DELHI PUBLIC SCHOOL, VINDHYANAGAR
HALF-YEARLY EXAMINATION (2024-25)
CLASS -X Time:3 Hrs.
SUBJECT- MATHEMATICS Max Marks:80
General Instructions:
This Question Paper has 5 SectionsA, B, CD andE.
Section Ahas 20 MCQs carrying 01 mark each.
Section Bhas 5 questions carrying 02 marks each.
Section Chas 6 questions carrying 03 marks each.
Section Dhas 4 questions carrying 05 marks each.
Section Ehas 3 case based integrated units of assessment (04 marks each) with subparts of the
values of1, 1and 2 marks each respectively.
AlQuestions are compulsory. However, an internal choice in 2 Qs of5 marks, 2 Qs of3 marks and 2
Questions of 2 marks has been provided. An internal choice has been provided in the 2 marks
questions of Section E
Draw neatfgures wherever required. Take =22/7 wherever required ifnot stated.
SECTION-A
Q1. The ratioof LCM and HCF of the least even and the least prime number is
(a) 1:2 (b) 2:1
(c) 1:1 (d) 1:3
Q2. The number of polynomials having zeroes as - 2 and 5 is
(a) 1 (b) 2
(c) 3 (d) more than 3
Q3. The value of kfor which the lines 5x + 7y=3 and 15x + 21y =k coincide is
(a) 9 (b) 5
(c) 7 (d) 18
Q4. If a, Bare the roots of the eguation x2-5x+ k=0, then what is the value of ksuch
that a -B=1
(a) 1 (b) 3
(c) 4 (d) 6
Q5. The sum of firstn terms of an AP is (4n t 2n). The nth term of this AP is
(a) (6n -2) (b) (7n -3)
(c) (8n - 2) (d) (8n + 2)
A
Q6. In the figure, if DE // BC, AD =3cm, BD =4 cm
and BC =14 cm, then DE equals
(a)7 cm (b)6 cm
(c) 4 cm (d) 3 cm
Page 1 of 6
, Q7. The value of a, so that point (4, a) lies on the line 3x - 2y = 5is
(a) 2 (b)3
(c) 7/2 (),5/2
Q8. The value of sin 600 cos 300 + sin 200cos 600 is equal to
(a)tan 600 (b) cos 0o
(c) sin 300 (d) none of these
Q9 Irp and q are positive integers such that p = ab² and q = a?b, where a, b
are prime
numbers, then the LCM (p, g) is
(a) ab
(b) a2b2
(c) a3b2
(d) a³b3
Q10 If the zeroes of the quadratic
polynomial x² + (a + 1)x + b are 2 and - 3, then
(a) a =-7, b=-1
(b) a =5, b=-1
(C) a = 2, b = -6 (d) a = 0, b=-6
Q11 Two lines are given to be parallel. The
equation of one of the lines is 3x - 2y=5. The
equation of the second line can be
(a) 9x +8y =7 (b) -12xX- 8y =7
(c) -12x + 8y =7 (d) 12x + 8y = 7
Q12 The discriminant of the equation (3x +1)2 +
(x-2)2 = 50 is
(a) 1810 (b) 1802
(C) 1804 (d) 1820
Q13 The common difference of the AP 1,
1-p,1-2p
(a) 1 (b) 1/p
(c) -1 (d) - 1/p
Q14 It is given that AABC ~ ADFE, ZA=309, 2C= 509, AB = 5 cm,AC = 8 cm and DF =7.5
cm.Then, which of the following is true?
(a) DE = 12 cm, ZF=500 (b) DE = 12 cm, ZF=1000
(c) EF = 12 cm, D= 100o (d) EF = 12 cm, ZD.=300
Q15 IfP(-1,1) is the mid-point of the line segment joiningA (-3, b) and B (1, b+4) then b=
(a) 1 (P) -1
(c) 2 (d) 0
Q16 Given cos (A - B) =V3/2 and sin (A + B) =V3/2. Then Aand Brespectively are
(a) 30°, 450 (b) 459, 150
(c) 600, 450 (d) None of these
Page 2 of 6
HALF-YEARLY EXAMINATION (2024-25)
CLASS -X Time:3 Hrs.
