Mathematics - Paper

MODEL PAPER - 3
1
CONTINUOUS & COMPREHENSIVE EVALUATION
SUMMATIVE ASSESSMENT
MODEL PAPER - 3
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.
Perimeters of two similar triangles ABC, PQR are 80 cm, 36 cm respectively and PQ = 9 cm find AB.
2.
If the radius of the sphere is 2.8 cm then find the volume.
3.
Evaluate
4.
Find the median of first five natural numbers
5.
In observer making an angle of elevation ° with the top of the clock tower which is ‘r’ meters away
from him. Draw the diagram for the situation.
6.
Define ogive curve.
7.
A bag contain 3 red balls and 4 blue balls A ball is drawn at random from the bag. What is the probability
that the ball drawn is red.
a
b
a
r
e
d
y
H
2cot 45
1  T an 2 45
,
B
E
C
D
SECTION - II
Note : 1.
Answer the following questions.
2.
Each question carries two mark
6 × 2 = 12 M
8.
A solid iron rod has a cylindrical shape. Its height is 12 cm and base diameter is 7 cm then find the total
volume of 5 rods?
9.
What is the probability of drawing black ‘2’ from a deck of cards?
10.
Show that Tan2 + Tan4 = sec4 – sec2
11.
In the rightangle triangle the hypotenuse is 5 cm more than twice of the third side and the third side 4m
less than the hypotenuse then find the sides of the triangle.
12.
A person observes two banks of a river at angles of depression x1 and x2(x1 < x2) from the top of a tree
of height ‘h’ which is at a side of a river. The width of the river is d. Draw the diagram for this situation.
13.
If AP and AQ are the two tangents of a circle with centre ‘O’ so that POQ = 120° then find PAQ .
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MATHEMATICS - PAPER - II
2
SECTION - III
Note : 1.
2.
14.
4 × 4 = 16 M
Internal choice is given in each question.
Each question carries four mark
(a) A solid metallic sphere of diameter 36 cm is merted and recast into a number of smaller ones each
diameter 4
2
cm and height 4 cm. Find the number of cones so formed.
3
(OR)
(b) Find the area of the segment shaded in figure if PQ = 12 cm, PR = 5 cm, and QR is the diameter
of the circle with centre O.
Q
15.
P
12 cm
5 cm
O
a
b
a
r
e
d
y
H
.
d
(a) Construct a triangle ABC with some measurements and construct another triangle which is similar
to ABC and each side
5
of the side of ABC.
3
(OR)
,
B
E
C
D
(b) Draw a line segment AB of length 12 cm. Taking A as centre, draw a circle of radius 6 cm and
taking B as centre draw another circle of radius 3 cm. construct tangents to each circle from the
centre of the other circle.
16.
(a) Fin the mean of the following data
Marks
0  9 10  17 20  29 30  39 40  49 50  59
No.of students
3
7
13
20
8
6
(OR)
(b) The following table gives the distribution of the life time of 225 electrical equipments.
Life time(in hours) 0  20 20  40 40  60 60  80 80  100 100  120
Frequency
10
52
81
35
29
38
17.
(a) Show that
Tan  sec   1
= sec  + Tan 
Tan  sec   1
(OR)
(b) When dice thrown twice 1. Find the probability to get 6 on both the dice 2. Find the probability
that 6 does not appear.
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MODEL PAPER - 3
3
SECTION - IV
Note : 1.
Each question carries
2
=5M
mark.
(b) 5
1  cos2 x
cos x
(c) 21
Tanx
(b)
sin x
1  Tan 2 x
(c)
(b) 1
(d)
1  sin 2 x
(c) 2
(b) 49.23
(d) 3
a
b
a
r
e
d
y
H
(c) 81.45
(
)
(
)
(
)
1  cos 2 x
cos x
If fixi = 1390, fi = 35 then the mean x =
(a) 39.71
)
(d) 12
Probability of certain event
(a) – 1
21.
1
sin x =
(a)
20.
2
1 Mean of 13 observation is 8 one observation 20 is deleted the mean of remaining observation(
(a) 7
19.
1
Choose the correct answer.
2.
18.
10 ×
.
d
(d) None of these
A
22.
Form the adjoining figure DE//BC, x = __________ cm
x+4
D
x+3
2x – 1
B
(a) 7
23.
(b) 60
(b) 13
If cot  =
(a)
27.
(
(c) 70
(c) 14
)
(d) None of these
)
(d) 15
The shadow of a tower is 3 times to the height of the tower then find the angle of elevation with the
sun
(
)
(a) 60°
26.
(d) None
When 25 observations are arranged in ascending order then the median is _______ observation
(
(a) 12
25.
(c) 13
x+1
C
If the diagonals of Rhombus are 24 cm and 32 cm respectively then the perimeter = _______ cm
(a) 80
24.
,
B
E
C
D
(b) 2
E
(b) 30°
(c) 70°
(d) 90°
7
1  sin 

then
8
cos 
7
11
(b)
819
4
(c)
112
7
(d)
(b) 9, 5, 7
(c) 400, 300, 500
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)
(
)
113  8
7
Which of the following form a right angled triangle
(a) 9, 15, 12
(
(d) 2,
5,1