## CBSE SAMPLE PAPER FOR Maths class10

**SECTION A**

**1. Values of k for which the quadratic equation 2x2 – kx + k = 0 has equal roots is**

**(A) 0 only (B) 4**

**(C) 8 only (D) 0, 8**

**2. The list of numbers – 10, – 6, – 2, 2,... is**

**(A) an AP with d = – 16 (B) an AP with d = 4**

**(C) an AP with d = – 4 (D) not an AP**

**3. If the first term of an AP is –5 and the common difference is 2, then the sum of the first**

**6 terms is**

**(A) 0 (B) 5**

**(C) 6 (D) 15**

**4. At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the**

**circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is**

**(A) 4 cm (B) 5 cm**

**(C) 6 cm (D) 8 cm**

**5. If the perimeter of a circle is equal to that of a square, then the ratio of their areas is**

**(A) 22 : 7 (B) 14 : 11 (C) 7 : 22 (D) 11: 14**

**6. The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a**

**(A) square (B) rectangle**

**(C) rhombus (D) trapezium**

**7. A shuttle cock used for playing badminton has the shape of the combination of**

**(A) a cylinder and a sphere (B) a cylinder and a hemisphere**

**(C) a sphere and a cone (D) frustum of a cone and a hemisphere**

**8. A cone is cut through a plane parallel to its base and then the cone that is formed on one**

**side of that plane is removed. The new part that is left over on the other side of the**

**plane is called**

**(A) a frustum of a cone (B) cone**

**(C) cylinder (D) sphere**

**9. A contractor plans to install two slides for the children to play in a park. For the**

**children below the age of 5 years, she prefers to have a slide whose top is at a height**

**of 1.5 m, and is inclined at an angle of 30 ° to the ground, where as for the elder**

**children she wants to have a steep side at a height of 3 m, and inclined at an angle of**

**60 ° to the ground. What should be the length of the slide in each case?**

**10. A bag contains lemon flavoured candies only. Malini takes out one candy without**

**looking into the bag. What is the probability that she takes out**

**(i) an orange flavoured candy? (ii) a lemon flavoured candy?**

**11. John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the**

**product of the number of marbles they now have is 124. Find out how many marbles**

**they had to start with.**

**12. Which term of the A.P. 3, 8, 13, 18, … is 78?**

**13. Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a**

**triangle whose sides are 4/3 times the corresponding side of ΔABC. Give the**

**justification of the construction.**

**14. Find the area of a quadrant of a circle whose circumference is 22 cm.**

**15. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the**

**resulting cuboids.**

**16. Determine if the points (1, 5), (2, 3) and (− 2, − 11) are collinear.**

**17. Check whether (5, − 2), (6, 4) and (7, − 2) are the vertices of an isosceles triangle.**

**18. A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri**

**will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one**

**pen at random and gives it to her. What is the probability that**

**(i) She will buy it? (ii) She will not buy it?**

**19. Find the values of k for each of the following quadratic equations, so that they have two**

**equal roots.**

**(I) 2x2 + kx + 3 = 0 (II) kx (x − 2) + 6 = 0**

**20. Show that a1, a2 … , an , … form an AP where an is defined as below**

**(i) an = 3 + 4n (ii) an = 9 − 5n**

**Also find the sum of the first 15 terms in each case.**

**21. A quadrilateral ABCD is drawn to circumscribe a circle (see given figure) Prove that**

**AB + CD = AD + BC**

**23. A container shaped like a right circular cylinder having diameter 12 cm and height 15**

**cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and**

**diameter 6 cm, having a hemispherical shape on the top. Find the number of such**

**cones which can be filled with ice cream.**

**24. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose**

**sides are 7/5 of the corresponding sides of the first triangle.**

**Give the justification of the construction.**

**25. A kite is flying at a height of 60 m above the ground. The string attached to the kite is**

**temporarily tied to a point on the ground. The inclination of the string with the ground**

**is 60°. Find the length of the string, assuming that there is no slack in the string.**

**26. Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of ΔABC.**

**(i) The median from A meets BC at D. Find the coordinates of point D.**

**(ii) Find the coordinates of the point P on AD such that AP: PD = 2:1**

**(iii) Find the coordinates of point Q and R on medians BE and CF respectively such**

**that BQ: QE = 2:1 and CR: RF = 2:1.**

**(iv) What do you observe?**

**(v) If A(x1, y1), B(x2, y2), and C(x3, y3) are the vertices of ΔABC, find the coordinates of**

**the centroid of the triangle.**

**27. Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.**

**28. Two customers Shyam and Ekta are visiting a particular shop in the same week**

**(Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another**

**day. What is the probability that both will visit the shop on**

**(i) the same day? (ii) consecutive days? (iii) different days?**

**29. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it**

**would have taken 1 hour less for the same journey. Find the speed of the train.**

**30. Two water taps together can fill a tank in 9 hours. The tap of larger diameter takes 10**

**hours less than the smaller one to fill the tank separately. Find the time in which each**

**tap can separately fill the tank.**

**31. Prove that opposite sides of a quadrilateral circumscribing a circle subtend**

**supplementary angles at the centre of the circle.**

**32. A right triangle whose sides are 3 cm and 4 cm (other than hypotenuse) is made to**

**revolve about its hypotenuse. Find the volume and surface area of the double cone so**

**formed. (Choose value of π as found appropriate.)**

**33. A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters**

**of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.**

**34. The angles of elevation of the top of a tower from two points at a distance of 4 m and**

**9 m. from the base of the tower and in the same straight line with it are**

**complementary. Prove that the height of the tower is 6 m.**

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