SUBJECT- MATHEMATICS Max Marks:80
General Instructions:
This Question Paper has 5 SectionsA, B, CD andE.
Section Ahas 20 MCQs carrying 01 mark each.
Section Bhas 5 questions carrying 02 marks each.
Section Chas 6 questions carrying 03 marks each.
Section Dhas 4 questions carrying 05 marks each.
Section Ehas 3 case based integrated units of assessment (04 marks each) with subparts of the
values of1, 1and 2 marks each respectively.
AlQuestions are compulsory. However, an internal choice in 2 Qs of5 marks, 2 Qs of3 marks and 2
Questions of 2 marks has been provided. An internal choice has been provided in the 2 marks
questions of Section E
Draw neatfgures wherever required. Take =22/7 wherever required ifnot stated.
SECTION-A
Q1. The ratioof LCM and HCF of the least even and the least prime number is
(a) 1:2 (b) 2:1
(c) 1:1 (d) 1:3
Q2. The number of polynomials having zeroes as - 2 and 5 is
(a) 1 (b) 2
(c) 3 (d) more than 3
Q3. The value of kfor which the lines 5x + 7y=3 and 15x + 21y =k coincide is
(a) 9 (b) 5
(c) 7 (d) 18
Q4. If a, Bare the roots of the eguation x2-5x+ k=0, then what is the value of ksuch
that a -B=1
(a) 1 (b) 3
(c) 4 (d) 6
Q5. The sum of firstn terms of an AP is (4n t 2n). The nth term of this AP is
(a) (6n -2) (b) (7n -3)
(c) (8n - 2) (d) (8n + 2)
A
Q6. In the figure, if DE // BC, AD =3cm, BD =4 cm
and BC =14 cm, then DE equals
(a)7 cm (b)6 cm
(c) 4 cm (d) 3 cm
Page 1 of 6
, Q7. The value of a, so that point (4, a) lies on the line 3x - 2y = 5is
(a) 2 (b)3
(c) 7/2 (),5/2
Q8. The value of sin 600 cos 300 + sin 200cos 600 is equal to
(a)tan 600 (b) cos 0o
(c) sin 300 (d) none of these
Q9 Irp and q are positive integers such that p = ab² and q = a?b, where a, b
are prime
numbers, then the LCM (p, g) is
(a) ab
(b) a2b2
(c) a3b2
(d) a³b3
Q10 If the zeroes of the quadratic
polynomial x² + (a + 1)x + b are 2 and - 3, then
(a) a =-7, b=-1
(b) a =5, b=-1
(C) a = 2, b = -6 (d) a = 0, b=-6
Q11 Two lines are given to be parallel. The
equation of one of the lines is 3x - 2y=5. The
equation of the second line can be
(a) 9x +8y =7 (b) -12xX- 8y =7
(c) -12x + 8y =7 (d) 12x + 8y = 7
Q12 The discriminant of the equation (3x +1)2 +
(x-2)2 = 50 is
(a) 1810 (b) 1802
(C) 1804 (d) 1820
Q13 The common difference of the AP 1,
1-p,1-2p
(a) 1 (b) 1/p
(c) -1 (d) - 1/p
Q14 It is given that AABC ~ ADFE, ZA=309, 2C= 509, AB = 5 cm,AC = 8 cm and DF =7.5
cm.Then, which of the following is true?
(a) DE = 12 cm, ZF=500 (b) DE = 12 cm, ZF=1000
(c) EF = 12 cm, D= 100o (d) EF = 12 cm, ZD.=300
Q15 IfP(-1,1) is the mid-point of the line segment joiningA (-3, b) and B (1, b+4) then b=
(a) 1 (P) -1
(c) 2 (d) 0
Q16 Given cos (A - B) =V3/2 and sin (A + B) =V3/2. Then Aand Brespectively are
(a) 30°, 450 (b) 459, 150
(c) 600, 450 (d) None of these
Page 2 of 6
