Mathematics - Class X Question Paper - Central Board Of Secondary Education Page 11

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Q. NO.
VALUE POINTS
Marks
Q8.
Here a = 3 , d = 12
∴ t
= 3 + (54 —1).12 = 639
1
54
Let n be number of terms
∴ t
= 639 + 132 = 771
½
n
Ü 3 + ( n—1).12 = 771
1
∴ n = 65
½
OR
Writing Sn = a + (a+d) + (a+2d) + -------l. Where l =a +(n—1) d
1
∴ Sn = l + (l—d) + (l —2d) + --------+a
∴ 2 Sn = (a+l) + (a+l) + (a+l) + -------+ (a+l) = n )a+l)
1
n
n
Sn =
(a+l) =
[2a +(n -1) d]
1
2
2
Q9.
Here a=1, d=2
Let t
= 199
n
∴ 1 + (n—1).2 = 199
1
∴ n = 100
½
100
∴ S
.
=
[2.1 + (100—1).2]
1
100
2
=50 [200]
= 10,000
½
Q10. Correct figure
½
DE
DO
In ∆ ABD,
=
-------- (i) [EO||AB]
1
EA
OB
DO
CF
Similarly in ∆ BCD,
=
------ (ii)
½
OB
FB
DE
CF
(i) and (ii) Ü
=
1
EA
FB
SECTION B
3x + 4
4
Q11.
=
1
(x+1) (x+2)
x + 4
Ü 4 (x+1) (x+2) = ( x+4) (3x +4)
½
or 4x² + 12x + 8 = 3x² + 16x + 16
½
or x² — 4x — 8 = 0
1
Solving to get x =2 + 2œ 3, 2—2œ 3,
1
146

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