Goa Board Class 10 Question Paper Apr 2018 Mathematics English

2018 IV 04 0930 Seat No. :

Time : 2½ Hours MATHEMATICS (E)

Subject Code
S 0 2 1

Total No. of Questions : 8 (Printed Pages : 8) Maximum Marks : 80

INSTRUCTIONS : i) Answer each main question on a fresh page.
ii) All questions are compulsory.
iii) The question paper consists of 8 questions, each of
10 marks.
iv) There is no overall choice. However, internal choice has
been provided in 3 questions of 3 marks each.
v) In questions on constructions, the drawing should be clear
and exactly as per the given measurements. The
construction lines and arcs should also be maintained.
vi) Graph paper will be supplied on request.
vii) Use of calculator and Mathematical tables is not
permitted.

1. A) Select and write the most appropriate alternative from those given below : [1]
If
and
are the zeroes of the polynomial x2 + 6x + 5 then (
 )  _______
a) – 36 b) – 6 c) 6 d) 36
B) Using Euclid’s division algorithm find the H.C.F. of 255 and 867. [2]
C) Assuming that 5 is an irrational number, prove that 2 + 3 5 is also an
irrational number. [3]
D) If 3 and
3 are the zeroes of the polynomial 2x4 – 3x3 – 5x2 + 9x – 3.
Find the other two zeroes of the polynomial. [4]

2. A) Select and write the most appropriate alternative from those given below : [1]
One card is drawn from a well shuffled deck of 52 cards. The probability of
getting a face card is _______
1 3 3 1
a) b) c) d)
52 52 13 4
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B) A die is thrown once. Find the probability that the number appears on the top
face of the die is [2]
i) a prime number
ii) more than 4.
C) Find the roots of any one of the following quadratic equations : [3]
i) 8x2 – 14x + 5 = 0 (By factorisation method)
ii) 2x2 – 7x + 3 = 0 (By completing the square method).
D) Find two consecutive odd positive integers, sum of whose squares is 394. [4]

3. A) Select and write the most appropriate alternative from those given below : [1]
If 7x + 3y = 11 and 3x + 7y = –1 then x – y =
a) 3 b) 4 c) 10 d) 12
B) The following is a pair of linear equations in two variables :
7x – 5y = 4 and
14x + ky = – 4.
Answer the following questions with reference to the given pair of equations : [2]
i) Write down the condition for unique solutions.
ii) Find the value of k.
C) Find the solution of any one of the following pair of linear equations : [3]
i) 2x + 3y = 5 and
3x + 4y = 6 (By elimination method)
ii) x – 4y = 11 and
2x + 5y = – 4 (By cross-multiplication method)

D) Find the solution of the following pair of linear equations graphically : [4]
2x + y = 7 and
x + 2y = 8
Rewrite and complete the following tables.
2x + y = 7 x + 2y = 8

x x

y y

(Plot atleast 3 points for each line using a graph paper)

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4. A) Select and write the most appropriate alternative from those given below : [1]
The 12 th term of the arithmetic progression 9, 14, 19, 24 ....... is _______
a) 45 b) 46 c) 54 d) 64
B) The following table shows the daily income of 50 workers : [2]
Daily Income Number of Workers
(in Rs.)
100
400 18
400
700 15

700
1000 10
1000
1300 7

Find the Median of the above given data.
C) A man bought a scooter with 12 monthly instalments. He paid ` 6,000 as first
instalment and thereafter for each instalment he paid ` 250 less than the
previous month. By instalment if he paid ` 3,150 extra over the original price,
then find the original price of the scooter. [3]
D) The following table shows the marks scored by 40 students in Mathematics :

Marks Scored No. of Students Class Mark Deviation fd
(C.I.) (f ) (x ) d = x
a
E E

E E E E

0
10 2



10
20 5




20
30 14



30
40 9



40
50 6




50
60 4



Total
f = 40
E

fd = __
E E

Taking the class mark denoted by ‘a’ of the class-interval 20 – 30 as the
assumed mean, rewrite and complete the table and also find the mean of the
marks by the assumed mean method. [4]

