CHENNAI SAHODAYA SCHOOLS COMPLEX
COMMON EXAMINATION
CLASS -10
MATHEMATICS -041
Time Allowed: 3 Hours Maximum MARKS :80
Roll No.: Date: 27/01/2023
CODE - I
General Instructions:
1. This Question Paper has 5 Sections A, B, C, D, and E.
2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.
4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.
5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each.
6. Section E has 3 Case Based integrated units of assessment (4 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 2 marks, 2 Qs of 3 marks
and 2 Questions of 5 marks has been provided. An internal choice has been provided in the 2
marks 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 Marks
1. The smallest number divisible by all natural numbers from 1 to 10 is 1
(a) 2020 (b) 2520 (c)1010 (d) 5040
2. If the roots of 𝑥 2 + 4𝑚𝑥 + 4𝑚2 −𝑚 − 1 = 0 are real, then 1
(a) 𝑚 = −1 (b) 𝑚 ≤ −1 (c)𝑚 ≥ −1 (d) 𝑚 ≥ 0
3. If one zero of the polynomial 𝑥 2 − 8𝑥 + 𝑘 exceeds the other by 2 , then the value 1
of 𝑘 is
(a) 35 (b) 25 (c)15 (d)5
4. The pair of equations 2𝑥 + 𝑘𝑦 = 1 and 5𝑥 − 7𝑦 = 5 has no solution when 1
13 −13
(a) 𝑘 = 5 (b) 𝑘 = 5
−14 −16
(c) 𝑘 = (d) 𝑘 =
5 5
5. AOBC is rectangle whose three vertices are A(0,3) B(5,0) and O(0,0). The length 1
of its diagonal is
(a) 5 (b) 4 (c)√34 (d √44
6. In ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹 , ∠𝐵 = ∠𝐸 , ∠𝐹 = ∠𝐶 and AB = 3 DE. Then the two 1
triangles are
(a)congruent but not similar (b) similar but not congruent
(c)neither congruent nor similar (d)congruent as well as similar
Page 1 of 7
, 7. In the given figure AB= a , AC= b, AD = BD and ∠𝐵 = 90°, 1
then the value of tan 𝜃 is
𝑎 𝑎
(a) 2− 2
(b) √𝑏2 − 2
2√𝑏 𝑎 𝑎
𝑏 𝑏
(c) (d)
√𝑎2 +𝑏2 2√𝑎2 + 𝑏2
8. In the figure given, AD= 4 cm , BD = 3 cm , CD = 12 cm 1
then 𝑠𝑒𝑐 𝜃 is
5 12 13 12
(a) (b) (c) (d)
12 5 5 13
9. 1
D and E are respectively the points on the sides AB and AC of
∆𝐴𝐵𝐶 such that 𝐴𝐷 = 2𝑐𝑚, 𝐵𝐷 = 3 𝑐𝑚, 𝐵𝐶 = 7.5 𝑐𝑚 and
𝐷𝐸 ∥ 𝐵𝐶 , then the length of 𝐷𝐸 (𝑖𝑛 𝑐𝑚 ) is
(a)2.5 (b) 3 (c) 5 (d) 6
10. ∆ 𝐴𝐵𝐶 ~ ∆ 𝐷𝐸𝐹 , such that AB = 9.1 𝑐𝑚 and DE = 6.5 𝑐𝑚. If the perimeter of 1
∆ 𝐷𝐸𝐹 is 25 𝑐𝑚, then the perimeter of ∆𝐴𝐵𝐶 is
(a)36𝑐𝑚 (b) 30𝑐𝑚 (c) 34𝑐𝑚 (d) 35𝑐𝑚
11. In the figure, AB is a chord of a circle with centre O and AC is 1
the diameter. ∠𝐴𝐶𝐵 = 50°, and AP is a tangent to the circle at
A. Then ∠𝐵𝐴𝑃 𝑖𝑠
(a)65° (b) 60° (c) 50° (d) 40°
12. If the areas of 2 circles are is the ratio 4:9, then the ratio of the perimeters of the 1
semicircles is
(a) 2: 3 (b) 3:2 (c) 1: 2 (d) 1: 3
13. From a solid, right circular cylinder of height 14 cm and base radius 6 cm, a right 1
circular cone of same height and same radius is removed. The volume of the
remaining solid is
(a) 1112 𝑐𝑚3 (b) 1056𝑐𝑚3 (c) 1000𝑐𝑚3 (d) 1058𝑐𝑚3
14. If the mean and median of a frequency distribution are 20 and 24 respectively, then 1
the value of mode is
(a) 30 (b) 32 (c) 28 (d) 12
15. The length of the minor arc of a circle is (2) 𝑡ℎ of its circumference. Then the 1
9
angle subtended by the arc at the centre of the circle is
(a) 80° (b) 60° (c) 45° (d) 30°
Page 2 of 7
COMMON EXAMINATION
CLASS -10
MATHEMATICS -041
Time Allowed: 3 Hours Maximum MARKS :80
Roll No.: Date: 27/01/2023
CODE - I
General Instructions:
