II, (2015-2016)
SUMMATIVE ASSESSMENT – II
MATHEMATICS /
Class – X /
X
90
Maximum Marks : 90
3
Time allowed : 3 hours
(i)
(ii)
31
6
1
3
4
10
2
11
4
(iii)
(iv)
General Instructions :
(i)
(ii)
(iii)
(iv)
All questions are compulsory.
The question paper consists of 31questions divided into four sections A, B, C and D.
Section-A comprises of 4 questions of 1 mark each, Section-B comprises of 6 questions
of 2 marks each, Section-C comprises of 10 questions of 3 marks each and Section-D
comprises of 11 questions of 4 marks each.
There is no overall choice.
Use of calculator is not permitted.
/ SECTION-A
1 4
1
Question numbers 1 to 4 carry one mark each.
1
A.P.
Does the cubes of natural numbers form an A.P. ? Give reason.
100 m
2
60
1
1
The string of a kite is 100 m long and it makes an angle of 60 with the horizontal. Assuming
that there is no slack in the string, find the height of the kite.
3
Page 1 of 7
52
1
What is the probability that a leap year has 52 Sundays ?
4
(3, 7)
(5, 7)
Find the distance of the point (3, 7) from the point (5, 7).
1
/ SECTION-B
5 10
2
Question numbers 5 to 10 carry two marks each.
1 2
x  11 x10
3
5
2
Find the roots of the quadratic equation :
6
AP
1 2
x  11 x10
3
5
9
2
Determine the common difference of the AP whose 3rd term is 5 and the 5th term is 9.
7
2
, ABBC
AEEC
In the given figure, ABBC.
Prove that AEEC.
8
PQR
ABC
BX
3
5
PQR
CBX
BX
?
3
times the corresponding sides of PQR
5
draw a ray BX such that CBX is an acute angle. How many points will be marked on the ray
To construct a ABC similar to PQR with the sides
Page 2 of 7
2
BX at equal distances and also write whetter the new triangle will lie inside or outside the
original triangle.
9
8 cm
P, 9 cm
2
P
Point P is such that it is at a distance of 9cm from a circle of radius 8cm. Find the length of the tangent
drawn from P to the circle.
3.5 cm
10
2
6 cm
Find the a actual capacity of a vessel shown in the figure, if the radius of base is 3.5 cm and
height of the cylindrical part is 6 cm.
/ SECTION-C
11 20
3
Question numbers 11 to 20 carry 3 marks each.
11
(2k1)x22(k3)x(k5)0
k
3
For what value(s) of k, will the quadratic equation (2k1)x22(k3)x(k5)0 have real and
equal roots ?
12
13
3
1
Find the sum of all two digit natural numbers which when divided by 3 yield 1 as remainder.
AB4 cm, BC5 cm
AC7 cm
ABC
ABC
3
3
5
7
Construct a ABC of sides AB4 cm, BC5 cm and AC7 cm. Construct another triangle similar to
5
ABC such that each of its sides is of the corresponding side of ABC.
7
ABC
14
Page 3 of 7
45
60
3
A kite, flying at a height of 45 metres from the ground level, is attached to a string inclined at 60 to
the horizontal. Find the length of the string.
15
5,4,3,2,1, 0, 1, 2, 3
x
A number x is chosen from 5,4,3,2,1, 0, 1, 2, 3.
Find the probability that x< 3.
16
k
P(1, 3)
A(k, 7)
B(9, k)
Find the value of k, if the point P(1, 3) is equidistant from the points A(k, 7) and B(9, k).
3
17
A(5, 1), B(8, 3), C(4, 0)
D(1, 4)
Show that the points A(5, 1), B(8, 3), C(4, 0) and D(1, 4) are the vertices of a rhombus.
3
18
14 cm
5
10
x< 3.
3
10 3
35
22
7
A wall clock is hung in a class room whose minute hand is 14 cm long. How much area is swept by the
22
minute hand during the break time that starts at 10.05 am and ends at 10.35 am. (Use
)
7
19
3.5 cm
14 cm
3
7
cm
12
A solid metallic cylinder of radius 3.5 cm and height 14 cm is melted and recast into a number
7
of small solid metallic balls, each of radius
cm. Find the number of balls so formed.
12
20
3
20 m
30
12 m
In the given figure, a trapezium shaped wall of a 20 m high bridge displays an advertisement in the
form of two sectors of central angle 30 each and radius 12 m each. Find the area of shaded portion.
Page 4 of 7
/ SECTION-D
21 31
4
Question numbers 21 to 31 carry 4 marks each.
21
8 km
1
40
4
2 km
A sailor can row a boat 8 km downstream and return back to the starting point in 1 hour 40 minutes.
If the speed of the stream is 2 km per hour, find the speed of the boat in still water.
22
5 7
100
Find the sum of natural numbers less than 100 which are divisible by
5 or 7.
2y
23
y
Solve :
2y
y
4
2 y 5 25
; y ≠ 3, 4.
4
y 3
3
2 y 5 25
; y ≠ 3, 4.
y 3
3
4
24
4
O
ABCD
B90
AD23 cm, AB29 cm
DS5 cm
A circle with centre O is inscribed in a quadrilateral ABCD in which B90. If AD23 cm, AB29
cm and DS5 cm, find the radius of the circle.
Page 5 of 7
4
25
PQR
PQ=6 cm, QR=8 cm
S
Q=90
PR
QS
Q, R 4
P
Let PQR be a triangle, where PQ=6 cm, QR=8 cm and Q=90. Draw QS perpendicular to PR. The circle
through Q, R and S is drawn. Construct tangents from P to the circle.
26
X
AB
B
60
4
X
40 m
Y
45
AB
XB
The angle of elevation of the top B of a tower AB from a point X on the ground is 60. At a point Y, 40
m vertically above X, the angle of elevation of the top is 45. Find the height of the tower AB and the
distance XB.
27
52
4
(i)
(ii)
(iii)
All the queens are removed from a well-shuffled deck of 52 playing cards. A card is drawn at
random from the remaining pack. Find the probability of drawing a.
(i)
a king
(ii)
a black card
(iii)
a face card
28
D, E,
A, B
F
ABC
(6,2), (0, 6)
C
BC, AC
4
AB
ABC
(4, 8)
4DEF
If D, E, and F are mid-points of sides BC, AC and AB of ABC respectively, where the coordinates of A,
B
and
C
are
respectively
(6,2),
(0,
6)
and
(4, 8), then using coordinate geometry, prove that area of ABC4 area of DEF.
20m
29
10m
14m
7m
22
7
A farmer in a village had an agricultural field in the form of a rectangle of length 20m and
width 14m. In one corner, he dug a well 10m deep and 7m in diameter. The earth taken out
of the well was spread evenly over the remaining part of the field. Find the rise in the level of
his field. He told the villagers that any person can draw the water from this well and can use
22
the water. What values of farmer are depicted here ? (Use 
)
7
(
Page 6 of 7
4
30
PQRS
6 cm
PQ, QR
RS
PQ
QS
4
PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semi-circles PQ and
QS are drawn on their respective diameter as shown in the figure. Find the perimeter of the shaded
region.
31
4
1:2:3
A cone, a hemisphere and a cylinder stand on equal bases and have same heights as the radii
of
the
bases.
Show
that
their
volumes
are
in
the
ratio
1 : 2 : 3.
-o0o0o0o-
Page 7 of 7