MBOSE Class 10 Question Paper 2019 for Mathematics New Course

Total No. of Printed Pages—11
X/19/M (N)

2019

MATHEMATICS

( New Course )

( FOR REGULAR CANDIDATES WITH PRACTICALS/
INTERNAL ASSESSMENT )

Full Marks : 80
Pass Marks : 24

Time : 3 hours

The figures in the margin indicate full marks for the questions

General Instructions :
(i) The question paper consists of 30 questions divided into
five Sections—A, B, C, D and E.
(ii) Section—A contains 8 questions of 1 mark each.
Section—B contains 7 questions of 2 marks each.
Section—C contains 8 questions of 3 marks each.
Section—D contains 4 questions of 4 marks each.
Section—E contains 3 questions of 6 marks each.
(iii) There is no overall choice. However an internal choice has
been provided in three questions of 3 marks each, two
questions of 4 marks each and two questions of 6 marks
each.
(iv) In question on construction, the drawing should be neat
and exactly as per the given measurements.
(v) Questions which are meant for Visually Handicapped
(Blind) Students, should be answered by them only.
(vi) Use of Calculator/Mobile Phone is not permitted.

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SECTION—A
( Marks : 8 )

( Question Nos. 1 to 8 carry 1 mark each )

a
1. If is a rational number (b ¹ 0) in its lowest form, then what is
b
a
the condition on b so that the decimal representation of is
b
terminating?

2. Check, whether x = -2 is a solution of the equation
x 2 - 3x + 2 = 0 or not.

3. Find the 17th term of the sequence a n = 4n - 3.

4. Find the value of x (0º < x < 90º ) in tan 5x = 1.

5. Determine whether the given sides a = 7 cm, b = 24 cm and
c = 25 cm are sides of a right-angled triangle or not.

6. State SSS-similarity criterion.

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7. Find the circumference of a circle whose diameter is 35 cm.
22
(Use p = )
7

8. Define class-mark of a class interval.

SECTION—B
( Marks : 14 )

( Question Nos. 9 to 15 carry 2 marks each )

9. Determine k so that k + 2, 4k - 6, 3k - 2 are the three
consecutive terms of an A.P.

10. Evaluate :

4 1
+ - cos2 45º
2 2
cot 30º sin 60º

11. Prove that

2
2 cos2 q + =2
1 + cot2 q

12. Find the coordinates of the centroid of the triangle whose
vertices are (-2, 3), (2, - 1) and (4, 0).

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13. If the point P (x, y ) is equidistant from the points A (5, 1) and
B (1, 5), then prove that x = y.

14. The areas of two similar triangles ABC and PQR are in the ratio
9 : 16. If BC = 4·5 cm, find the length of QR.

15. If the tangent at a point P to a circle with centre O cuts a line
through O at Q such that PQ = 24 cm and OQ = 25 cm, then
find the radius of the circle.

instead of Question No. 15 given above ]

15. (a) Define a circle. 1

(b) How many tangents can be drawn from a point outside
the circle? 1

SECTION—C
( Marks : 24 )

( Question Nos. 16 to 23 carry 3 marks each )

16. Using ruler and compass only, construct a D PQR with sides
QR = 7 cm, PQ = 6 cm and ÐPQR = 60º. Then construct another
3
triangle whose sides are th of the corresponding sides
5
of DPQR. (Only traces of construction are required.)

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instead of Question No. 16 given in Page No. 4 ]

16. (a) In a right-angled triangle, the square of the hypotenuse is
equal to the sum of the squares of the other two sides.

( State whether True or False ) 1

(b) Define similar triangles. 2

17. In the adjoining figure,
A

B D C

BD AB
DABC is such that = , ÐB = 70º, ÐC = 50º. Find ÐBAD.
DC AC
Or
In the given figure,
T

O P

T¢

find PT , if OP = 41 cm and OT ¢ = 9 cm.

