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MODEL PAPER - 4
1
CONTINUOUS & COMPREHENSIVE EVALUATION
SUMMATIVE ASSESSMENT
MODEL PAPER - 4
MATHEMATICS - PAPER - II
X CLASS
Max Marks : 40]
[Time : 2 : 45 hrs
SECTION - I
Note : 1.
2.
7×1=7M
Answer all the following questions.
Each question carries one mark
.
d
1.
In ABC, DE//BC AD = 2 cm, BD = 3 cm and AC = 7.5 cm find CE.
2.
A tangent is drawn to a circle of radius 6 cm from a point 10 cm away from the centre. find the length
of the tangent.
3.
a
b
a
r
e
d
y
H
1  Tan 2 A
3
and
If sin A =
1  Tan 2 A
2
4.
Raghu tord, If we fold a rectangular sheet along length or width the cylindrical shape formed will have
same volume”. Do you agree with Raghu’s statement? Give reason.
5.
A bag contains 8 red, 10 blue and 12 while balls. Find the probability that the drawn ball is Find the
probability that the drawn ball is (i) blue (ii) red or white
6.
Haritha said, “The mean of first 100 odd numbers is 100”. Justify your answer.
7.
Construct a tangent to a circle of radius 3 cm.
,
B
E
C
D
SECTION - II
Note : 1.
Answer the following questions.
2.
Each question carries two mark
8.
6 × 2 = 12 M
9.
Ramu is running a milk shop. Gopi went to buy a litre of milk from Ramu’s shop. As 1 litre measuring jar
was not available, Ramu had taken a cone shaped vessel of same height and base radius as that of 1
litre measuring jar and poured twice in Gopis vessel.
Does Gopi get a litre of milk by doing so? Give your reason.
A circle touches all the four sides of a quadirlateral ABCD. Prove that AB + CD = BC + AD
10.
Show that
11.
Two dice are rolled simultaneously and counts are added. Write the sample space and complete the
table give below
1  sin A
= sec A + Tan A
1  sin A
Event :Sum on 2dice
2
3 4 5 6 7 8 9 10 11 12
Pr obability
1
36
1
36
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MATHEMATICS - PAPER - II
2
12.
The following are the marks of a students in a class 35, 21, 27, 30, 24, 38, 48, 32, 34. find the (i) mean
(ii) median.
13.
If 3 Tan A = 4, then find sin A and cos A
SECTION - III
Note : 1.
2.
14.
4 × 4 = 16 M
Internal choice is given in each question.
Each question carries four mark
(a) A, B, C are semi-circles of diameters 14 cm and E is a semi-circle having circle D. ‘O’ is the
centre of semicircle E Find the area of the shaded region.
E
D
A
C
B
a
b
a
r
e
d
y
H
(OR)
.
d
(b) A metallic sphere of radius 4.2 cm is melted and recast into a cylinder of radius 6 cm. Find the
lateral surface area of the cylinder.
15.
(a) Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle 60°.
(OR)
(b) The distribution below gives the weight of 30 students of a class. Find the median weight of the
students by drawing ogive curves.
,
B
E
C
D
Weight in kg 40  45 45  50 50  55 55  60 60  65 65  70 70  75
No.of students
2
3
8
6
6
3
2
16.
(a) ABC is a right triangle, right angle at C. Let BC = a CA = b, AB = c and let ‘P’ be the length of
perpendicular from C on AB. Prove that (i) PC = ab (ii)
1
1
1
 2 2
2
P
a
b
(OR)
(b) The angle of elevation of top of a tower from the foot of the building is 60° and the angle of
elevation of the top of the tower from top of the building and the distance between the building and
the tower.
17.
(a) Find
x2 1
if x = cosec  + cot 
x2 1
(OR)
(b) The ages of (in years) of 360 patients treated in a hospital on a particular day are given below.
Agesin years
10  20 20  30 30  40 40  50 50  60 60  70
Number of patients
90
40
60
20
120
30
Find the mean age of a patient by a suitable method.
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MODEL PAPER - 4
3
SECTION - IV
Note : 1.
19.
Each question carries
1
4
(b)
3
4
(d)
=5M
(c)
3
2
(d)
(c) 17 cm
(b) 196 cm2
a
b
a
r
e
d
y
H
(c) 2cm2
(No. of students)
cumulative
frequency
)
(
)
.
d
(
)
(
)
(
)
(d) 154 cm2
(d) 36 : 25
In ABC, B  90 , AB = 3 , BC = 1 then A =
,
B
E
C
D
(
(d) 7 cm
(c) 5 : 6
(b) 45°
)
1
2
The ratio of two corresponding sides of triangles of area 25 cm2 and 36cm2 is
(b) 2 : 3
(
2
3
The area of a circle that can be inscribed in a square of side 14 cm is
(a) 30°
24.
(c)
(b) 119cm
(a) 25 : 36
23.
1
2
The height of a Right circular cone is 12 cm and its base radius is 5 cm, its slant height is
(a) 140 cm2
22.
2
mark.
(b) 1
(a) 13 cm
21.
2
cos2 20° + cos2 70° =
(a) 0
20.
1
The probability of an event is 25% and the probability of its complement is
(a)
1
Choose the correct answer.
2.
18.
10 ×
(c) 60°
(d)
50
40
30
20
10
5
10
15
20
25
30
35
x
Upper limits (marks)
A student draws a cumulative frequency curve for the marks obtained by 40 students of a class as
shown above the median marks obtained by the students of the class is
(
)
(a) 10
25.
(b) 15
(c) 20
(d) 25
Formula to find mode of a grouped data is

f f

1
0
(a) l   2f  f  f   h
 1 0 2

f 0  f1 
h
 2f 0  f1  f 2 
(c) l  
(
f f
1
0
(b) l  2f  (f  f )  h
1
0
2
f f
0
1
(d) l  2f  f  f  h
1
0
2
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)
MATHEMATICS - PAPER - II
26.
No. of tangents that can be drawn to a circle is/are
(a) 1
27.
4
(b) 2
(
(c) 3
)
(d) Infinite
The length of the are AB is one-fourth of the circumference of the circle. If the radius of the circle is 14
cm, the area of the sector is
(
)
O
14 cm
A
(a) 92 cm2
(b) 154 cm2
,
B
E
C
D
14 cm
B
(c) 98 cm2
(d) 616 cm2
a
b
a
r
e
d
y
H
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.
d