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SUMMATIVE ASSESSMENT – II,
II,
MATHEMATICS /
Class – X /
X
Time allowed : 3 hours
Maximum Marks : 80
3
80
General Instructions :
(i)
(ii)
(iii)
(iv)
(v)
All questions are compulsory.
The question paper consists of 34 questions divided into four sections A, B, C and D.
Section-A comprises of 10 questions of 1 mark each, Section-B comprises of 8 questions of 2
marks each, Section-C comprises of 10 questions of 3 marks each and Section-D comprises
of 6 questions of 4 marks each.
Question numbers 1 to 10 in Section-A are multiple choice questions where you are to select
one correct option out of the given four.
There is no overall choice. However, internal choices have been provided in 1 question of
two marks, 3 questions of three marks each and 2 questions of four marks each. You have to
attempt only one of the alternatives in all such questions.
Use of calculator is not permitted.
(i)
(ii)
34
10
1
8
3
6
(iii)
1
(iv)
2
10
4
10
2
3
4
3
2
(v)
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SECTION–A /
Question numbers 1 to 10 carry one mark each. For each question, four alternative
choices have been provided of which only one is correct. You have to select the correct
choice.
1 10
1
1.
For what value of k, x 2 is a solution of the equation kx2 2 x40
(A)
k1
(B)
k0
(C)
k 2 2
(D)
k2
k
2.
kx2 2 x40
x 2
(A)
k1
(B)
k0
(C)
1
11th term of A.P. 3,  , 2, __________ is.
2
k 2 2
(D)
k2
(A)
28
(C)
38
(D)
 48
1
2
(C)
38
(D)
 48
1
2
(B)
22
1
3,  , 2, __________
2
(A)
3.
4.
28
(B)
22
The distance between two parallel tangents in a circle of radius 3.5 cm is :
(A)
7 cm
(B)
14 cm
(C)
3.5 cm
(D)
1.75 cm
3.5 cm
(A)
7 cm
(B)
14 cm
(C)
3.5 cm
(D)
1.75 cm
AT is a tangent to a circle at A with centre O from an external point T, such that
OT8 cm and OTA30. The length of AT (in cm) is :
2
(A)
3 2
T
(B)
O
OT8 cm
5.
11
AT
(C)
4 3
(D)
AT
4
OTA30
cm
2
3 2
4 3
(A)
(B)
(C)
(D)
4
In given figure, O is the centre of a circle of radius 6 cm. At a distance of 10 cm from O, a
point P is taken. Two tangents PQ and PR are drawn to the circle from this point. Then
area of quadrilateral PQOR is :
(A)
60 cm2
(B)
28 cm2
O
(C)
6
PQ
PR
48 cm2
(D)
O 10 cm
30 cm2
P
PQOR
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6.
7.
8.
(A)
60 cm2
(B)
28 cm2
(C)
48 cm2
(D)
30 cm2
To divide a given line segment AB at a point P such that AP : AB2 : 5, the line is to be
divided in the ratio :
(A)
2:3
(B)
3:2
(C)
2:5
(D)
5:2
P
AP : AB2 : 5
AB
(A)
2:3
(B)
3:2
(C)
2:5
(D)
5:2
The radius of wire is decreased to one-third. If volume remains the same, the length will
become :
(A)
3 times
(B)
6 times
(C)
9 times
(D)
27 times
(A)
3
(B)
6
(C)
9
(D)
27
If radii of two circles are 8 cm and 6 cm respectively, then the radius of the circle having
area equal to the areas of the two circles is :
(A)
14 cm
(B)
2 cm
(C)
10 cm
(D)
None of these
8 cm
6 cm
9
(A)
14 cm
(B)
2 cm
(C)
10 cm
(D)
If the height and length of the shadow of a man are the same, then the angle of
elevation of the sun is
(A)
30
(B)
60
(C)
45
(D)
15
10
(A)
30
(B)
60
The probability of an impossible event is
(A)
1
(B)
1
(A)
1
(B)
(C)
1
45
(D)
15
(C)
2
(D)
0
(C)
2
(D)
0
SECTION-B /
Question numbers 11 to 18 carry two marks each.
11
11.
12.
13.
18
2
Determine the roots of the following quadratic equation :
4 5 x217x3 5 0
4 5 x217x3 5 0
Find the middle most term of the A.P.
11, 7, 3, ……. , 45.
11, 7, 3, ……. , 45
In given figure, a circle touches the side QR of PQR at A and sides PQ and PR on
producing at S and T respectively. If PS8 cm, find the perimeter of PQR.
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PQR
S
14.
15
T
QR
A
PS8 cm
PQ
PR
PQR
Find the perimeter of a sector of a circle with diameter 8 cm if angle of the sector is 36 (use
22

