• ## This are previous year questions which will help you to prepare for board

1.If Sn denotes the sum of first n terms of an A.P. prove that S12=3(S8-S4)

2.The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find
the 28th term of this A.P.

3.Five cards—ten, jack, queen, king, and an ace of diamonds are shuffled face downwards. One card is picked at random.
(i) What is the probability that the card is a queen?
(ii) If a king is drawn first and put aside, what is the probability that the second card picked up is the (i) ace? (ii) king?

4.Find the ratio in which the point P (x, 2) divides the line segment joining the points
A (12,5) and B (4,-3). Also, find the value of x.

5.Prove that the area of triangle whose vertices are (t, t - 2), (t + 2, + 2) and (t +3, t) is independent of t.

6.Two circular pieces of equal radii and maximum area, touching each other are cut
out from a rectangular card board of dimensions 14 cm x 7 cm. Find the area of the
remaining card board.

7.From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of
the same height and same diameter is hollowed out. Find the total surface area of the remaining solid ?

8.Solve the following systems of equations graphically:

A.  x+y =3
2x + 5 = 12

B. 2x-5y+4=0
2x+y-8=0

9.solve the equations by any method:

A. 4+5y=7
x
3 +4y=5
x

B.  5   +   1.  = 2
x-1     y-2
6   -     3.  =1
x-1       y-2

10.A Man travels 370 km partly by train and partly by car. If he covers 250 km by train and the rest by car, it takes him 4 hours. But, if he travels 130 km by train and the rest by car, he takes 18 minutes loger. Find the speed of the train and that of the car.

11.If D and E are points on sides AB and AC respectively of a triangle  ABC such that DE ll  BC and BD=CE. Prove that triangle ABC is isosceles.