1. This Question Paper has 5 Sections A, B, C, D, and E.
2. Section A has 20 Multiple Choice Questions (MCQs) carrying 1 mark each.
3. Section B has 5 Short Answer-I (SA-I) type questions carrying 2 marks each.
4. Section C has 6 Short Answer-II (SA-II) type questions carrying 3 marks each.
5. Section D has 4 Long Answer (LA) type questions carrying 5 marks each.
6. Section E has 3 Case Based integrated units of assessment (4 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 2 marks, 2 Qs of 3 marks
and 2 Questions of 5 marks has been provided. An internal choice has been provided in the 2
marks 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 Marks
1. The smallest number divisible by all natural numbers from 1 to 10 is 1
(a) 2020 (b) 2520 (c)1010 (d) 5040
2. If the roots of 𝑥 2 + 4𝑚𝑥 + 4𝑚2 −𝑚 − 1 = 0 are real, then 1
(a) 𝑚 = −1 (b) 𝑚 ≤ −1 (c)𝑚 ≥ −1 (d) 𝑚 ≥ 0
3. If one zero of the polynomial 𝑥 2 − 8𝑥 + 𝑘 exceeds the other by 2 , then the value 1
of 𝑘 is
(a) 35 (b) 25 (c)15 (d)5
4. The pair of equations 2𝑥 + 𝑘𝑦 = 1 and 5𝑥 − 7𝑦 = 5 has no solution when 1
13 −13
(a) 𝑘 = 5 (b) 𝑘 = 5
−14 −16
(c) 𝑘 = (d) 𝑘 =
5 5
5. AOBC is rectangle whose three vertices are A(0,3) B(5,0) and O(0,0). The length 1
of its diagonal is
(a) 5 (b) 4 (c)√34 (d √44
6. In ∆𝐴𝐵𝐶 and ∆𝐷𝐸𝐹 , ∠𝐵 = ∠𝐸 , ∠𝐹 = ∠𝐶 and AB = 3 DE. Then the two 1
triangles are
(a)congruent but not similar (b) similar but not congruent
(c)neither congruent nor similar (d)congruent as well as similar
Page 1 of 7
, 7. In the given figure AB= a , AC= b, AD = BD and ∠𝐵 = 90°, 1
then the value of tan 𝜃 is
𝑎 𝑎
(a) 2− 2
(b) √𝑏2 − 2
2√𝑏 𝑎 𝑎
𝑏 𝑏
(c) (d)
√𝑎2 +𝑏2 2√𝑎2 + 𝑏2
8. In the figure given, AD= 4 cm , BD = 3 cm , CD = 12 cm 1
then 𝑠𝑒𝑐 𝜃 is
5 12 13 12
(a) (b) (c) (d)
12 5 5 13
9. 1
D and E are respectively the points on the sides AB and AC of
∆𝐴𝐵𝐶 such that 𝐴𝐷 = 2𝑐𝑚, 𝐵𝐷 = 3 𝑐𝑚, 𝐵𝐶 = 7.5 𝑐𝑚 and
𝐷𝐸 ∥ 𝐵𝐶 , then the length of 𝐷𝐸 (𝑖𝑛 𝑐𝑚 ) is
(a)2.5 (b) 3 (c) 5 (d) 6
10. ∆ 𝐴𝐵𝐶 ~ ∆ 𝐷𝐸𝐹 , such that AB = 9.1 𝑐𝑚 and DE = 6.5 𝑐𝑚. If the perimeter of 1
∆ 𝐷𝐸𝐹 is 25 𝑐𝑚, then the perimeter of ∆𝐴𝐵𝐶 is
(a)36𝑐𝑚 (b) 30𝑐𝑚 (c) 34𝑐𝑚 (d) 35𝑐𝑚
11. In the figure, AB is a chord of a circle with centre O and AC is 1
the diameter. ∠𝐴𝐶𝐵 = 50°, and AP is a tangent to the circle at
A. Then ∠𝐵𝐴𝑃 𝑖𝑠
(a)65° (b) 60° (c) 50° (d) 40°
12. If the areas of 2 circles are is the ratio 4:9, then the ratio of the perimeters of the 1
semicircles is
(a) 2: 3 (b) 3:2 (c) 1: 2 (d) 1: 3
13. From a solid, right circular cylinder of height 14 cm and base radius 6 cm, a right 1
circular cone of same height and same radius is removed. The volume of the
remaining solid is
(a) 1112 𝑐𝑚3 (b) 1056𝑐𝑚3 (c) 1000𝑐𝑚3 (d) 1058𝑐𝑚3
14. If the mean and median of a frequency distribution are 20 and 24 respectively, then 1
the value of mode is
(a) 30 (b) 32 (c) 28 (d) 12
15. The length of the minor arc of a circle is (2) 𝑡ℎ of its circumference. Then the 1
9
angle subtended by the arc at the centre of the circle is
(a) 80° (b) 60° (c) 45° (d) 30°
Page 2 of 7
