Board Paper of Class 10 2011 Maths (SET 2) - Solutions

In figure 3, APB and CQD are semi-circles of diameter 7 cm each, while ARC and BSD are semi-circles of diameter 14 cm each. Find the perimeter of the shaded region.

OR

Find the area of a quadrant of a circle, where the circumference of circle is 44 cm.

Two concentric circles are of radii 7 cm and r cm respectively, where r > 7. A chord of the larger circle, of length 48 cm, touches the smaller circle. Find the value of r.

Find the values(s) of x for which the distance between the points P(x, 4) and Q(9, 10) is 10 units.

Find whether − 150 is a term of the AP 17, 12, 7, 2,…?

Two cubes, each of side 4 cm are joined end to end. Find the surface area of the resulting cuboid.

Draw a line segment of length 6 cm. Using compasses and ruler, find a point P on it which divides it in the ratio 3:4.

Find the value of k so that the quadratic equation kx (3x − 10) + 25 = 0, has two equal roots.

A coin is tossed two times. Find the probability of getting not more than one head.

In fig. 4, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively. If area of ΔABC = 21 cm², then find the lengths of sides AB and AC.

Two dice are rolled once. Find the probability of getting such numbers on two dice, whose product is a perfect square.

OR

A game consists of tossing a coin 3 times and noting its outcome each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

If two vertices of an equilateral triangle are (3, 0) and (6, 0), find the third vertex.

OR

Find the value of k, if the points P(5, 4), Q(7, k) and R (9, −2) are collinear.

Find the roots of the following quadratic equation:

Find the value of the middle term of the following AP:

−6, −2, 2, ……, 58.

OR

Determine the AP whose fourth term is 18 and the differences of the ninth term from the fifteenth term is 30.

Find the area of the major segment APB, in Fig 5, of a circle of radius 35 cm and ∠AOB = 90°.

From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30° and 45° respectively. Find the distance between the cars.

The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14 cm). If the volume of bucket is 5390 cm³, then find the value of r.

Draw a triangle ABC with side BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct a triangle whose sides are times the corresponding sides of ΔABC.

If P(2, 4) is equidistant from Q(7, 0) and R(x, 9), find the values of x. Also find the distance PQ.

Prove that the lengths of tangents drawn from an external point to a circle are equal.

A motor boat whose speed is 20 km/h in still water, takes 1 hour more to go 48 km upstream than to return downstream to the same spot. Find the speed of the stream.

OR

Find the roots of the equation

If the sum of first 4 terms of an AP is 40 and that of first 14 terms is 280, find the sum of its first n terms.

OR

Find the sum of the first 30 positive integers divisible by 6.

From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 10 m high building are 30° and 60° respectively. Find the height of the tower.

Find the area of the shaded region in Fig. 6, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD, where the length of each side of square is 14 cm.

A toy is in the shape of a solid cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 21 cm and 40 cm respectively, and the height of cone is 15 cm, then find the total surface area of the toy. [π = 3.14, be taken]