Series RMT|
Code No. RSPL/2
Candidates must write the Code on the
Roll No.
title page of the answer-book.
Please check that this
question
paper contains 12
printed pages.
Code number given on the right hand side of the question paper should be
written on the title page of the answer-book by the candidate.
Please check that this question paper contains 38 questions.
Please write down the Serial Number of the question before attempting it.
MATHEMATICS (STANDARD)
Maximum Marks : 80
Time Allowed: 3 Hrs
General Instructions:
1.
This question paper has 5 Sections A, B, C, D, and E.
2.
Section A has 20 MCQ's 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 of assessment (04 marks each)
with sub-parts of the values of 1, 1 and 2 marks each respectively.
7.
All questions are compulsory. However an internal choice in 2 questions of
5 marks, 2 questions of 3 marks and 2 questions of2 marks has been provided.
An internal choice has been provided in the 2 marks questions of Section E.
8.
Draw neat figures wherever required. Take n =
whereever required if not
stated.
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P.T.O.
SECTION - A
mark each.
Section A consists of 20 questions of I
1.
If HCF and LCM of two numbers are 4 and 9696, then the product of two
numbers is
2.
(a) 9696
(b) 24242
(c) 38784
(d) 4848
lfa and ß are
(a)
zeroes
ofthe polynomial x+ 2x -4,
2
(c) 0
thens
6)
(d) None of these
3. Ifthe equation x+ 4x +k =0 has real and distinct roots, then
(a) k<4
(b) k>4
(c) ks4
(d) k24
4. If 31x + 43y =117 and 43x+31y = 105, then the value of x +y is
5.
(a) 3
(b) 2
(c) 0
(d) None of these
The
points (-4, 0), (4, 0) and (0, 3) are vertices of a/an
(a) right triangle
(c)equilateraltriangle
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(b) isosceles triangle
(d)scalenetriangle
6.
A vertical pole of length 20 m casts a shadow 10 m long on the ground and at the
same time a tower casts a shadow 50 m long, then the height of the tower is
(a) 100 m
(b)
(c)
(d) None of these
25 m
120 m
3 n d sin o = , 3 then the value of 0+ ¢ is
7. If cos 0 = a
2
2
(a) 30°
(b) 60°
(c) 90°
(d) 120°
sin 0
1+cos
(a)
Is equal to
(b)
cos 0
cos 0
sin 0
(d)
(c)-cos0
sin 6
9.
cos 0
sin0
cos
In the given figure, QA L AB and PB L AB, then AQ is
9 units
10 units
0
6 units B
(a) 15 units
(b) 8 units
(c) 5 units
(d) 9 units
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P.T.0.
In the given
10.
QPO
figure, PQ
are two
and PR
circle with centre O.
tangents to the
=25°, then 2QOR is
O
(b)
(a) 50
(d) 130°
(c) 120°
11.
IfAABC ADEF, ZA
12.
100°
=
47°, ZE
=
50°, then 2C is
(a) 47
(b) 50°
(c) 97
(d) 83°
In the given figure, perimeter of the sector is
60
3.5 cm
32
(a)em
3
(c)
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11
3
cm
b)
22
cm
(d) 10.5 cm
I
13.
Volume
of two spheres
are
in the ratio 64:27. The ratio
(a) 3:4
(b) 4:3
(c) 9: 16
14.
d) 16:9
If the class marks of
class size 3 is 13.5, then lower limit is
(a) 12.5
(b) 12
(c) 14
15.
16.
of their surtace ac
(d) 14.5
The area of a circle is 220 cm. The area of square inscribed in it is
(a) 49 cm2
(b) 70 cm
(c) 140 cm
(d) 150 cm*
If class size is 4 and the lower limit of first class is 8, if there are 7 classes then
upper limit of last class is
17.
(a) 36
(b) 32
(c) 40
d) 28
The probability that a non-leap year has 53 Sundays, is
(a)
(b)
(c)
d)
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5
7
P.T.0.
If tan 45°
18.
-cos 30
=
x
sin 45°
cos
45°, then
(d)
(c)
Direction:
a
19
=
(b)-2
(a) 2
by
x
In the question number 19 and 20,
statement
a statement
of Reason (R). Choose the correct
Statement A (Assertion): 6"
Statement R (Reason): 5
can
not
of Assertion (A)
is
followed
option.
number
end with 0 for any natural
is an irrational
n.
number.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct
explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true and reason (R) is not the correct
explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
d) Assertion (A) is false but reason (R) is true.
20.
Statement A (Assertion): The ratio in which x-axis divide the line segment
joining the points (1, 5) and (-2, -7) is 5:7.
Statement R (Reason): Given four points A, B, C and D will form a square if
AB = BC = CD = DA
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Both
a
assertion (A) and
reason
(R)
are
true and reason (R) is the
rect
explanation of assertion (A).
rect
(b) Both assertion (A) and reason (R) are true and reason (R) is not the corre
explanation of assertion (A).
(c) Assertion (A) is true but
reason
d) Assertion (A) is false but
reason
(R) is false.
