PSEB Math Paper Set 1 2015

PSEB Class-X

Mathematics paper 2015  Set-A

Time allowed: Three Hours                                                    Maximum marks-50

1)      If  =  =   then what will be the solution of pair of linear equation?   1

a)      Write the common difference of Arithmetic progression 3,1,-1,-3…... 1

b)`     Fill in the blanks(?) if DADE~DABC then =                                      1

c)       What is the value of  ?                                                                       1

d)      Write the formula to find the volume of cuboid?                                   1

2)      Find the HCF and LCM of 15,12 and 21 using the factorization method.  2

3)      Divide 2x²+7x-1 by x+4.                                                                        2

4)      Find the roots of quadratic equation 6x²-x-2=0                                     2

5)      Which term of the A.P.: 2,7,12,17…….is 77?                                      2

                                                Or

          Find the sum of first 22 terms of the A.P.: 9,4,-1,….

6)      ABC is an isosceles triangle , right angled at C. Prove  that AB²=2AC².  2

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

7)      Draw a  line segment of length 7.4 cm and divide it in the ratio 5:8.     2

                                                     Or

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

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

i)       red?

ii)      white?

iii)     not green?                                                                                             2

9)      Find all possible solutions of the following pair of linear equations:

          5x+6y=16   and 2x-2y=2                                                                      3

10)    A ladder 5 m long reaches a  window 4 m above the ground .Find the distance of the foot of the ladder from the base of the wall.                              3

11)    If  A(-4,-5),B(-1,-6),C(4,5) and D(-5,7) 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(-3,5) and (2,-5) in the ratio 2:3.                                                                     3

12)    Prove that  =                                                                       3

13)    An observer 1.5 m tall away from the chimney. The angle of elevation of the top of chimney from eyes is 45.Find the height of the chimney.                    3

14)    From each corner of a square of side 12 cm a quadrant of a circle of radius 3 cm is cut and also a circle of diameter 6 cm is cut as shown in the adjacent fig. Find the area of remaining portion of the square.                                            3

                                     

                                                         

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

Daily expenditure	100-150	150-200	200-250	250-300	300-350
Number of households	4	5	12	2	3

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

                                                           Or

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

Weight(in Kg)	45-50	50-55	55-60	60-65	65-70	70-75	75-80
Number of Students	2	3	8	6	6	3	2

16)    Prove that in a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then the opposite the first side is a right angle  5

                                                 Or

Two tangents AB and AC are drawn to a circle with centre O from the external point A .Prove thatÐBAC=2ÐOBC                                                                         5

17)    A metallic sphere of radius 2.1 cm is melted and recast into the shape of a cylinder of radius 3 cm. Find the height of the cylinder.                                      5

                                                          Or

A drinking glass is in the shape of a frustum of a cone of height 14 cm.The diameters of two circular ends are 36 cm and 30 cm.Find the capacity of the glass.5