Set 7
Set 7
Set 7
GENERAL INSTRUCTIONS
SECTION-A
(1 mark each)
1. Write the first five square numbers.
2. If the sum of the digits of a number is divisible by three, then the number is divisible by which number?
3. Factorise y 2 2 y 15
4. A polyhedron is having 8 vertices and 12 edges. How many faces of it are there?
5. Express 35 34 as a power of 3 with positive exponent.
6. The sides of a triangle are 3x 1, x 2 and 4x + 6, then find its perimeter.
SECTION-B
(2 marks each)
7. If each edge of a cube is doubled
(a) How many times will its surface area increase?
(b) How many times will its volume increase?
8. If 16 shirts of equal size can be made out of 24 m of cloth, how much cloth is needed for making one shirt?
9. Factorise:
(a) 12 x 36
(b) 22 y 33z
10. Evaluate: 3 1372 3 1458
11. On Sunday 845 people went to zoo. On Monday only 169 people went. What is the percent decrease in the people
visiting the zoo on Monday.
12. Simplify : 3x 4 x 5 3 and find its value
1
(a) x 3 (b) x :
2
SECTION-C
(3 marks each)
3 4 9 10 1 3
13. Simplify:
2 5 5 3 2 4
14. Observe the following table, where x and y are in inverse variation :
SECTION-D
(4 marks each)
23. A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time (a) the length of the shadow
cast by another pole 10 m 50 m high (b) the height of a pole which cast a shadow 5 m long.
24. Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are
drinking water from the pond. Find the number of deer in the herd.
25. The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20% we get
the same perimeter. Find the length and breadth of the rectangle.
26. Diameter of cylinder A is 7 cm and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without
doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders.
Check whether the cylinder with greater volume also has greater surface area.
27. (a) Draw the graph of the function y = 3x + 1.
(b) The given graph represents the total runs scored by two batsmen A and B, during each of the ten different matches
in the year 2014.
1
29. Calculate the amount and compound interest on Rs. 10,800 for 3 years at 12 % per annum compounded is
2
annually.
30. (a) Add : p ( p q), q q r and r r p
(b) Add: 2x z x y and 2y z y x
(c) Subtract: 31 ( I 4m 5n) from 4l 10n 3m 2l
(d) Subtract: 3a a b c 2b a b c from 4c a b c
Solutions
Section ‘A’
(1 mark each)
1. 1,4,9,16,25 1
2. If the sum of the digits of a number is divisible by three, then the number will be divisible by 3. 1
3. y 2 2 y 15
y 2 5 3 y 15
y 2 5 y 3 y 15 ½
y y 5 3 y 5
y 5 y 3 ½
4. Number of vertices (V)=8
Number of edges (E) = 12.
Let the number of faces be F
Now, using Euler's formula
F+V=E+2
We have,
F + 8 = 12 + 2
F + 8 = 14
F 14 8
F = 6. 1
Thus, the required number of faces =6 1
1
5. 35 34 39 9
3
6. Let AB 3x 1
BC x 2
AC 4x 6
Since, perimeter of ABC AB BC AC
3x 1 x 2 4 x 6
3x 1 x 2 4x 6
6x 9 1
Section ‘B’
(2 marks each)
7. (a) Let the edge of cube be x
According to question, edge of cube is doubled = 2x
The surface area of cube when edge is doubled = 6l 2
6 2x
2
6 4x2
4 x 6x2
The surface area of cube is 4 time increase. 1
(b) The volume of cube when edge is doubled
(2 x)3
8x3
The volume of cube is 8 time increase, when edge is doubled. 1
8. Cloth needed of 16 shirt = 24 m
24 3
Cloth needed for 1 shirt 1
16 2
=1.5m 1
2 1458
3 729
3 243
3 81
3 27
3 9
3 3
1
1
Since
3
1372 3 1458 3 2 2 7 7 7 2 3 3 3 3 3 3
23 73 33 33
2 7 3 3
=126 1
11. People went to the Zoo on Sunday = 845
People went to the Zoo on Monday =169
Decrease in the people 845 169 676
Decrease value of Monday = Decrease % of 845
1
x
676 845
100
676 100
x
845
x =80
80% people decreased on Monday. 1
12. 3x 4 x 5 3 3x 4 x 5 3
12 x2 15x 3
12 3 15 3 3
2
(a) For x=3,
12 9 45 3
108 45 3 66 1
2
1 1 1
(b) For x , 12 15 3
2 2 2
15
3 3
2
15
6
2
12 15 3
1
2 2
Section ‘C’
(3 marks each)
13. 3 4 9 10 1 3 3 2 3
(3 2)
