Page 1 of 10
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)
Page 2 of 10
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.
2.
3.
4.
If x1 is a common root of the equations ax2ax30 and x2xb0, then the value of
ab is :
(A)
3
(B)
3.5
(C)
6
(D)
3
2
2
ax ax30
x xb0
x1
ab
(A)
3
(B)
3.5
(C)
6
(D)
3
If the common difference of an A.P. is 5, then value of a18a13 is :
(A)
5
(B)
20
(C)
25
(D)
30
5
a18a13
(A)
5
(B)
20
(C)
25
(D)
30
A quadrilateral PQRS is drawn to circumscribe a circle. If PQ, QR, RS (in cm) are 5, 9, 8
respectively, then PS (in cm) equals :
(A)
7
(B)
6
(C)
5
(D)
4
PQRS
PQ, QR
RS cm
5, 9
8
cm
PS
(A)
7
(B)
6
(C)
5
(D)
4
If two tangents inclined at an angle 60 are drawn to a circle of radius 5 cm, then length of
each tangent (in cm) is equal to :
5 3
(A)
(B)
10
(C)
3
(D)
5 3
2
5 cm
60
cm
5 3
(B)
10
(C)
3
(D)
5 3
2
In the given figure, the pair of tangents PQ and PR drawn from an external point P to a
circle with centre O are inclined to each other at 90. If length of each tangents is 5 cm, then
the radius (in cm) of the circle is :
(A)
5.
(A)
10
(B)
O
90
7.5
(C)
P
5
PQ
5 cm
(D)
2.5
PR
cm
Page 3 of 10
(A)
6.
7.
8.
9
10
10
(B)
7.5
(C)
5
(D)
2.5
2
Triangle PQR is constructed similar to triangle ABC with scale factor . Triangle PQR is :
3
(A)
smaller than triangle ABC
(B)
same as triangle ABC
(C)
bigger than triangle ABC
(D)
none of these
2
ABC
PQR
PQR
3
(A)
ABC
(B)
ABC
(C)
ABC
(D)
3
The volume (in cm ) of the largest right circular cone that can be cut off from a cube of edge
4.2 cm is :
(A)
9.7
(B)
77.6
(C)
58.2
(D)
19.4
4.2
(A)
9.7
(B)
77.6
(C)
58.2
(D)
19.4
Area of a quadrant of a circle of circumference 22 cm, is (take 22/7)
(A)
3.05 cm2
(B)
3.5 cm2
(C)
9.625 cm2
(D)
35.5 cm2
22 cm
22/7
(A)
3.05 cm2
(B)
3.5 cm2
(C)
9.625 cm2
(D)
35.5 cm2
A girl sitting on the balcony is looking down at a flower pot placed on ground, then the
angle formed by her line of sight with the horizontal is called….
(A)
Angle of elevation
(B)
Angle of depression
(C)
reflex angle
(D)
complete angles
(A)
(B)
(C)
If p (E)0.05, then p (not E) is equal to :
(A)
0.05
(B)
0.5
p (E)0.05
p(
E)
(A)
0.05
(B)
0.5
(D)
(C)
0.9
(D)
0.95
(C)
0.9
(D)
0.95
SECTION-B /
Question numbers 11 to 18 carry two marks each.
11
11.
18
2
Find the values of k for which the following equation has equal roots.
(k12) x22 (k12) x20.
k
Page 4 of 10
12.
13.
(k12) x22 (k12) x20.
Which term of the A.P. 45, 41, 37, 33,…… is the first negative term ?
45, 41, 37,……
In the given figure, tangents AC and AB are drawn to a circle from a point A such that
BAC30. A chord BD is drawn parallel to the tangent AC. Find DBC.
A
BAC30
14.
AC
AC
BD
AB
DBC
In the given figure, a circular track is in the form of a ring whose inner circumference is
88 cm and outer circumference is 132 cm. Find its width.
(Ring)
88 cm
15
132 cm,
The solid, as shown in the figure, has a cube with a hemisphere on the top. The edge of the
cube is 6 cm and the diameter of the hemisphere is 4.2 cm. Find the total surface area of
the solid.
Page 5 of 10
6
4.2
16
17
18
A point P on x–axis is equidistant from A(6, 4) and B(2, 8). Find the coordinates
of P.
xP,
A(6, 4)
B(2, 8)
P
Find the coordinates of a point dividing the line segment joining the points P(3, 4) and
Q(1, 2) in ratio 2 : 1.
P(3, 4)
Q(1, 2)
2:1
A pack of 52 playing cards pack is shuffled well. A card is then drawn at random from the
pack of cards. Find the probability of getting :
(i)
a black face card,
(ii)
a queen.
52
(i)
(ii)
OR/
An urn contains 8 red, 6 white, 4 black balls. A ball is drawn at random from the urn.
Find the probability that the drawn ball is :
(i)
red or white,
(ii)
black.
8
6
4
(i)
(ii)
SECTION-C /
Question numbers 19 to 28 carry three marks each.
19 28
3
19.
If 5 is a root of the quadratic equation 2x2px150 and the quadratic equation
P (x2x)k0 has equal roots, find the value of k.
2x2px150
5
P (x2x)k0
k
OR /
Solve, for value of x : 4x22 (a2b2) xa2 b20.
x
4x22 (a2b2) xa2 b20.
Page 6 of 10
20.
If 12th term of an A.P. is 13 and the sum of its first four terms is 24, what is the sum of its
first 10 terms ?
12
13
24
10
21.
In the given figure a circle touches the sides PQ, QR and PR of PQR at the points X, Y and
1
Z respectively. Show that PXQYRZ XQYRZP (Perimeter of PQR)
2
PQ, QR
PQR
PR
PXQYRZ XQYRZP
1
2
X, Y
Z
PQR
OR/
In the given figure, from an external point P, tangents PX and PY are drawn to a circle with
centre O. If AB is another tangent to the circle at C and PX14 cm, find the perimeter of
PAB.
O
C
22.
P
AB
PX14 cm
PX
PY
PAB
Construct a right triangle in which the sides containing the right angle are 5 cm and
4
4 cm. Construct a similar triangle whose sides are
times the sides of the right triangle
5
drawn.
5
4
Page 7 of 10
23.
4
5
In given figure, find the area of the shaded region, where ABCD is a square of side 7 cm
22 

