SubjectCode: 041

SQP-2
Mathematics-Standard
Time Allowed: 3 Hours Maximum Marks: 80

General Instructions:
1. This Question Paper has 5 Sections A-E.
2. Section A has 20 MCQs carrying 01 mark each.
3. Section B has 5 questions carrying 02 marks each.
4 Section C has 6 questions carrying 03 marks each.
5. Section D has 4 questions carrying 05 marks each.
6. Section E has 3 case based integrated units ofassssment (04 marks each) with sub-parts of the values of1
and 2 marks each respectively.
7
All Questions are
compulsory. However,
an internal choice in 2 Qs
of5
marks, 2 Qs of3 marks amd 2
2 marks has been provided. An internal choice has been provided in the 2 marks questions of Section E.
Qs of

8. Draw neat figures wherever required. Take n= 22/7 wherever required if not stated.

SECTION A
Section A consists of 20 questions of1 mark each.
1. Find the value of k for which the equation (k- 12) x* +2 (k- 12) x +2 = 0 equal and real solutions.
(a) 12 (b) 14
(c) Both (a) and (b) (d) None of the above
2. PA and PB are tangents to the circle with centre 0. If ZAPB = 60°, then ZPAB is
(a) 30° (b) 60° (c)90° (d) 15°
3. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 7+v5 (b) 5 (c) 10 (d) 12
4. If tan 45° - cos 30° = x sin 45° cos 45°, then x =

(a) 2
5.
(b) -2
( (d)
The radius of a sector of a circle with central
is
angle 90° is 7 cm. The area of the minor segment of the circle

(a) 77/2 cm (b) 14 cm (c) 18 cm (d) 24 cm2

6. Find the distance between the
points, A(2a, 6a) and B(2a+V3a, 5a).
(a) v2a = 2a (b) vaa =2a
7.
(c)v6a =2a (d) v10a=4
A
box contains 100
discs, numbered from I to 100. If one disc is drawn at random from the box, then the
probability that it bears a prime number less than 30, is
7
(a) To0 (b) 10 4 9
(c) 50 (d) 50
8. Solve the
quadratic equation for x: 4/3x + 5x -23 = 0

/3 (b) (c) 2 (d)

-3 2
16 43
Class 10
9. A tangent PQ at a point P of a circle of radius 8 cm meets a line through the centre O at a point Q so that OQ
=17 cm. Find the length of PQ
(a) 10 cm (b) 20 cm (c) 15 cm (d) 0.5 cm
10. From the given figure, the angle of depression of point C from the point P is
P

A&602

(a) 45 (b) 90° (c) 75 (d) 30

11. Four observations are 2, 4,6 and 8. The frequencies ofthe first three observations are 3, 2 and 1 respectively.
If the mean of the observations is 4, then the frequency of the fourth observation is
(a) 8 (b) 4 (c) (d) 2
12. A month is selected at random from a year. The probability that it is May or July is

a) ( (d)
3
13. The zeroes ofthe quadratic polynomial x+ kx + k,where k> 0 .
(a) are both positive (b) are both negative
(c)are always equal (d) are always unequal
14. In the given figure, D and E are two points lying on side AB, such that AD = BE. If DP || BC and EQ || AC,
then

E
B
Q
(a) PQIAB (b) PQ AB (c) PQ|| CD (d) PQ= AC
2 sin A + 3 cots A
15. If cosec A =
2 then, the value or Is
4(tan? A cos
-

A)
(a) 1 (b) 2 (c) 3 (d) 0
16. A wall 8 m long casts a shadow 5 m long. At the same time, a tower casts shadow 50
of tower is
a m
long, then the height
(a) 20 mn (b) 80 mn (c) 40 m (d) 200 m
17. The ratio of the volumes of two spheres is 8: 27. The ratio between the
radius of two spheres is
(a) 2:3 (b) 4:27 (c)8:9 (d) 4:9
18. Find the area of a quadrant of a circle, where the cirCumference of circle is 44 cm.
| Use T= :
(a) 38.5 cm (b) 77 cm (c) 60 cm er.
(d) 154 cm
DIRECTION: In the question number 19 and 20, a
statement ot Assertion
Reason (R). Choose the correct (A) is
option. followed by a statement of
19. Statement A (Assertion): The
arithmeuc mean or the following frequency
Class interval 0-10 |10-20 20-30 30-40 distribution is 25.
Frequency 5 18 15
40-50
Statement R (Reason) : Mean (x) =
16 6
S is its frequency. ,where x= (lower +
limit upper limit) of
(a) Both assertion (A) and it class interval and
Both assertion (A) and reason
reason (R) are
true and
reason (R) is the
(c) (R) are true
Assertion (A) is true but and reason correct
(d) Assertion (A) is false but reason (R) is
false. (R) is not the correct explanation of assertion (A).
Mathematics-Standard
reason (R) is
true. explanation of assertion (A).
 .
Statement A
(Assertion) : 2V2 is not the root of the quadratic equation = 0.
Statement R
(Reason) : The root of a quadratic x"-4V4 TO
D o n assertion (A) and reason (R) are true and equation satisfies it. correct explanation Or assertion (A)
reason (R) is the
Oboth assertion (A) and reason (R) are true and reason (R) is not the correct explanaion assertion (A) or
(c) Assertion (A) is true but reason
(d) Assertion (A) is false but reason (R) false.
is
(R) is true.

