Class-X

Mathematics

Set-B

Time allowed: Three Hours                                       Maximum Marks:50

1.       If  =  then what will be the solution of pair of linear  equation?             1
2.       Write the common difference of Arithmetic progression(A.P.) 4,2,0,-2,……      1
3.       Fill in the blank?: if ΔADE∼ΔABC then    =                                                  1
4. What is the value of     ?                                                                                   1
5. Write the formula to find the volume of cylinder.                                                    1
6. Find the HCF and LCM of 12,15 and 21 using the prime factorization method.    2
7. Divide 2x2+9x-2 by x+5.                                                                2
8. Find the roots of the quadratic equation9x2-3x-2=0                                                 2
9. Which term of the A.P.3,8,13,18……..is 78?                                                           2

                                Or

Find the sum of first 22 terms of  A.P. 7,2,-3,……                                                  2

10. ABC is an isosceles triangle, right angled at A. Prove that BC2=2AB2.                  2

Or

   Prove that the tangents drawn at the ends of a diameter AB of a circle are parallel.      2

11. Draw a line segment of length 7.6 cm and divide it in the ratio 5:8.               2

                                          Or

Construct a triangle similar to a given triangle PQR with its side equal to  of the corresponding sides of the triangle PQR.                                                           2

12. A box contains 8 red marbles,4 white marbles and 5 green marbles. One marble is taken out of the box at random.What is the probability that the marble taken out will be

1. Green         ii) red?           iii) not white?                                 2

13. Find all possible solutions of the following pair of linear equations:

3x+4y=10 and 2x-2y=2                                                                        3

14. A ladder 15 m long reaches a window 12 m above the ground. Find the distance of the foot of the ladder from base of the wall.                                               3
15. If A(-5,7),B(-4,-5),C(-1,-6) and D(4,5) are the vertices of a quadrilateral ABCD, then find the area of the quadrilateral.                                                            3

Or

        Find the coordinates of the point which divides the join of the line segment of the points

       (-1,7) and (4,-3) in the ratio 2:3.                                                  3

16)     Prove that:   =                           3

  17)    An observer 1.5 m tall is 23.5m away from a chimney. The angle of elevation of the top of chimney from her eyes is 450.Find the height of the chimney.     3

18)    From each corner of a square of side 4 cm a quadrant of circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in adjacent fig. Find the area of the remaining portion  of the square.                                                                                                      3

                                          Or

The cost of fencing a circular field at the rate rate of Rs.12 per meter is Rs.2,640.

The field is to be ploughed at the rate of Rs.0.25 per m2.Find the cost of ploughing the field.   3                                                                                                                                                            

19)    The table below shows the daily expenditure on food of 25 households in locality.

Find the mean daily expenditure on food by a suitable method.                                 3

The distribution below gives the weight of 30 students of a class. Find the median weight of the students.                                                                                                                           3

20)   Prove that in a right angle triangle, the square of the hypotenuse is equal the sum of the squares of the other two sides.                                                                                            5

                                Or

Two tangents KL and KM are drawn to a circle with centre O from the external point K. Prove that ∠LKM=2∠OLM.                                                                                                  5

21)        A metallic sphere of radius 6.3 cm is  melted and recast into the shape of a cylinder of a cylinder of radius 9 cm. Find the height of the cylinder.                                                     5

22)        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.                             5