and semicircles are drawn with each side of the square as diameter.  Use  
7 

ABCD
7 cm
22

  7
24.


A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its open top
is 5 cm. It is filled with water upto the brim. When lead shots, spherical in shape and of
diameter 1 cm are dropped into the vessel one fourth of water flows out. Find the number
of lead shots dropped into the vessel.
8
5
1
4
1
OR/
A hemispherical tank, full of water, is emptied by a pipe at the rate of 1
4
litres
7
per second. How much time will it take to empty the tank, if it is 1 m in diameter ?
(Use 
22
)
7
1
4
7
1

25
26
22
7
The angle of elevation of the top of the tower from two points at distances a and b metres
from the base and in the same straight line with it are complementary. Prove that the
height of the tower is ab metres
a meter
b meter
ab meter
The vertices of a quadrilateral ABCD are A(8, 7), B(4, 5), C(1, 6), D(4, 5). Find
the area of the quadrilateral ABCD.
ABCD
A(8, 7), B(4, 5), C(1, 6)
D(4, 5)
Page 8 of 10
27
ABC is an isosceles triangle with ABAC and vertex A is on y-axis. If the coordinates of
vertex B and C are (5, 2) and (3, 2) respectively, then find the coordinates of vertex A.
Also find the length of median AD.
ABC
ABAC
A,yB
C
(5, 2)
28
(3, 2)
A
AD
Find the probability that a non leap year chosen at random has
(i)
52 Sundays
(ii)
53 Sundays
(i)
52
(ii)
53
SECTION-D /
Question numbers 29 to 34 carry four marks each.
29 34
4
29.
A two digit number is such that the product of its digits is 18. When 63 is subtracted from
the number, the digits interchanges their places. Find the number.
18
63
OR /
The denominator of a fraction is one more than twice the numerator. If the sum of the
16
fraction and its reciprocal is 2
, find the fraction.
21
16
2
21
30.
Each year a tree grows 5 cm less than it did the preceding year. If it grew by 1 m in the first
year, in how many years will it have ceased growing ?
5 cm
1m
31.
Prove that the lengths of tangents drawn from an external point to a circle are equal.
32.
A bucket made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm.
The radii of its lower and upper ends are 8 cm and 20 cm, respectively. Find the cost of the
bucket if the cost of metal sheet used is Rs. 20 per 100 cm2 (3.14)
16
8
20
100
20
3.14
OR/
Water in a canal 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much
area will it irrigate in 30 minutes, If 8 cm of standing water is needed ?
Page 9 of 10
6
33.
34.
1.5
10
/
30
8
A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of
uniform thickness. Find the thickness of the wire.
1
8
18
A man on cliff observes a boat at an angle of depression of 30 which is approaching the
shore to the point immediately beneath the observer with a uniform speed. Six minutes
later, the angle of depression of the boat is found to be 60. Find the total time taken by the
boat to reach the shore.
30
60
-oOo-
Page 10 of 10