**Section-A**

Q.No. (1) If ax^{2}+bx+c=0 has equal roots. Find the value of c.

Q.No. (2)A tower stands on the ground. From a point on the ground which is 20 m away from the foot of the tower, the angle of elevation of the top of the tower is 30°. Find the height of the tower.

Q.No. (3) one card is drawn from a well shuffled deck of 52 cards. Find the probability of getting the queen of diamond.

Q.No. (4)If angle between two radii of a circle is 125°.Find the angle between the tangents at the ends of the radii.

**Section-B**

Q.No. (5) If two tangents inclined at an angle 600 are drawn to a circle of radius 3cm, then find the length of each tangent

Q.no. (6) Two concentric circles of radii 13 cm and 12 cm are given. Find the length of the chord of the larger circle which touches the smaller circle.

Q.No. (7) What is the nature of roots of the quadratic equation 2x^{2} - √5 x + 1.

Q.No.(8) Find a, b and c such that a , 7 , b , 23 , c are in A.P.

Q.No.(9) Find the relation between x and y such that the point P(x , y) is equidistant from the points A(7,1) and B(3,5)

Q.No.(10)Find the ratio in which the point P(-4,x) divides the line segment joining the points A(-5,-4) and B(-2,3) and also find the value of x.

**Section-C**

Q.No. (11) Find three numbers in A.P whose sum is 15 and the product is 80.

Q.No. (12) Sum of the areas of two squares is 468 m^{2}. If the difference of their Perimeter is 24, formulate the quadratic equation of the sides of the two squares.

Q.No. (13) The angle of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are complementary. Prove that the

height of the tower is 6m.

Q.No.(14) Determine the ratio in which the line 2x + y – 4 = 0 divides the line segment joining the points A(2 , -2) and B(3, 7).

Q.No. (15) A die is thrown once. What is the probability that it shows (i) 3 (ii) 4 (iii) number greater than 4.

Q.No.(16) A teacher brings clay in the classroom to give the concept of surface area and volume in mensuration . He makes a cone of radius 6cm and height 24 cm with the clay. Then he moulds that cone in to sphere. Find the radius of sphere formed. Do teaching aids enhance the teaching learning process? Justify your answer.

Q.No.(17) Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond Whichis 50 m long and 44 m wide. In what time will the label of water in the pond rise by 21cm?

Q.No.(18) An ice-cream cone is full of ice cream having radius 5cm and height 10cm. Calculate the volume Of ice-cream provided that its 1/6 part is left unfilled with ice-cream.

Q.No.(19) Three metallic solid cubes whose edges are 3cm, 4cm & 5cm are melted and formed into a single cube. Find the surface area of cube so formed.

**Please click the link below to download CBSE Class 10 Mathematics Sample Paper 2018 Set D**