SECTION B
Section B consists of 5 questions of 2 marks each.
lMayank made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one
end (see
figure). The height of the cylinder is 1.45 m and its radius is 30 cm. Find the total surtace area of
the bird-bath.
10cm

45 m

T OR
A toy is in the form of a
cylinder with two hemispheres at two ends. If the height of the cylinder is 12 cm,
and its base is of diameter 7 find the total surface
cm, area of the toy.

2 CILl

-7 cm-
22. Which term of the A.P. 3, 14, 25, 36, will be 99 more than its 25th term?
...

23. Represent the following equations graphically: x + y 3 0, 2x + 3y 7 0 -

= -

24. In the given figure, PA and PB are

tangents to the circle from an external
touching the circle at Q. If PA 12 cm, QC QD 3 cm, then find PC+ PD.point
P. CD is another
= = =
tangent

O
P

25. A, B and C starts at the same time in the same direction to

run around a circular
round in 252 seconds, B in 308 seconds and Cin 198 stadium. A completes a
seconds, all starting at the same
will they meet again at the point. After what time
starting point?
OR
Three numbers are in the ratio 1:2:3 and their HCFis 12. Find
the positive square root of largest number.
SECTION C
Section Cconsists of 6 questions
of 3 marks each.
26. Obtain
the zerocs of the quadratic polynomial 3x-8x 43 and verity the
zeroes and coefficients. relationship between its
27. It is
given that
AABC- AFDF such that AB= 5 cm, AC 7 cm, DF- 15 cn and DE 12
ofthe remaining sides of the triangles.
=
cm. Find the lengths
18
Class 10
 OR
In the given figure, AB || DE and BD || EF. Prove that DC =
CF x AC.

A-

28. Show that (V3 + Vs is an irrational number.

29. A ladder which is inclined at an angle of 60° to the horizontal reaches a 11 m long wall at a point 2.35 m beloW

the top of the wall. Find the length of the ladder. (Use y3 = 1.73)
30. Iffrom an external point B, two tangents BC and BD are drawn to a circle with centre O such that cDB
120°. prove that BC + BD = BO, i.e., B0 = 2BC.

OR
circle of radius 3 of 60° to then find length of each tangent.
If two tangents angle
are inclined at an a cm,

31. A die is thrown once. Find the probability ofgetting:

(i) a prime number;
(ii) a number lying between 2 and 6;
(iii) an odd number.

SECTION D
Section D consists of4 questions of 5 marks each.

1+ cos A

32. Prove that

cosec A- cot A cosec A+cotA =
2(2cosec"A -1) cos?A
cosec A+cot A cosec A-cot A
OR
n 4 sin A cos A

cosA sinA and n =

cos A + sin A, then show that -m= . cos A-sin A cot A - tan A
If m =
-

n
The tangents at A and B
16 of a circle of radius 10 cm.

33. In the given figure, AB is a chord of length cm

intersect at a point P. Find the length of PA.

OR
ABCD in which ZB =90°. If AD = 23 cm, AB = 29
In the given figure, a circle is inscribed in a quadrilateral
circle.
c m and DS
=
5 cm, find the radius (r) of the

D O B

of a right circular cylinder with cone on one end. The height and radius of base of the
34. A 10y is in the form
Cylindrical part are 13 cm
and 5 cm respectively. The base of the conical part are sanme as that ofthe cylinder.
Calculate: the surface area of the toy, if the height of the cone is 12 cm. [Take T = 22/7]

Mathematics Standard 19
 to the
difference
is 20 1s
equal
common
. The Sum of the first n terms A.P. whose first term is 8 and the 1s o. Td

of an difference
first term is -30 and the
conmmon
u r s t 2n terms of another A.P. whose

SECTION E
compulsory. consider
Case study based questions a r e
preferred
modes of communication
interpreting the distribution ofages
across
36. You are interested in
Phone call
the data given below. Email
Letter
Age-group Text Message WhatsApp 0
0
16 0
1-5
2 5
6-10
15 8
11-15
3 10
4 21
16-2
0
30 32
21-25 20 2
23 29
26-30
follow:
the questions that
Cse the above information to
answer

use text message

for c o m m u n i c a t i o n .
(i) of people who
Find the average age
communication.
who phone call for
(ii) Find the average age of people
use

communication.
who WhatsApp for
(iii) Find the model age of people
use

OR
Letter for communication.
Find the median of people who use
graph paper. But
points (4, -1) and (-3, 2)
on a
students to mark the
37. In a Maths class, teacher asked the
Shweta mistakenly located the points (-1, 4) and (3,-2).

Based the
given information, answer the questions that follow
on

(i) The distance between the

points, that teacher asked to mark is
(i) The mid point of the line joining the
points plotted by Shweta is
(ii) The coordinates of the point which divides
the join of points
plotted by Shweta in the ratio 1: 2 is
OR
If all the four
points are
plotted on graph paper, then the mid
a
in II Quadrant is point of the line joining the points lying
38. Anil went for a walk in the
evening near
path of train A is given by railway
Anil that track
with his father who is an
equation expert in mathematics. He told
His father
put some question to Anil.
x +
2y= 4 and path of train B is
20 Help Anil to solve the given by equation 2x+ 4y 12. =
of questions Anil's father.

Class 10
(i) Equation x 2y 4 intersects the x-axis and y-axis at which points?
+ =

() Dra the graph of given equation. Find the coordinates of point of intersection of two given equations.
(ii) Equation 2x + 4y 12 intersects the x-axis and y-axis at which points?
=

OR
Show that the system of linear equation represented by two given lines are inconsistent.