2 5 5 3 2 4 5 8
1
6 3
(6) 1
5 8
6 1 3
5 6 8
1 3
5 8
8 15 7
1
40 40
14. Let x1 p1 , x2 200, x3 300
and y1 60, y2 30, y3 p2
Since, x and y are in inverse variation. 1
(a) x1 y1 x2 y2
p1 60 200 30
200 30
p1 100 1
60
(b) Also, x2 y2 x3 y3
200 30 300 p2
200 30
p2 20 1
300
15. Let the number be x.
According to question,
5
8 x 3x 1
2
or, 8x 20 3x
or, 8x 3x 20
[Transposing 3x to LHS and 20 to RHS]
1
or, 5x = 20
[Dividing both sides by 5]
20
or, x
5
or, x=4 1
Hence, the required number is 4.
45 60 28 43
1 1 1 1
16.
5 5 5 5
45 60 28 43
1 1
1
5 5
15 15
1 1
1
5 5
(5)15 (5)15 1
0
17. Let the present age of granddaughter be x.
and the present age of grandfather = 10 x 1
According to question,
10 x x 54
or, 10 x x 54
or, 9 x 54
54
or, x or , x 6 years 1
9
Hence, granddaughter's age = 6 years
and grandfather's age
6 10 60 years 1
18. (a) Steps of Construction:
(i) Draw BC = 5 cm.
(vi) With B as centre and radius equal to CD draw another arc, cutting the previous arc at A. 1
19. Here, l = 7 m, b = 6 m, h = 15 m
Volume of cuboid = l b h
7 6 15
630 m3 ½
Since, 1 m 1000 L
3
Volume
Water level
Base Area
624.6
76
= 14.8 m ½
Fall in water level 15 14.8
= 0.2 m or 20 cm ½
3
20. (a) Since, P = Rs. 31250, n = 2 years, R = 8% p.a.
4
3
8
8 4
2
Then, A 31250 1 1 1
100 100
2
27 53
31250
25 50
27 27 53
31250 Rs.38637
25 25 50
Hence, C.I. 38637 31250 Rs. 7387 ½
(b) Since, C.P. = Rs. 750 and S.P = Rs. 875
C.P. < S.P.
Gain = Rs. (875 - 750) = Rs. 125
Gain
Then, Gain% 100
C.P.
125
100
750
50 2
% 16 % 11/2
3 3
21. AD = BC = b
CO = AO’ = h
ABCD is parallelogram divided into 2 triangles i.e., ABC ACD
Section ‘D’
(4 mark each)
23. (a) Let the length of the shadow be x m.
Height 5 m 60 cm 10 m 50 cm
Length 3 m 20 cm x
1
5 m 60 cm = 5.60 m
3 m 20 cm = 3.20 m
10 m 50 cm = 10.50 m
5.60 10.50
3.20 x
10.50 3.20
x
5.60
x = 6m 1
(b) Let the height of a pole be y m.
X 0 1 2
Y 1 4 7
1
1
(b) (i) The horizontal axis (or the x-axis) indicates the matches played during the year 2014. The vertical axis (or the
y-axis) shows the total runs scored in each match. 1
(ii) The dotted line shows the runs scored by Batsman A. (This is already indicated at the top of the graph).
1
28. (a) a b (a ) (b )
4 4 2 2 2 2
(a 2 b2 )(a 2 b2 )
(a b)(a b)(a 2 b2 ) 1
(b) p 4 81 ( p 2 )2 (9)2
( p 2 9)( p 2 9)
[(p)2 (3)2 ]( p2 9)
( p 3)( p 3)( p 2 9) 1
(c) x4 ( y z)4 ( x2 )2 {( y z)2 }2
{x 2 ( y z)2 }{x2 ( y z)2 }
{x ( y z)}{x ( y z)}{x 2 ( y z)2 } 1
( x y z )( x y z ){x ( y z ) }
2 2
Therefore, p 2 q 2 r 2 pq qr rp
31. (b) First expression
2 x z x y 2 xz 2 x2 2 xy
Second expression
2 y z y x 2 yz 2 y 2 2 xy
Now, adding the two expressions
2 xz 2 x 2 2 xy
2 xy 2 yz 2 y 2
2 xz 2 x 2 4 xy 2 yz 2 y 2
Therefore, 2 x2 2 y 2 4 xy 2 xz 2 yz
32. (c) We have, 31( I 4m 5n)
3l 12lm 15In
2