SMT. SULOCHANADEVI SINGHANIA SCHOOL, THANE
Class Sub· e�t Date
Exam
Prelims
X
Maths 16-01-1.4
Marks Time
80
2 ½ hrs
No. of sides
6
General Instructions:
1. Attempt all questions from Section A.
2. Attempt any four questions from Section B.
3. All working, including rough work, must be clearly shown, and must be
done on the same sheet as rest of the answer.
4. Omission of" essential working will result in Joss of marks.
SECTION A
(Attempt all questions from this section)
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Question 1
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in the
Choose the correct answer to the question from the given option�.aQ�\vrite
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separate answer sheet.
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1} The centroid of triangle whose vertices are (5, -6), (-2, 3)�aha-.f6, 15) is
A) (1, -4)
2)
B) (-1, -4)
C) (-1, 4) ,. :· �·\'
•��· D) (1, 4)
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t <
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5sec2 A - Stan2 A + 1 is equal to
A)-4
B)6
C)4
,
�,
D)7
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3) The reflection of the point A (5, 0) in �)ltt'y = 0 is
a., ''"' ·'l...
A)(5, 0)
B) (0, 5)
D) (0, -5)
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r
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4) If n term of an AP is 13 �J *�>hen the 20 th term is
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'('°"-.:\ .,
D) -76
B) 67�,)�) .C) 76
A) -67
th
�. �:-:�s
5)Arjun invests �s�8�qo:·in buying shares of face value Rs.100 each at a
premium-oJil'0o/�ithe number of shares he bought is
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D) 800
C) 80
A) 88 ,". ."·
. '·.,' B)880
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6) �{-.,}' -;;-"intercept of the line whose equation is llx - Sy+ 2
- �
'
B)�
·��
S
!J 11
C)
11
D)�
= 0 is
2
S
7) If6 is the mean proportional between two numbers 'x' and 'y' and 48 is the
third pr oportional to 'x' and 'y', then the numbers are:
A) x = 3, y = 12
B)x = 4, y = 9
C)x = 6, y = 6
D) x = 9, y = 24
8) The value of k for which the quadratic equation 16x2
and equal roots are
A) 6, -
1
6
B) 36, -36
+ 4kx + 9 = O has real
D) 6, -6
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(9) If x E R . then the solution: set for 5 - 3x � -2x + 2, is
A) all real numbers less than. or equal to 3
B) all real numbers greater than or equal to 3
C) all real numbers less than or equal to (-3)
D) all real numbers greater than or equal to (-3)
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(10) Find the class mark of the modal class for the following distribution:
Class
Interval
Frequency
A) 12.5
0-5
5 - 10
l 0·- 15
15- 20
10
15
12
20
B) 20
C) 17.5
D) 22.5
20 -25
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(11) The slope of a line perpendicular to the line passing throui� t��'.j�i'nts (2, 5)
r
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and (-3, 6) is
.
A) -l
s
B) 5
C) -5
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(12) In the adjoining figure, sides MN, NL an.�fi:'l:M of
liLM N touch a circle at the points -A}i��).nd C
respectively. If AN=5cm, CL=4cm-�hf.CM=6cm,
then the perimeter of 11LMN is, .11.>_.; �::··
.
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A) 15cm
B) 40cm
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D) 60C7V-·��< "'
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(13) In the given figure,:��jl·t5E, then the length of CD is
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C) 30cm
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A
N
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"->·"
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A) 1013cm
B) 3.5cm
C) 2.5cm
D) 2.7cm
on the ground, then the sun's
(14) If a pole 6m high casts shadow 2v3m long
elevation is
A) 30°
B) 60°
C) 45 °
2
D) 90 °
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(15) Assertion (A): The curved sw-face area of cylinder with radius 2cm �d height
10cm is 40rrcm 2 .
Reason (R): The volume of cone is one third the volume of cylinder.
(A) Both Assertion and Reason are true and R is the correct explanation of A.
(B) Both Assertion and Reason are true ahd R is not the correct explanation of A.
(C) Assertion is true but Reason is false:
(C) Assertion is false but Reason is true.
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Question 2
A) Prove thefollowing trigonometric identity:
cot0+cosec 0-1
cot0-cosec 0+1
1+ cos0
---sin 0
D
B) In the adjoining figure, 0 is the.centre of
the circle and LAOC = 110° .
(i) LADC
Find:
(ii) LABC
C) If X
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(iii) LOAC
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.
•
✓2a+1+✓2a-1
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-�• th�n ��)�operties of proportion, prove that :
= ../za+f.
'·'
x2 -4ax + 1,.,_�:)l�
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[4]
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,1
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Question 3
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A) Mr. Joseph ��t1q"a recurring deposi t acc�unt in a bank for 3 years. If the rate
.'"\,.
?<. ..7.
of interest i!; ��,. .p.a. and the bank pays Rs.1776 as interest at the time of
maturity.(�ci)(QThe monthly deposit (ii) The amount at the time of maturity.
,f�
[41
..;,
�)���ace area of a sphere is 1386 cm 2. If the sphere is melted and reca.st into
•,..,,�lid cylind�rs of radius 3.5cm and height 6cm. Calculate: (i) Radius of the
sphere (ii) Number of cylinders recast.
[4]
C) Use graph paper for this question.
[5]
(i) Plot A, B, C where A (2,4), B (-2,1 ), C (5,0)
(ii) Reflect points A and B ·on the x-axis and name them as A' and B'. Write their
co-ordinates.
