time Allowed: 3 Hrs. Maximum Marks : 80
General Instructions:
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
Section A consists of 20 questions of 1 mark each.
S.NO MA
. RKS
1 Let a and b be two positive integers such that a = p3q4 and b = p2q3 , where p and q are 1
prime numbers. If HCF(a,b) = pmqn and LCM(a,b) = prqs, then (m+n)(r+s)=
(a) 15 (b) 30 (c) 35 (d) 72
2 Let p be a prime number. The quadratic equation having its roots as factors of p is 1
(a) x2 –px +p=0 (b) x2–(p+1)x +p=0 (c) x2+(p+1)x +p=0 (d) x2 –px+p+1=0
3 If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is 1
(a)-2/3 (b) 2/3 (c) 1/3 (d) -1/3
4 If the system of equations 3x+y =1 and (2k-1)x +(k-1)y =2k+1 is inconsistent, then k = 1
(a) -1 (b) 0 (c) 1 (d) 2
5 If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), 1
then the coordinates of its fourth vertex S are
(a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2)
6 ∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively and 1
AB2: PQ2 = 4 : 9, then AM: PN =
(a) 3:2 (b) 16:81 (c) 4:9 (d) 2:3
, 7 If x tan 60° cos 60° = sin60° cot 60° , then x = 1
(a) cos30° (b) tan30° (c) sin30° (d) cot30°
8 If sinθ + cosθ = √2, then tanθ + cot θ = 1
(a) 1 (b) 2 (c) 3 (d) 4
9 In the given figure, DE ∥ BC, AE = a units, EC =b units, DE =x units and BC = y 1
units. Which of the following is true?
𝑎+𝑏 𝑎𝑥 𝑎𝑦 𝑥 𝑎
(a) x= (b) y= 𝑎+𝑏 (c) x= 𝑎+𝑏 (d) 𝑦 = 𝑏
𝑎𝑦
10 ABCD is a trapezium with AD ∥ BC and AD = 4cm. If the diagonals AC and BD 1
intersect each other at O such that AO/OC = DO/OB =1/2, then BC =
(a) 6cm (b) 7cm (c) 8cm (d) 9cm
11 If two tangents inclined at an angle of 60ᵒ are drawn to a circle of radius 3cm, then the 1
length of each tangent is equal to
(a)
3√3
cm (b) 3cm (c) 6cm (d) 3√3cm
2
12 The area of the circle that can be inscribed in a square of 6cm is 1
(a) 36π cm2 (b) 18π cm2 (c) 12 π cm2 (d) 9π cm2
13 The sum of the length, breadth and height of a cuboid is 6√3cm and the length of its 1
diagonal is 2√3cm. The total surface area of the cuboid is
(a) 48 cm2 (b) 72 cm2 (c) 96 cm2 (d) 108 cm2
14 If the difference of Mode and Median of a data is 24, then the difference of median 1
and mean is
(a) 8 (b) 12 (c) 24 (d) 36
15 The number of revolutions made by a circular wheel of radius 0.25m in rolling a 1
distance of 11km is
(a) 2800 (b) 4000 (c) 5500 (d) 7000
16 For the following distribution, 1
Class 0-5 5-10 10-15 15-20 20-25
Frequency 10 15 12 20 9
the sum of the lower limits of the median and modal class is
(a) 15 (b) 25 (c) 30 (d) 35
Subject- Mathematics (Standard)
Sample Question Paper
Time Allowed: 3 Hrs. Maximum Marks : 80
General Instructions:
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
Section A consists of 20 questions of 1 mark each.
S.NO MA
. RKS
1 Let a and b be two positive integers such that a = p3q4 and b = p2q3 , where p and q are 1
prime numbers. If HCF(a,b) = pmqn and LCM(a,b) = prqs, then (m+n)(r+s)=
(a) 15 (b) 30 (c) 35 (d) 72
2 Let p be a prime number. The quadratic equation having its roots as factors of p is 1
(a) x2 –px +p=0 (b) x2–(p+1)x +p=0 (c) x2+(p+1)x +p=0 (d) x2 –px+p+1=0
3 If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is 1
(a)-2/3 (b) 2/3 (c) 1/3 (d) -1/3
4 If the system of equations 3x+y =1 and (2k-1)x +(k-1)y =2k+1 is inconsistent, then k = 1
(a) -1 (b) 0 (c) 1 (d) 2
5 If the vertices of a parallelogram PQRS taken in order are P(3,4), Q(-2,3) and R(-3,-2), 1
then the coordinates of its fourth vertex S are
(a) (-2,-1) (b) (-2,-3) (c) (2,-1) (d) (1,2)
6 ∆ABC~∆PQR. If AM and PN are altitudes of ∆ABC and ∆PQR respectively and 1
AB2: PQ2 = 4 : 9, then AM: PN =
(a) 3:2 (b) 16:81 (c) 4:9 (d) 2:3
, 7 If x tan 60° cos 60° = sin60° cot 60° , then x = 1
(a) cos30° (b) tan30° (c) sin30° (d) cot30°
8 If sinθ + cosθ = √2, then tanθ + cot θ = 1
(a) 1 (b) 2 (c) 3 (d) 4
9 In the given figure, DE ∥ BC, AE = a units, EC =b units, DE =x units and BC = y 1
units. Which of the following is true?
𝑎+𝑏 𝑎𝑥 𝑎𝑦 𝑥 𝑎
(a) x= (b) y= 𝑎+𝑏 (c) x= 𝑎+𝑏 (d) 𝑦 = 𝑏
𝑎𝑦
10 ABCD is a trapezium with AD ∥ BC and AD = 4cm. If the diagonals AC and BD 1
intersect each other at O such that AO/OC = DO/OB =1/2, then BC =
(a) 6cm (b) 7cm (c) 8cm (d) 9cm
11 If two tangents inclined at an angle of 60ᵒ are drawn to a circle of radius 3cm, then the 1
length of each tangent is equal to
(a)
3√3
cm (b) 3cm (c) 6cm (d) 3√3cm
2
12 The area of the circle that can be inscribed in a square of 6cm is 1
(a) 36π cm2 (b) 18π cm2 (c) 12 π cm2 (d) 9π cm2
13 The sum of the length, breadth and height of a cuboid is 6√3cm and the length of its 1
diagonal is 2√3cm. The total surface area of the cuboid is
(a) 48 cm2 (b) 72 cm2 (c) 96 cm2 (d) 108 cm2
14 If the difference of Mode and Median of a data is 24, then the difference of median 1
and mean is
(a) 8 (b) 12 (c) 24 (d) 36
15 The number of revolutions made by a circular wheel of radius 0.25m in rolling a 1
distance of 11km is
(a) 2800 (b) 4000 (c) 5500 (d) 7000
16 For the following distribution, 1
Class 0-5 5-10 10-15 15-20 20-25
Frequency 10 15 12 20 9
the sum of the lower limits of the median and modal class is
(a) 15 (b) 25 (c) 30 (d) 35
