Mathematics - Class X Question Paper - Central Board Of Secondary Education Page 28

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Q. No.
Value Points
Marks
1
1
10
Q14. 1 +
+1 +
=
1
x—2
x—4
3
10
1
1
4
+
=
—2
=
Ü
3
x—2
x—4
3
2x —6
4
Ü
=
½
x²—6x+8
3
2
Ü 4x
—30x+50=0
1
2
Ü 2x
—10x—5x+25=0, Ü 2x(x—5)—5(x—5)=0 Ü (x—5)(2x—5)=0
1
5
Ü x = 5,
½
2
Q15. Let the usual speed of train be x km/hour
½
According to the problem
300
300
—
= 2
1
x
x+5
1500
2
Ü x
OR
= 2
+ 5x —750=0
1
x (x+5)
or
(x+30)(x—25)=0
Ü x=25 [Rejecting x = –30 as speed cannot be negative]
1
∴ The usual speed of train = 25 km/hour
½
Q16. OC = CD = OD Ü OCD is an equilateral traiangle
1
0
∴
∠
∠
∠
1 =
2 =
3=60
Again OA = OC and OB=OD
∴
OCA = β and
ODB= α
∠
∠
∠
∠
OAC =
OBD=
1
0
—2 β
∠
5 = 180
4 = 180 —2 α
∠
0
0
∠
∠
∠
180
—
1 =
5 +
4 = 120
1
0
0
0
—2(α + β) Ü α + β =120
120
= 360
½
0
∴
∠
∠
6 = 60° i.e,
CPD=60
½
163

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