(R) is true.
SECTION- B
Section B consists of5 questions of 2 marks each.
21.
The sum of two numbers is 137 and their difference is 43. Find the numbers.
22.
Prove that the lengths of tangents drawn from an external point to a circle are
equal.
23.
ABCD is
a
trapezium
at the point O.
24.
The
length
of a
in which AB
|| DC and its diagonals
intersect each other
Show that A0_ CO
pendulum
is 14
cm.
The
pendulum swings through
an
angle
of
60. Find the length of the arc describe by bob of the pendulum.
OR
A horse is tied to a peg at the corner of a square shaped grass field of side 14 cm.
If the area which horse cannot graze is 157.5 m. Find the length of the rope by
which horse is tied.
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1
P.T.O.
25. Prove that
1-sin sec0- tan
1+sin 0
0
OR
Prove t h a t t a n - 1 1+tan e
sin
0.
SECTION -C
Section C consists of 6
questions of 3 marks each.
26. Prove that 2 + 3 is an irrational number.
27.
Ifa and B are the roots of the equation x + 3x - 4 =0 then find the value of
1
a
28.
A two-digit number is such that the sum of its digits is 11. The number obtained
by reversing the order of digits is 7 more than the twice of original number. Find
the number.
OR
A fraction becomes ifthe denominator is increased by 1 and it will becomes
when both the numerator and denominator are increased by 1. Find the
fraction.
29.
If 3 sin 0 + 4 cos 0 = 5, prove that 3 cos 6-4 sin 0 = 0.
30.
Prove that the centre of a circle touching two intersecting lines lies on the angle
bisector of the lines.
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8
OR
n
the given figure, from an external point P, a tangent PD and a line
PAB is drawn to
prove that PD
a
circle with centre O. OM is
perpendicular
on
= PA - PB.
the
ent
cn0
P
B
31.
M
A card is drawn at random from a well-shuffled deck of playing cards. Find the
probability that the card drawn is
i)
a card of spade or an ace.
(i) neither
a
jack nor a king.
ii) a black king.
SECTION- D
Section D consists of 4 questions of 5 marks each.
32. The present age of a girl is 3 years more than three times the age of her sister
Three years hence, the girl's age will be 10 years more than twice the age of her
sister. Find their present age.
OR
A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted
from the number, the digits are reversed. Find the number.
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P.T.O.
33.
Sides AB, AC and median AD of a AABC are respectively proportional
to sides PQ. PR and median PS of another triangle PQR. Show that
AABC
34.
From
APQR.
a
solid cube of side 7
cm, a
conical
cavity of height
is hollowed out. Find the volume and surface
area
7
and radius 3
cm
cm
of remaining solid.
OR
A
right-angled triangle whose sides
the sides
are
3 cm, 4
cm
and 5
cm
is revolved about
volume of two
containing the right angle in two ways. Find the ratio of
cones so formed. Also, find the difference of their curved surface area. (n = 3.14)
35.
Compare the modal ages of two groups of students appearing for
an
entrance
examination.
Age (in years)
16- 18 18
18-20
20-22
22-24 24-26
Group A
50
78
46
28
23
Group B
54
89
40
25
17
SECTION - E
Case study based questions are compulsory.
36.
The floor of a design is given in figure. It has alternate grey and white blocks
taking O as origin and each block as 1 unit. A plant lover wants to construct a
square shape garden PQRS in the middle of the floor.
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On the basis of above answer the
following
i)What are the coordinates of the corners P, Q, R and S?
ii) Find the
(ii) Find the
length of side of the garden.
area
of the floor excluding the
garden.
OR
Find the distance of the mid-point of PS from corner Q and R.
37.
Harish
deposits
5 in his
on third day he deposits
piggy bank on first day, on second day he deposits
9, on fourth day he deposits
continues. On the basis of above
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answer
11
the
7,
11 and this process
following:
P.T.O.
i) The amount deposited by Harish on 10th day.
ii) The amount deposited by Harish on nth day.
ii) The total amount deposited by Harish in 10 days.
OR
To collect 7 1440 for how many
The students of
38.
days he has
to
deposit money?
that it
class X visited Qutb Minar. Teacher told them
building built in 1193 by Qutb-ud-din Aibak. Teacher asked them
to
see
18 the
the top of
the Qutb Minar using clinometer and to measure its height by using the concept
of trigonometry.
A students of height 2 metres is at distance of 71 metres from the foot of
Qutb Minar observe that the angle of elevation of top of the minar as 45°
On the basis of above answer the following:
(i) Draw the neat labelled diagram to show the above situation.
(i) Find the height of Qutb Minar.
(i) If the student move away from Qutb Minar and again observe that the
angle of elevation of top of Qutb Minar become 30°. Find distanee travelled
(Use 3
by the boy.
= 1.73)
OR
Ifa boyof height 1.6 m stands on a platform which is 1 m high and observes
that angle of elevation of Qutb Minar is 45°. Find the distance of platform
from Qutb Minar.
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