)
7
8 cm
36
22
(
)
7
A juice seller was serving his customers using glasses. The inner diameter of the
cylindrical glass was 5 cm, but the bottoms of the glass had a hemispherical raised portion
which reduces the capacity of the glass. If the height of the glass was 10 cm, find the
apparent capacity and actual capacity of the glass : (Use 3.14)
5 cm
10 cm
16
(3.14
)
If the points A(1, 2), B(4, q), C(p, 6 ) and D(3, 5), are the vertices of a parallelogram ABCD,
find the values of p and q.
A(1, 2), B(4, q), C(p, 6 )
D(3, 5)
ABCD
p
q
17
Find the ratio in which the line segment joining the points X(1, 5) and Y(4, 5) is
divided by the x-axis.
X(1, 5)
Y(4, 5)
x-
18
Two coins are tossed together. Find the probability of getting both Heads or both Tails.
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OR/
A card is drawn from a well shuffled pack of 52 cards. Find the probability that it is not a
king of club.
52
SECTION-C /
Question numbers 19 to 28 carry three marks each.
19 28
3
19.
20.
21.
x  1
x 2

 3, x  1, 2
x 1
x 2
x  1
x 2
x

 3, x  1, 2
x 1
x 2
OR/
Solve for x :
If roots of a quadratic equation (bc) x2(ca) x(ab)0 are real and equal, then
prove that 2bac
(bc) x2(ca) x(ab)0
2bac
The sum of first 6 terms of an A.P. is 42. The ratio of its 10th term to its 30th term is 1 : 3.
Find the first term and the thirteenth term of the A.P.
42
10
30
1:3
13
Prove that the tangent at any point of a circle is perpendicular to the radius through the
point of contact.
OR/
Prove that the line segment joining the points of contact of two parallel tangents passes
through the centre.
22.
23.
24.
Draw tangents to a circle of radius 3 cm from a point P at a distance of 5 cm from its centre.
3 cm
5 cm
P
Three horses are tied at 3 corners of a triangular plot having sides 20 m, 30 m and 40 m
22 

with ropes of 7 m length each. Find the area where the horses can graze.  use 
7 

20 m, 30 m
40 m
7m
22


  7

The cost of painting the total outside surface of a closed cylindrical oil tank at 60 paise per
sq. cm. is Rs. 237.60. The height of the tank is 6 times the radius of the base of the tank.
22
Find height and radius of the tank. (use 
)
7
60
237.60
6
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( 
25
22
7
)
OR /
The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into a cone of
22
height 28 cm. Find the diameter of the base of the cone so formed. (use 
)
7
616 cm2
28 cm
22
(
)
7
A straight highway leads to the foot of a tower. A man standing at the top of the tower
observes a car at an angle of depression of 30, which is approaching the foot of the tower
with a uniform speed. Six seconds later, the angle of depression of the car is found to be
60. Find the time taken by the car to reach the foot of the tower from this point.
30
60
26
27
If the coordinates of points A and B are (2, 2) and (2, 4) respectively, find the
3
coordinates of a point X such that AX  AB and X lies on the line segment AB.
7
A
B
(2, 2)
(2, 4)
X
3
AX  AB
X
AB
7
Find the area of the triangle formed by joining the mid-points of the sides of the triangle
ABC whose vertices are A(0, 1), B(2, 1), C(0, 3). Find the ratio of this area to the area of
the given triangle ABC.
ABC
A(0, 1), B(2, 1)
C(0, 3)
ABC
28
From tickets marked with numbers 2 to 31, one ticket is drawn at random. Find the
probability that it is
(i)
a multiple of 7
(ii)
an even number
(iii)
a prime number
2 31
(i)
7
(ii)
(iii)
SECTION-D /
Question numbers 29 to 34 carry four marks each.
29 34
4
29.
11
hrs. The tap of smaller diameter takes
12
2 hours more than the larger one to fill the tank separately. Find the time in which each
tap can separately fill the tank.
Two water taps together can fill a tank in 2
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2
11
12
2
OR/
A student scored a total of 32 marks in class tests in mathematics and science. Had he
scored 2 marks less in Science and 4 more in Mathematics, the product of his marks would
have been 253. Find his marks in two subjects.
32
2
4
253
30.
The first and the last terms of an AP are 17 and 350 respectively. If the common difference
is 9, how many terms are there and what is their sum ?
17
350
9
31.
In given figure, PQ is a chord of length 8 cm in a circle of radius 5 cm. The tangents at P
and Q intersect at a point T. Find the length of TP.
5 cm
T
32.
PQ
8 cm
P
Q
TP
A hollow metallic cylinder whose outer radius is 4.3 cm and internal radius is 1.1 cm and
whole length is 4 cm, is melted and recast into a solid cylinder 12 cm long. Find the
diameter of solid cylinder.
4.3 cm
1.1 cm
4 cm
12 cm
OR /
A vessel is in the form of an inverted cone. Its height is 8 cm. It is fill with water up to
brim. When 100 lead shots each of which is a solid sphere of radius 0.5 cm are dropped in
the vessel, one fourth of water flows out. Find the diameter of its top.
8 cm
100
0.5 cm
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33.
The slant height of a frustum of a cone is 4 cm and the perimeter of circular ends are 18 cm
and 6 cm. Find the cost of painting its curved surface at Rs. 10 per square centimeter.
4 cm
18 cm
6 cm
10
34.
Find the height of a mountain if the elevation of its top at an unknown distance from the
base is 60 and at a distance 10 km further off from the mountain, along the same line, the
angle of elevation is 30.
60
10 km
30
-o0o-
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