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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