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instead of Question No. 17 given in Page No. 5 ]

17. (a) Define secant of a circle. 1
(b) A tangent to a circle is _____ to the radius through the
point of contact.
( Fill in the blank ) 1

(c) Two triangles are said to be equiangular, if their
corresponding angles are _____.
( Fill in the blank ) 1

18. A steel wire when bent in the form of a square encloses an area
of 121 cm2 . If the same wire is bent in the form of a circle, then
22
find the area of the circle. (Use p = )
7

Or

The minute hand of a clock is 7 cm long. Find the area of the
face of the clock by the minute hand between 9 A.M. and
22
9:35 A.M. (Use p = )
7

19. A box contains 20 cards numbered from 1 to 20. A card is
drawn at random from the box. Find the probability that the
number on the drawn card is—

(a) divisible by 2 or 3;

(b) a prime number.

20. Using Euclid’s division algorithm, find the HCF of 9367 and
3451.

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21. Find the sum of the following series :

72 + 70 + 68 + ... + 40

22. If a, b are zeroes of the polynomial p (x ) = 3x 2 - 2x - 6, then
find a 2 + b2 .

23. Prove that
sin 70º cosec 20º
+ - 2 cos 70º× cosec 20º = 0
cos 20º sec 70º
Or
a
If tan q = , then show that
b
a sin q - b cos q a 2 - b 2
=
a sin q + b cos q a 2 + b 2

SECTION—D
( Marks : 16 )

( Question Nos. 24 to 27 carry 4 marks each )

24. The product of Reena’s age (in years) 5 years ago and her age
8 years later is 30. Find her present age.
Or
The area of a rectangle gets reduced by 80 square units, if its
length is reduced by 5 units and the breadth is increased by
2 units. If we increase the length by 10 units and decrease the
breadth by 5 units, the area is increased by 50 square units.
Find the length and breadth of the rectangle.

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25. A kite is flying at a height of 75 m from the level ground,
attached to a string inclined at 60º to the horizontal. Find the
length of the string, assuming that there is no slack in it.
(Use 3 = 1·73)

Or
A vertically straight tree, 15 m high, was broken by the wind in
such a way that its top just touched the ground and made an
angle of 60º with the ground. At what height from the ground did
the tree break? (Use 3 = 1·732)

instead of Question No. 25 given above ]

25. (a) If sec q + tan q = m and sec q - tan q = n, then prove that
mn = 1. 2

(b) If sin q = cos q, then q = 45º.
( State whether True or False ) 1

(c) 1 + cot2 q = _____. ( Fill in the blank ) 1

26. Find the value of ‘p’ for which the given points (-3, 9), (2, p ) and
(4, - 5) are collinear.

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27. Prove that, if a line is drawn parallel to one side of a triangle
intersecting the other two sides, then the other two sides are
divided in the same ratio.

instead of Question No. 27 given above ]

27. (a) What is the length of the altitude of an equilateral triangle
of side 2 cm? 2

(b) State mid-point theorem. 2

SECTION—E
( Marks : 18 )

( Question Nos. 28 to 30 carry 6 marks each )

28. Solve the following system of linear equations graphically :

x - y +1 = 0
3x + 2y - 12 = 0
Find the area of the triangle formed by the lines and x-axis (plot
at least three points for each graph).

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instead of Question No. 28 given in Page No. 9 ]

28. Solve the following system of linear equations :

2x - 3y = 13
7x - 2y = 20

29. A metallic bucket, open at the top, of height 24 cm is in the
form of the frustum of a cone, the radii of whose lower and
upper circular ends are 7 cm and 14 cm respectively.

(a) Find the volume of water which can completely fill the
bucket.

(b) Find the area of the metal sheet used to make the bucket.
22
(Use p = )
7

Or

From a solid cylinder whose height is 8 cm and radius 6 cm, a
conical cavity of height 8 cm and of base radius 6 cm is
hollowed out. Find the volume of the remaining solid. Also, find
the total surface area of the remaining solid. (Use p = 3·14)

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30. The following distribution shows the daily pocket allowances of
children of a locality. The mean pocket allowance is R 18. Find
the missing frequency f :

Daily pocket allowance (in R) 11–13 13–15 15–17 17–19 19–21 21–23 23–25

Frequency 7 6 9 13 f 5 4

Or

The following table shows the ages of the patients admitted in a
hospital during a year :

Age (in years) 5–15 15–25 25–35 35–45 45–55 55–65

No. of patients 6 11 21 23 14 5

Find the mode of the data given above.

HHH

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