### Mix Important previous year questions of class 10

1.The king, queen and jack of clubs are removed from a deck of 52 playing cards and theremaining cards are shuffled. A card is drawn from the remaining cards. Find the
probability of getting a card of
(1) heart
(2) queen
(3) clubs

2.In Figure , there are two concentric circles with centre of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP =12 cm, find the length of BP.

3.Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to the smaller circle from a point on the larger circle. Also, measure its length.

4.Draw a right triangle ABC in which AB = 6 cm, BC = 8 cm and angle B = 90°. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and Construct tangents from A to this circle.

5.Find the ratio in which the line segment joining (-2,-3) and (5,6) is divided by (i) x-axis
(ii) y-axis. Also, find the coordinates of the point of division in each case.

6.find the area of quadrilateral , the coordinates of whose are (-4,-2),(-3,-5),(3,-2),(2,3)

7.A chord of a circle of radius 10 cm subtends a right angle at the centre. Find:
(i) area of the minor sector
(ii) area of the minor segment
(iii) area of the major sector
(iv) area of the major segment

8.A well with inner radius 4 m is dug 14 m deep. Earth taken out of it has been spread
evenly all around a width of 3 m it to form an embankment. Find the height of the embankment.

9.The difference between the outer and inner curved surface area of a hollow
right circular cylinder 14 cm long is 88 cm2 . If the volume of metal used in making the cylinder is 176 cm3, find the outer and inner diameter of the cylinder.

10.A toy is in the form of cone mounted on a hemisphere of radius 3.5 cm. The total height
che toy is 15.5 cm find the total surface area and volume of the toy.

11.If sec 2A = cosec (A - 42°), where 2A is an acute angle, find the value of A.

12.Any point X inside triangle DEF is joined to its vertices. From a point P in DX, PQ is drawn
parallel to DE meeting XE at Q And QR is drawn parallel to EF meeting XF in R. Prove that PR ll DF