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SUMMATIVE ASSESSMENT – II, 2012
65001
II, 2012
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 choice 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.
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(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.
Which of the following equations has the product of its roots as 4 ?
(A)
x24x40
(B)
x24x40
(C)
x24x40
(D)
x24x240
4
(A)
x24x40
(B)
x24x40
(C)
x24x40
(D)
x24x240
2.
For what value of k ; k2, 4k6, 3k2 are three consecutive terms of an A.P. ?
(A) 1
(B)
1
(C)
3
(D)
3
k
k2, 4k6
3k2
(A) 1
(B)
1
(C)
3
(D)
3
3.
In the given figure, PA and PB are tangents to the circle with centre O. If OAB25 then
APB is :
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(A)
60
PA
(A)
4.
60
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(B)
PB
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50
O
(C)
25
(B)
50
(C)
25
(D)
OAB25
155
APB
(D)
155
(D)
80
In given figure, BAC60 and AB is a diameter, then CBD is :
(A)
60
(B)
30
(C)
45
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BAC60
(A)
5.
60
(B)
CBD
AB
30
(C)
45
(D)
80
In the given figure, TP and TQ are tangents to the circle with centre O such that
POQ110, then PTQ is equal to :
(A)
60
(B)
TP
70
TQ
(C)
80
O
(D)
90
POQ110
PTQ
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(A)
6.
60
(B)
70
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(C)
80
(D)
90
A
To divide a line segment AB in the ratio 2 : 5, a ray AX is drawn such that BAX is acute.
Then points are marked at equal intervals at AX. The minimum number of these points
is :
(A) 2
(B)
7
(C)
5
(D)
3
AB
2:5
AX
BAX
AX
(A)
7.
2
(B)
7
(C)
5
(D)
3
The circumference of the edge of a hemispherical bowl is 132 cm. When  is taken as
22
, the capacity of the bowl in cm3 is.
7
(A)
2772
(B)
924
(C)
19404
(D)
9702
22
एक अधधगोरीम कटोये के ससये की ऩरयसध 132 सेभी है , जफकक 
सरमा गमा है । कटोये
7
की धारयता (घनसेभी भं) है :
(A)
2772
(B)
924
(C)
19404
(D)
9702
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8.
Two coins of diameter 2 cms and 4 cms respectively are kept one over the other as
shown in the figure. The area of the shaded ring shaped region in square cm is :

(A)
(B)
2
(C)
3
(D)
4
दो ससक्के जजनके व्मास क्रभश् 2 सेभी तथा 4 सेभी हं , एक दस
ू ये के ऊऩय यखे गए हं , जैसा कक
आकृ सत भं कदखामा गमा है । छामाॊककत वरम के आकाय के बाग का ऺेत्रपर (वगध सेभी भं) है :

(A)
9.
2
(C)
If the length of the shadow of a tower is
sun is :
(A)
45
(B)
30
(A)
10.
(B)
45
(B)
30
A
If probability of happening of an event is
event is :
(A)
0
(B)
0
(B)
4
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(C)
60
(D)
90
3
(C)
60
(D)
90
5
then the probability of non-happening of this
9
1
(C)
4
9
(D)
2
3
1
(C)
4
9
(D)
2
3
5
9
(A)
(D)
3 times its height, then the angle of elevation of
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3
SECTION-B /
Question numbers 11 to 18 carry two marks each.
11
11.
18
2
Find the roots of the following quadratic equation :
15x210 6 x100
15x210 6 x100
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12.
Which term of the Arithmetic Progression
3, 10, 17, ……… will be 84 more than its 13th term.
3, 10, 17, ………
13.
13
84
A tangent PT is drawn parallel to a chord AB of a circle, as shown in given figure. Prove
that APB is an isosceles triangle.
AB
PT
APB
14.
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In the given diagram, is a design where in, circles of diameter 2 cms are touching each other.
The area of rectangle leaving the areas of circles (shaded area) has to be painted. Find out
the area to be painted.
(Take 3.14)
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दी गइध आकृ सत भं , एक कडजाइन फना हुआ है जजसभं 2 सेभी व्मास वारे वृत्त, ऩयस्ऩय स्ऩशध कय यहे हं ।
वृत्तं के ऺेत्रपर को छोड़ कय आमत के शेष ऺेत्रपर को ऩंट कयना है (छामाॊककत बाग को)। ऩंट कयने
वारे ऺेत्र का ऺेत्रपर ऻात कीजजए। (3.14 रीजजए)
15.
A metallic solid sphere of radius 4.2 cm is melted and recast into the shape of a solid
cylinder of radius 6 cm. Find the height of the cylinder.
4.2 सेभी त्रत्रज्मा के धातु के ठोस गोरे को त्रऩघराकय 6 सेभी त्रत्रज्मा के एक ठोस फेरन भं ढारा गमा।
फेरन की ऊॉचाई ऻात कीजजए।
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16.
Show that A(1, 0), B(3, 1), C (2, 2) and D(2, 1) are the vertices of a parallelogram ABCD.
A(1, 0), B(3, 1), C (2, 2)
17.
D(2, 1)
ABCD
x y 1
If the midpoint of the line segment joining A  ,
and B (x1, y3) is C (5, 2),
2 
2
find x, y.
x y 1
A ,
2 
2
C (5, 2),
B (x1, y3)
x, y
18.
A die is thrown once. Find the probability of getting
(i)
an even prime number
(ii)
a multiple of 3.
(i)
(ii)
3
OR/
A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. A ball is drawn at
random from the bag. Find the probability that it is :
(i)
black
(ii)
not green
5
8
4
7
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(i)
(ii)
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SECTION-C /
Question numbers 19 to 28 carry three marks each.
19 28
3
19.
Find the roots of the following equation :
1
1
1
1
  
