MBOSE Class 10 Question Paper 2019 for Mathematics Old Course

Total No. of Printed Pages—16
X/19/M (O)

2019

MATHEMATICS

( Old Course )

( COMPARTMENTAL AND IMPROVEMENT CANDIDATES WITH
INTERNAL ASSESSMENT )

Full Marks : 80
Pass Marks : 24

( NON-REGULAR, PRIVATE AND COMPARTMENT WITHOUT
INTERNAL ASSESSMENT )

Full Marks : 100
Pass Marks : 30

Time : 3 hours
The figures in the margin indicate full marks for the questions

General Instructions :

(i) This question paper consists of 32 questions divided into
six Sections A, B, C, D, E and F.

(ii) Marks allocated to every question are indicated against
each.

(iii) Question Nos. 1 to 30 (Section—A to Section—E) are to
be answered by Compartmental and Improvement
Candidates with Internal marks.

(iv) Question Nos. 1 to 32 (Section—A to Section—F) are to
be answered by Compartmental Candidates without
Internal marks/Non-Regular/Private Candidates.

/6 [ P.T.O.

( 2 )

(v) In Question Nos. 1 to 8 of Section—A and Question
No. 31 sub Nos. (a) to (d) of Section—F, there are four
options marked (A), (B), (C), (D). Only one of these
options is correct. The letter indicating the correct answer
should be written in capital in the answer book.

(vi) In question on construction, the drawing should be neat
and exactly as per the given measurements.

(vii) Questions which are meant for Visually Handicapped
(Blind) Students, should be answered by them only.

(viii) Use of Calculator/Mobile Phone is not permitted.

SECTION—A
( Marks : 10 )
( Question Nos. 1 to 10 carry 1 mark each )
1. Which of the following is the correct alternative of the decimal
representation of an irrational number?

(A) Non-terminating, repeating

(B) Terminating

(C) Terminating, repeating

(D) Non-terminating, non-repeating

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( 3 )

2. A polynomial of degree n has at most
(A) ( n + 2 ) zeroes

(B) 2n zeroes

(C) ( n - 2 ) zeroes

(D) n zeroes

3. The discriminant of the quadratic equation 2x 2 - 5x - 4 = 0, is

(A) -57

(B) -57

(C) 57

(D) -7

4. The second term of an AP whose first term, a = 3 and common
difference, d = -4 is

(A) 1

(B) -1

(C) 3

(D) -4

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( 4 )

5. In D ABC, if XY ||BC and AX = 2 cm, XB = 3 cm, AY = 4 cm,
then YC is equal to

(A) 2 cm

(B) 3 cm

(C) 4 cm

(D) 6 cm

6. In D ABC right angled at B, if AC = 17 cm, AB = 8 cm,
BC = 15 cm, then cot A is equal to

15
(A)
8

8
(B)
15

17
(C)
8

8
(D)
17

7. The sine of any acute angle ‘q’ in a right triangle is equal to the
cosine of its

(A) reflex angle

(B) obtuse angle

(C) complementary angle

(D) supplementary angle

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( 5 )

8. Area of a semicircle whose radius is 7 cm, is

(A) 154 cm2

(B) 11 cm2

(C) 77 cm2

(D) 49 cm2

9. Fill in the blanks : ½+½=1

(a) If a line divides any two sides of a triangle proportionally,
it must be _____ to the third side.

(b) A _____ is a line which touches a circle at one point only.

10. Define cumulative frequency.

SECTION—B
( Marks : 12 )
( Question Nos. 11 to 16 carry 2 marks each )

11. Find a quadratic polynomial whose zeroes are 2 + 3
and 2 - 3.

12. Solve the quadratic equation, x 2 - x - 20 = 0 by completing the
square.
Or
Find the 8th term from the end of the AP 7, 10, 13, ..., 184.

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1 3 cosecq
13. If sin q = , then find the value of
2 1 + cot2 q

14. Prove that
2 tan 30°
= 3
1 - tan2 30°

Or

Find the value of q, if 2 sin 2q = 3, for 0° < q < 90°.

15. The areas of two similar triangles are 121 cm2 and 64 cm2
respectively. If the median of the first triangle is 12·1 cm, then
find the corresponding median of the other triangle.

Or

The perimeters of two similar triangles are 24 cm and 32 cm
respectively. If one side of the first triangle is 12 cm, then find
the corresponding side of the other triangle.

16. In a right D ABC, right angled at A, AD is drawn perpendicular
to BC. Prove that AB 2 - BD 2 = AC 2 - CD 2 .

C

D

B A

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( 7 )

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 16 given in Page No. 6 ]

16. (a) The perimeter of a circle is referred to as the _____ of
the circle.
(Fill in the blank) 1

(b) In a right-angled triangle, the side opposite to right angle
is hypotenuse.
(State True or False) 1

SECTION—C
( Marks : 18 )
( Question Nos. 17 to 22 carry 3 marks each )

17. The LCM of two numbers 396 and 576 is 6336. Find
their HCF.

18. Find the sum of the series :
82 + 72 + 62 + L to 12th terms
Or
If the length of a rectangular field is decreased by 5 m, its area is
decreased by 70 m2 . If the width is increased by 6 m, the area is
increased by 180 m2 . Determine the length and width of the
rectangle.

