Goa Board Class 10 Question Paper June 2019 Mathematics CWSN English

2019 VI 17 0230 Seat No.

Time : 3 Hours MATHEMATICS (E)
(For Children with Special Needs)
Subject Code

S 0 2 5

Total No. of Questions : 7 (Printed Pages : 11) Maximum Marks : 65

INSTRUCTIONS : (i) Answer each main question on a new page.

(ii) All questions are compulsory.

(iii) The question paper consists of seven questions.

(iv) There is no overall choice. However, internal choice

has been provided in two questions of three marks

each and one question of four marks.

(v) In question on construction, the drawing should be

neat and exactly as per the given measurement. The

construction lines and arcs should also be

maintained.

(vi) Chart of tables 2 to 9 will be supplied on request.

(vii) Use of Calculator and Mathematical tables is not

permitted.

(viii) The numbers on the right side indicate marks.

1. (A) Select and write the most appropriate alternative from those provided

below : 1

If x + y = 10 and x – y = 4, then the value of y is ................

(a) 2

(b) 3

(c) 4

(d) 7

(B) A pair of linear equations in two variables is given below : 2

x + 4y = 6

3x + 12y = 18

Answer the following questions :

(i) Write the condition for infinitely many solutions.

(ii) Verify whether the equations have infinitely many solutions.

(C) By elimination method, find the solution of any one of the following

equations : 3

(i) 2x + 3y = 14

4x – y = 14

(ii) x + 3y = 9

2x + y = 8

(D) Attempt any one of the following : 4

(i) The cost of 2 pens and 1 eraser together is Rs. 26, while the

cost of 1 pen and 2 erasers together is Rs. 22. Find the cost of

each pen and each eraser.

(ii) The sum of two natural numbers is 20 and their difference is

8. Find the two natural numbers.

2. (A) Select and write the most appropriate alternative from those provided

below : 1

When the quadratic polynomial x – 3x2 – 4 is compared with its general

form ax2 + bx + c, then value of a is .................

(a) –4

(b) –3

(c) 1

(d) 2

(B) Attempt the following : 2

(i) Find the sum of the zeroes of the polynomial 2x2 + 7x + 5.

(ii) Find the product of the zeroes of the polynomial x2 + 2x – 15.

(C) Divide x3 + 6x2 + 14x + 18 by x + 2 and write the quotient and the

remainder. 3

(D) A bag contains 6 green balls, 5 red balls and 4 blue balls. If a ball

is drawn at random from the bag. What is the probability that it will

be : 3

(i) a red ball ?

(ii) a blue ball ?

(iii) a white ball ?

3. (A) Select and write the most appropriate alternative from those provided

below : 1

The roots of the quadratic equation (x + 6) (x + 7) = 0 are ......................

(a) +6 and +7

(b) –6 and –7

(c) +6 and –7

(d) –6 and +7

(B) Attempt the following : 2

(i) Write the quadratic equation x 2 – 18 = –3x in the form

ax2 + bx + c = 0.

(ii) Find the roots of the quadratic equation x2 – 36 = 0.

(C) Find the roots of any one of the following : 3

(i) x2 + 7x + 12 = 0 (by factorisation method)

(ii) x2 + 4x – 21 = 0 (by quadratic formula method)

(D) The following frequency distribution table shows the marks obtained

by the students of a class in a test. 4

Marks Obtained No. of Students Class Marks fi × xi

C.I. (fi) (xi)

0—10 2 — —

10—20 3 — —

20—30 6 — —

30—40 10 — —

40—50 7 — —

50—60 2 — —

fi = ..... fixi = .....

Rewrite and complete the table. Also find the mean of the marks obtained

by the direct method. (Write your answer correct upto two places of

decimal)

4. (A) Select and write the most appropriate from those provided below : 1

45
The decimal form of the rational number is ..................
4

(a) 0.11

(b) 1.12

(c) 11.25

(d) 112.5

(B) The product of two numbers is 1000. If their HCF is 5, then find their

L.C.M. 2

(C) Using Euclids division algorithm, find the H.C.F. of 145 and 30. 2

(D) Find the sum of the first 10 terms of the A.P. 5, 10, 15, 20, ........ 3

5. (A) Select and write the most appropriate alternative from those provided

below : 1

In POD, O = 90°, OD = 3 cm, PO = 4 cm and PD = 5 cm, then

tan P = .................

3
(a)
5

3
(b)
4

5
(c)
4

5
(d)
3

5
(B) In PTS, T = 90°, If cos P = , then find : 2
13

(i) The length of TS.

(ii) The length of sin P.

(C) Substitute the known numerical values of trigonometric ratios and find
the value of : 3

3 tan 2 45 4 sin 2 30 8 cos2 60

(D) Find the distance between the points N(4, 0) and A(10, 8) using the

distance formula. 3
6. (A) Select and write the most appropriate alternative from those provided
below : 1

In BET, YZ ET. If BY = 2 cm, YE = 5 cm, BZ = 6 cm, then

ZT = ........................

(a) 5 cm

(b) 8 cm

(c) 15 cm

(d) 21 cm

(B) If DEF ~ MPT, DE = 4 cm, EF = 5 cm, MP = 8 cm and

MT = 6 cm. Find : 2

(a) length PT

(b) length DF.

(C) In ABC, B = 90° and BD AC. With reference to the figure given
below, fill in the blanks to complete the proof : 3

Statements Reasons
In BDC and ABC
(i) BDC = ................. Each is a right angle
(ii) C = C ....................................
(iii) BDC ~ ABC ....................................
(D) In the figure given below, P is the centre of a circle. QR and QT are
two tangents drawn from point Q to a circle at R and T respectively.
With reference to the figure answer the following questions to complete
the proof : 4

(i) Name the side equal to side PR.

(ii) Name the common side of PRQ and PTQ ?

(iii) Name the right angles of PRQ and PTQ ?

(iv) By which criterion/theorem are PRQ and PTQ congruent ?

7. (A) Select and write the most appropriate alternative from those provided

below : 1

If diameter of a circle is 8.2 cm, then its radius is .............. cm.

(a) 4.01

(b) 4.1

(c) 8.2

(d) 16.4

(B) In the following figure, O is the centre of the circle with radius 9 cm.

O – HAT is the sector and HOT = 40°. 2

Find :

(i) Area of sector O – HAT (Do not substitute the value of )

(ii) Length of arc HAT (Do not substitute the value of )

(C) Draw a line segment JK of length 6 cm and divide it into 4 equal parts.

(Use only a pair of compasses and ruler). 3

(D) Draw a circle with centre ‘O’ and radius 3.5 cm. Take a point A at

a distance of 8.7 cm from the centre O. Using a pair of compasses and

ruler, construct two tangents AM and AN to the circle. Measure and

state the length of each tangent segment. 3