ab x
a
b
x
1
1
1
1
  
ab x
a
b
x
OR/
Out of a group of swans,
7
times the square root of the total number are playing on the
2
shore of a tank. The two remaining ones are playing in the water. Find the total number of
swans.
7
2
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20.
How many three digit numbers are such that when divided by 7, leave a remainder 3, in
each case.
7
21.
3
Prove that the angle between the two tangents to a circle with centre O, drawn from an
external point, is supplementary to the angle subtended by the line segment joining the
points of contact at the centre.
OR/
Prove that the parallelogram circumscribing a circle is a rhombus.
22.
Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an
angle of 45.
5
23.
45
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In the given figure, a semicircle is drawn on AB as diameter, and O is center. Semi circular
flower beds are formed on AO and OB as diametes. If AB is 28 m, find the area of the
shaded region.
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दी गइध आकृ सत भं, AB को व्मास भान कय, कंद्र O का एक अधधवत्त
ृ खीॊचा गमा। AO तथा OB को व्मास
भान कय अधधवत्त
ृ ीम पूरं की क्मारयमॉॊ फनाइध गइध । मकद AB28 भी है तो छामाॊककत बाग का ऺेत्रपर
ऻात कीजजए।
24.
The circumference of the base of a conical tent is 44 m. If the height of tent is 24 m, find the
length of the canvas used in making the tent, if the width of the canvas is 2m.
22 

 Use  7 
एक शॊक्वाकाय टं ट के आधाय की ऩरयसध 44 भी तथा ऊॉचाई 24 भी है । इसभे रगने वारे 2 भी चौड़ाई के
केनवस (कऩड़े ) की रम्फाई ऻात कीजजए।[ 
22
का प्रमोग कीजजए ]
7
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25.
A 1.6 m tall girl stands at a distance of 3.2 m from a lamp post and casts a shadow of 4.8 m
on the ground. Find the height of the lamppost.
1.6
26.
3.2
Find the point of the x-axis which is equidistant from the points (5, 4) and (2, 3). Also find
the area of triangle formed by these points.
x-
27.
(5, 4)
(2, 3)
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The line segment joining the points A(3, 2) and B(5, 1) is divided at the point P in the ratio 1 :
2 and P lies on the line 3x18yk0. Find the value of k.
P
P
28.
4.8
A(3, 2)
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3x18yk0
A
1:2
k
The king, queen and jack of clubs are removed from a pack of 52 playing cards and then the
remaining pack is well shuffled. One card is selected from the remaining cards. Find the
probability of getting
(i)
a heart
(ii)
a king
(iii)
a club
52
(i)
(ii)
(iii)
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SECTION-D /
Question numbers 29 to 34 carry four marks each.
29 34
4
29.
A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more books for the
same amount, each would have cost him Rs. 1 less. How many books did he buy ?
80
4
1
OR/
The denominator of a fraction is two more than its numerator. If the sum of the fraction
34
and its reciprocal is
, find the fraction.
15
34
2
15
30.
In a garden bed, there are 23 rose plants in the first row, 21 are in the 2nd, 19 in 3rd row and so
on. There are 5 plants in the last row. How many rows are there of rose plants ? Also find
the total number of rose plants in the garden.
23
21,
19
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31.
Prove that the lengths of two tangents drawn from an external point to a circle are equal.
32.
Find the volume of the largest solid right circular cone that can be cut out of a solid cube of
side 14 cm.
14 सेभी बुजा के एक ठोस घन भं से काट कय सनकारे जा सकने वारे फड़े से फड़े शॊकु का आमतन
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ऻात कीजजए।
OR/अथवा
A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is
19 cm and the diameter of cylindrical and hemispherical parts is 7 cm. Find the total surface
area of the solid.
एक ठोस, एक फेरन के आकाय का है जजसके दोनं ससयं ऩय एक अधधगोरा रगा हुआ है । इस ठोस की
कुर ऊॉचाई 19 सेभी है तथा फेरनाकाय तथा अधधगोराकाय बागं का व्मास 7 सेभी है । ठोस का सॊऩण
ू ध
ऩृष्ठीम ऺेत्रपर ऻात कीजजए।
33.
The radius of circular ends of a solid frustum of a cone are 33 cm and 27 cm. Its slant height
is 10 cm. Find the volume and the total surface area of frustum.
एक ठोस शॊकु के सछन्नक के वृतीम ससयं की त्रत्रज्माऍॊ 33 सेभी तथा 27 सेभी हं तथा इसकी सतमधक
ऊॉचाई 10 सेभी है । इस शॊकु के सछन्नक का आमतन तथा सम्ऩूणध ऺेत्रपर ऻात कीजजए।
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34.
The angle of elevation of a jet plane from a point A on the ground is 60. After a flight of 30
seconds, the angle of elevation changes to 30. If the jet plane is flying at a constant height
of 3000 3 m, find the speed of the jet plane.
60
30
30
3000 3
-o0o-
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