(iii) Give a geometrical name to the figure fonned by joining the points
. ABB'A'C. Find its Area.
(iv) Name two points from the figure which are invariant .on reflection in x-axis.
3
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SECTIONB
(Attempt any four questions from this section)
.Jftiestion 4
A) Solve the following inequation.and-represent the solution set on the number
line.
-2 <
.!_ - zx < 1 � x EN
[3]
- 2
3 -
6
1
B) The sum of three numbers in an A-P is (-12) and their product is 36 Find the
numbers.
[3]
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C) Mr. Rohit went to a department store and buys the foilowing articles.
'.,
Sr. No
Bought Items
Price per items
Quantity
1
A packet of sweets
Rs.450
3
2
Hair oil
Chess board
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Rs.300
. ·�ps.t
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2
Rs.500
Discount.
[4)
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_--'4,; 5%
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18%
l
10%
12%
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(i) Find the total amount of the GST Paid.._,._\)-... ••
(ii) The total bill amount including GST,P.a:°td�y him .
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Question 5
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A) Determine the ratio in ���-,tfi� line 2x + y
joining the points A(2,<��Gtiid B (3, 7).
=
4
divides the line segment
[3]
B) Construct a �ABC w:i��C/= 6.5cm, AB
5.5cm, AC
5cm.
down
the radius of the
Construct the incircle�fthe triangle. Measure and write
=
circle.
=
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AC'-·,�...... "-"
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L
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1 '
L
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;.f" �
C) In 4LMT{i""PQ II MN such that
LP,_�' PM= 6cm, MN= 20c�.
,..�,--\"
Fm,q���
(i) tile length of PQ
(ii) Area of Trapeziwn PQNM : Area of
Triangle LPQ
§
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Question 6
site banks of a ri�er. Betwee� the� in the
A) A and B are two points on the oppo
. Find the width of the nver 1f angles
river, is a boat with a mast of height 20m°
38 from the point A and 26 ° from the
of elevation of the tip of the mast are
foot of the mast are on the same level.
point B. The points A and B and the
re.
[5]
Give your answer to the nearest met
4
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' ..
B) Scores obtained bvJ 120
Scores
0-10
No.of
shooters
10-20
5
10
shooters m
. a shooting competition are given below.
20-30 30,-:- 40
18
40-50
50-60
26
19
.23
60-70 70-80
8
11
Use a g raph paper to draw
an ogive for the give� distribution taking 2cm
scores on one axis and 2C7!t
=:; 20 shooters on the o ther axi�.
Use the ogive to estimate:
(i} Median
(ii) The number of students
who obtained more than 60 scores.
= 10
[5]
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�estion 7
"'
.
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A) Solve the following equation and give your answer correct to three signl'�t\
figures.
x 2 - 3x - 9 = 0
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B) IfA :;
�] then find A 2 - SA+ 7 l, where I is an id��ii'ii�rix of
·
'>t
order 2 x 2. 1
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.
V. ,,"•
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C) Deepak bought 4500, Rs.10 shares paying 12% per·i\h��,'\
J11:Jiltf. He sold
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them when the price rose to Rs.23 and invested th��pr.gceeds in Rs.2S shares
¾·
\
paying 10% per annum, at Rs.18. Find the ch ��ira"his annual income.
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J{uestion 8
A) Construct a triangle
h
\,f�:
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ABC with AB\;=;�S:Scm, AC = 6cm, and LBAC = 105 ° .
i,,.
�t,
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Hence, (i) Construct the locus·of.R,cilii\s'·equidistant from BA and BC
(ii) Construct the locus of poiij's·�uidistant from Band C
(iii) Mark the point which;.&tisfies the above two loci as P.
[3]
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,.
- ,,.,,·z-�,,.
�- B) Cards bearing nu�ets 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20 are kept in a bag.
om from the bag. Find the probability of getting a card
A card is ·arafrl"�d
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t
is:
which
•
(i) A P..���nfuber: (ii� A number divisible by 4.
(ii9 A�n�er that 1s multiple of 6.
[3]
A
and
-4)
pojnts
(2,
the
(5,
B -2).
C)k��ght line passes �ough
AB
lme
the
of
e
Slop
(i)
d:
�
) (ii) The equation ofthe line AB
(iii) The value of k , ifAB passes through the point
p (k + 3, k-4)
[4 )
·t,
•
'Question 9
A) On a map drawn to a scale of1: 20,000 a rectangular plot ofland.ABCD has
AB = 32cm and BC=24cm. Calculate
(i) The diagonal distance of the plot in lan.
(ii) Toe area of the plot in square lan.
[3]
5
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[3]
B) Find the mean of the following distribution by step deviation method.
Class - Intervals
20-30
30-40
40-50
50-60
60-70
70-80
Frequency
10
.6
8
12
5
9
C) A plane travels a distance of 1600 km at an average speed of x km/hr. On the
return journey, due to bad weath�r as the speed was reduced by 40 km/hr, it
took 1 hour 20 minutes more than onward journey. Find x.
[4]
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�estion 10
A) The 5 th term of a G.P is 48 and the 8th term is 384. Find its ll th term.
B) What must be added to the polynomial 2x
remainder 10 when divided by (2x + 1).
3
-
3x
2
-
,
.,
",�>OJ
\!��
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Bx, so thatiS:1�]-v�s a
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' ✓-�-
•
C) The following distributio� represents the height of the student{'cr("a,\�hool:
Height
(in cm)
145- 150
No. of
students
34
150- 155
155 - 160
_,\
42
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('l�<f�"i65
165- 1'70
6
13
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