Mathematics Village
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
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
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
FORMULAE Algebra
FORMULAE
Algebra
1. (a + b)2 = a2 + b2 + 2ab
= (a - b) 2 + 4ab
2. (a- b) 2 = a2 + b2 - 2ab
= (a + b) 2 – 4ab
3. a2- b2 = (a - b) (a + b)
4. a2 + b2 = (a + b) 2 - 2ab = (a - b) 2 + 2ab
5. (a + b) 2 + (a- b) 2 = 2(a2
+ b2)
6. (a + b) 2 – (a
- b) 2 = 4ab
7. (a + b + c) 2 = a2 + b2
+ c2 + 2ab + 2bc + 2ca
8. a2 + b2 + c2 - ab - bc - ca =1/2[(a-b) 2 + (b -c) 2 + (c- a)
2]
9. (a + b)3 = a3 + b3 + 3ab
(a + b) = a3 + 3a2b + 3ab2 + b3
10. (a- b) 3 = a3 - b3 -3ab
(a -b) = a3 - 3a2b + 3ab2 - b3
11. a3 + b3 = (a + b) 3 -
3ab (a + b) = (a + b) (a2–- ab + b2)
12. a3 - b3= (a - b) 3 +
3ab (a- b) = (a- b) (a2 + ab + b2)
13. (a + b + c) 3 = a3 + b3
+ c3 + 3(a + b) (b + c) (c + a)
14. a3 + b3 + c3 – 3abc = (a + b + c) (a2 + b2 + c2
- ab - bc - ca)
If a + b + c = 0 then a3 + b3+ c3
= 3abc
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