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#1 2009-03-12 11:14:56

ganesh
Moderator
Registered: 2005-06-28
Posts: 15,197

Question Bank : Age Group 14-15 : XIII

1. Find the area of th quadrilateral formed by A(3, 4), B(-1, 6),
C(-3, -4), and D(6, 1).

2. The line joining (-4, 6) and (-1, -3) is perpendicular to the line joining (0, 4) and (3, a). Find a.

3. Show that x + y - 2 = 0 is perpendicular bisector of the line joining the origin and (2, 2).

4. Find the equation of the line which is concurrent with the lines y = x and y = 2 - x and perpendicular to the line y = 4x + 5.

5. If three or more parallel lines are intersected by two transversals, prove that the intercepts made by them on the transversal are proportional.

6. The bisector of the angle B and C of a triangle ABC meet the opposite sides at D and E respectively. If DE || BC, prove that the triangle is isosceles.

7. PQR is a triangle in which PQ = QR and Z is a point on the side PR such that QR[sup]2[/sup] = PR.RZ. Prove that QZ = QR.

8. If (A + B)[sup]2[/sup] = A[sup]2[/sup] + B[sup]2[/sup] and

,
find a and b.

9. Find Y. Given

.

10. Find the Standrard Deviation of the first five natural numbers.


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