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5. A) Select and write the most appropriate alternative from those given below : [1]
RP and RQ are tangent segments drawn from an external point R to a circle
with centre O. If
QRO  35 then the measure of
POQ  _____
a) 55° b) 70° c) 110° d) 145°

B) Given : Point O is the centre of a circle. MA and MB are two tangent segments
drawn from an external point M to the circle at A and B respectively. Prove
that : MA = MB. [3]

(Write only the proof with reasons)

C) Draw a circle with centre O and radius 2.7 cm. Take a point P at a distance
8.5 cm from the centre of the circle. Using a pair of compasses and ruler,
construct two tangents PS and PT to the circle. Measure and state the length
of the tangent segments. [3]

D) Using a pair of compasses and ruler, construct
ABC with sides AB = 8 cm,
3
BC = 9.5 cm and AC = 6.5 cm. Then construct  A
BC
whose sides are of
4
the corresponding sides of
ABC . [3]

6. A) Select and write the most appropriate alternative from those given below : [1]
If
ABC is right angled at C, then the value of sin (A + B) = _____
1 3
a) 0 b) 1 c) d)
2 2

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B) Attempt any one of the following : [3]
24
i) In
MAT,
A  90 and tan M
, then find :
7

a) The length of MT
b) The value of cos M
c) The value of sec T.
ii) Evaluate the following expression using known numerical values of
trigonometric ratios :
5 sin2 30° – 4 cos2 30° + 6 cot2 60°.

C) Prove the following identity : [2]

1
cosA
= cosec A
cot A
1+ cosA

D) Attempt the following :
i) Find the coordinate of the point which divides the line segment joining
the points (2, –1) and (–3, 4) internally in the ratio 3 : 2. [2]
ii) Find the area of
PQR whose vertices are P (5, 2), Q (–3, 7) and
R (2, –4). [2]

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7. A) Select and write the most appropriate alternative from those given below : [1]

ABC ~
PQR and ar (
ABC ) = 144 cm2, ar (
PQR) = 81 cm2. If QR = 27 cm
then BC = ______________ cm.

a) 9 b) 12 c) 36 d) 48

B) With reference to the given figure and the given conditions write only the
proof with reason of the following theorem. [3]

Given : In
DEF, DE  EF  DF


XYZ is constructed such that :

XY = DE, YZ = EF and
Y  90 .

Prove that :


DEF is a right angled triangle.

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C) Given : D is any point on side BC of
ABC . DE || AB and DF || AC.
A – F – B and A – E – C. EF and CB meet at H when produced as shown
in the fig. Prove that : [3]

HD2 = HB × HC

(Write only the proof with reasons)

D) From a point A on a bridge across a river BC, the angle of a depression of
the banks on opposite sides of river, B and C are 30° and 45° respectively. If
the bridge is at a height of 40 m as shown in the fig., find the width of the river BC.


3  1.732  [3]

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8. A) Select and write the most appropriate alternative from those given below :
i) The area of the circle that can be inscribed in a square of side 8 cm is
______ [1]
a) 8
b) 16
c) 32
d) 64

ii) If the surface area of a sphere is 196
cm2, then its radius is ________ cm. [1]
a) 7 b) 9 c) 11 d) 13
B) Attempt the following :
i) Find the area swept in one minute by a minute hand of a clock of length
12 cm. (Do not substitute for
) [1]
ii) Find the curved surface area of a right circular cylinder of diameter 7 cm
22
and height 11 cm. (Take
 ). [1]
7
C) A flower bed in the form of a rectangle of dimensions 25 m × 14 m with
semicircles on the outerside of the shorter sides of the rectangle as shown in
the fig. Calculate the number of rose plants that can be planted if each plant
requires 2m × 2m area. [3]

25 m

14 m

D) A right circular cylinder having radius 6 cm and height 15 cm is full of
ice-cream. The ice-cream is to be filled in cones of height 12 cm and radius
3 cm having a hemispherical top. Find the number of such cones that are
22
required to empty the cylinder. (Take
 ). [3]
7
_______________

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