Mathematics - Class X Question Paper - Central Board Of Secondary Education Page 13

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Q. NO.
VALUE POINTS
Marks
OR
cos 35°
tan 27° tan (90° - 27)°
+
- 3 tan²60°
2
sin (90° - 35)°
sin 30°
cos 35°
.
tan 27°
cot 27°
=
+
- 3 tan²60°
1
cos 35°
sin 30°
= 1 + 2 -9
= -6
1
Q16. Let A = (7, 10) ; B = (—2, 5) ; C = (3, —4)
½
∴ AB = œ (—2 —7)² + (5—10)²
½
= œ 106
BC = œ (3+2)² + (—4 — 5)²
= œ 106
½
CA = œ (7—3)² + (10+4)²
= œ 16 + 196
= œ 212
½
Ü AB=BC
½
and CA² = AB² + BC²
1
∴ A, B & C are vertices of an isosceles rt. triangle
½
OR
Let A = (-1, -1); B = (2, 3) ; C=( 8, 11)
½
AB = œ (2 + 1)² + (3+1)²
= œ 25
= 5
½
BC = œ (8—2)² + (11—3)²
= œ 36 +64
½
= 10
CA = œ (—1—8)² + (—1—11)²
= œ 225
½
= 15
∴ CA = AB + BC
1
∴ (-1, -1) ; (2, 3) and (8, 11) are collinear
1
148

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