# Mathematics Paper

```MODEL PAPER - 1
1
CONTINUOUS & COMPREHENSIVE EVALUATION
SUMMATIVE ASSESSMENT
MODEL PAPER - 1
MATHEMATICS - PAPER - II
X CLASS
Max Marks : 40]
[Time : 2 : 45 hrs
SECTION - I
Note : 1.
2.
7×1=7M
Each question carries one mark
.
d
a
1.
Show that cos 32o . cos 58o – sin 32o . sin 58o = 0.
2.
What is the probability of drawing a king from a deck of cards.
3.
A vertical pole is 10 mt high. The length of it’s shadow is 10 3 . What is the angle of elevation
of the sun.
4.
 ABC ~  DEF, BC = 3 cm, EF = 4 cm and area of  ABC = 54 cm2. Determine the area of
 DEF.
5.
Find the arithmetic mean of First Five prime numbers.
6.
Express sec  in terms of tan .
7.
A cylinder and a cone have bases of equal radii and of equal heights. Show that their volumes are
in the ratio 3 : 1.
Note : 1.
2.
8.
,
B
E
C
D
b
a
r
e
d
y
H
SECTION - II
6 × 2 = 12 M
Each question carries two mark
In a triangle ABC, AD is drawn perpendicular to BC prove that AB2 – BD2 = AC2 – CD2.
A
B
D
C
9.
Write the formulae of median of a grouped data and explain the terms in it.
10.
A box contains 5 red marbles, 9 white marbles and 6 green marbles, one marble is taken out the
box at random. What is the probability that the marble taken out will be
i) red
ii) white
iii) Non-green
MATHEMATICS - PAPER - I
11.
2
Prove that
4(sin4 30o + cos4 60o) –3 (cos2 45o – sin2 90o) = 2
12.
Calculate the mode for the following frequency distribution.
C.I
0  4 4  8 8  12 12  16
f
13.
4
8
5
6
22 

Find the surface area and volume of a sphere of radius 21 cm  use  =
.
7 

SECTION - III
Note : 1.
2.
14.
Internal choice is given in each question.
Each question carries four mark
.
d
a
(a) Two boys are in opposite sides of a pole of 100 mts. height. They measure the angle of
elevation of the top of the pole as 30o and 60o respectively. Find the distance through which the
boys are separated.
b
a
r
e
d
y
H
(OR)
(b) If sec  + tan  = a, show that sin  =
15.
4 × 4 = 16 M
a 2 1
a2 1
(a) The radius of a metallic sphere is 3 cm. It is melted and drawn into a wire having diameter
of the cross section as 0.2 cm. Find the length of the wire.
,
B
E
C
D
(OR)
(b) The frequency distribution of marks scored by 50 students in a test is given below. Find the
arithmetic mean.
Marks
0  19 20  39 40  59 60  79 80  99
No. of students
5
15
22
6
2
16.
(a) (i)
Show that the lengths of tangents drawn from an external point to a circle are equal.
(ii) The length of the minute hand of a clock is 14 cm. Find the area swept by the minute
hand in 15 minutes.
(OR)
(b) A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random
from the box. Find the probability that it bears (i) a two – digit number (ii) a perfect cube
number (iii) a number divisible by 10.
17.
(a) Draw 0 give curve for the following data. From the curve find out median.
Marks
0  5 5  10 10  15 15  20 20  25 25  30 30  35
No. of students
3
7
13
25
40
14
10
(OR)
MODEL PAPER - 1
3
(b) Construct an isosceles triangle whose base is 8 cm. and altitude is 4 cm. Then draw another
triangle whose sides are 1
1
times. The corresponding sides of the isosceles triangle.
2
SECTION - IV
Note : 1.
Each question carries
24.
o
2 sin 45 is
(c) 3
(b) 1
(c) –1
(
)
(
)
(d) 1
.
d
a
(d) none
b
a
r
e
d
y
H
(b) 4 : 5
(c) 16 : 25
(d) 25 : 16
The arithmetic mean of first n' natural number is
n
+1
2
(b)
n 1
2
,
B
E
C
D
(c)
n 1
2
(d)
(
)
n
2
If the diameter of the base of a right circular cylinder is 14 cm and it’s height is 20 cm. Then it’s
curved surface area is
(
)
(a) 594 cm2
23.
=5M
If one areas of two similar triangles are 16 cm2 and 25 cm2 respectively. Then the ratio their
corresponding sides is
(
)
(a)
22.
2
mark.
sin 4   cos 4 
sin 2   cos 2 
(a) 5 : 4
21.
2
(b) 4
(a) 0
20.
1
The value of cos 00 + sin 90o +
(a) 5
19.
1
2.
18.
10 ×
(b) 1188 cm2
(c) 440 cm2
(d) 1540 cm2
In  ABC, if the sides are 5, 12, 13 then  ABC is
(a) Scalene triangle
(b) Right angled triangle
(c) an acute angled triangle
(d) Obtuse angled triangle.
Among the following a correct statement is
(a) 0  P(I)  1
(b) 0 < P(I) < 2
(c) 0  P(I)
(
)
(
)
(d) None
25.
The angle between a tangent to a circle and the radius drawn at the end point of contact is _____
(
)
o
o
o
o
(a) 90
(b) 60
(c) 120
(d) 180
26.
The probability of drawing out a face card from a deck of cards is _____
(a)
27.
1
52
(b)
1
26
(c)
3
13
(d)
(b) 0
(c) 2
)
(
)
2
13
cos 80o
+ cos 59o . cosec 31o is equal to _____
sin 10o
(a) 1
(
(d) 3
```