19. The coordinates of A and B are ( 5 , - 9 ) and (11, K ). Find the
value of K if the distance AB is 10 units.

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1 + cos q
20. Prove that = cosecq + cot q
1 - cos q
Or

sin q - 2 sin 3 q
Prove that = tan q
2 cos 3 q - cos q

21. In a circle of radius 6 cm, a chord of 10 cm makes an angle
of 110° at the centre of the circle. Find the length of the arc
(use p = 22).
7

Or
A circular flower bed lies inside a rectangular field of size
25 m × 18 m. The area of the field excluding the flower bed is
296 m2 . Find the diameter of the flower bed (use p = 22).
7

22. If 65% of the population have black eyes and the rest have
brown eyes, then what is the probability that a person selected
at random has

(a) brown eyes;

(b) black eyes?

SECTION—D
( Marks : 16 )
( Question Nos. 23 to 26 carry 4 marks each )
23. The denominator of a fraction exceeds twice its numerator
by 1. If 3 be subtracted from the numerator and 2 from the
denominator, then the fraction becomes 1. Find the fraction.
3

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( 9 )

24. Find x so that the line segment with initial point A ( x, 4 ) and
terminal point B ( 3 , 0 ) is divided at C ( 2 , 1 ) in the ratio 3:1.

Or

Show that the points (4, 4), (3, 5), (–1, 1) are the vertices of a
right-triangle.

25. A vertical tree 15 m high is broken by the wind in such a
way that its top just touches the ground and makes an
angle of 60° with the ground. At what height from the ground
did the tree break? (Use 3 = 1·732)

Or

On the opposite sides of a tower two objects are located. Their
angles of depression from the top of the tower are 45° and 60°.
If the height of the tower is 300 m, then find the distance
between the two objects. (use 3 = 1·732)

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 25 given above ]

25. (a) Prove that 2
1 1
+ = 2 sec A
sec A + tan A sec A - tan A

(b) 1 + _____ = cosec2q. (Fill in the blank) 1

(c) tan A = sec (90°-A) (State True or False) 1

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( 10 )

26. Using ruler and compass only, construct a triangle similar
to a given DABC such that each of its sides is 3th of the
4
corresponding sides of D ABC. It is given that AB = 3 cm,
BC = 4 cm and CA = 5 cm. [only traces of construction are
required]

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 26 given above ]

26. (a) If two triangles are equiangular to one another, their
corresponding sides are _____.
(Fill in the blank) 1
(b) A parallelogram whose adjacent sides are equal is called
a trapezium.
(State True or False) 1
(c) _____ is the longest chord of a circle.
(Fill in the blank) 1
(d) Define an isosceles triangle. 1

SECTION—E
( Marks : 24 )
( Question Nos. 27 to 30 carry 6 marks each )

27. Solve the following system of linear equations graphically :
2x + 3y = 12
x - y =1
Find the coordinates of the vertices of the triangle formed by the
two straight lines and the y-axis. (Plot at least three points for
each graph)

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( 11 )

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 27 given in Page No. 10 ]
27. Solve the following system of linear equations :
2x + 3y = 28
3x - 4y = - 9
28. Prove that, the tangent at any point of a circle is perpendicular
to the radius through the point of contact. 4
In the adjoining figure, O is the centre of the circle and AB is a
tangent to a circle at P . Find the value of x. 2

O
40°
x°
A P B
[ For Visually Handicapped (Blind) Students only,
instead of Question No. 28 given above ]

28. (a) All chords of a circle are equal in length.
(State True or False) 1
(b) Define a secant of a circle. 1
(c) The lengths of two tangents drawn from an external
point to a circle are _____. (Fill in the blank) 1

(d) If the radius of a circle is 12 cm, then its diameter is _____.
(Fill in the blank) 1
(e) A triangle can have two obtuse angles.
(State True or False) 1
(f) State Basic Proportionality theorem. 1

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( 12 )

29. A cylindrical tube, open at both ends is made of iron 1 cm
thick. If its external diameter be 22 cm and its length 50 cm,
then find the volume of iron contained in the tube (use p = 22).
7

Or

A rocket is in the form of a cone of height 28 cm, surmounted
over a right circular cylinder of height 112 cm. The radius of
the bases of a cone and a cylinder are equal each being 21 cm.
Find the total surface area of the rocket (use p = 22).
7

30. The following frequency distribution gives the monthly
consumption of electricity of 68 consumers of a locality :

Monthly
Consumption
(in unit) 65–85 85–105 105–125 125–145 145–165 165–185 185–205

No. of
Consumers 4 5 13 20 14 8 4

Compute the median.
Or
Find the mean of the following data using any method :

Weight (in kg) 30–35 35–40 40–45 45–50 50–55 55–60

No. of Students 4 16 40 22 10 8

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SECTION—F
( Marks : 20 )

[ Candidates appearing for 100 marks ]

31. Answer the following as directed (any eight) : 1×8=8

(a) A number which has got more than two factors is called
(A) an odd number
(B) a prime number
(C) an even number
(D) a composite number (Choose the correct option)

(b) The zeroes of the polynomial (x + 2) (x - 3) are
(A) ( 2 , - 3 )
(B) ( - 2 , - 3 )
(C) ( 2 , 3 )
(D) ( - 2 , 3 ) (Choose the correct option)

(c) If a pair of linear equations a 1x + b1y + c 1 = 0 and
a 2 x + b2y + c 2 = 0 represents intersecting lines, then
a 1 c1
(A) ¹
a 2 c2

a 1 b1 c 1
(B) = ¹
a 2 b2 c 2

a 1 b1
(C) ¹
a 2 b2

a 1 b1 c 1 (Choose the correct option)
(D) = =
a 2 c2 c2

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(d) The common difference of the AP 1·8, 2·0, 2·2, 2·4, ... is
(A) 2
(B) 0·2
(C) –0·2
(D) 0·02 (Choose the correct option)

41
(e) has a terminating decimal representation.
22 ´ 5 ´ 7
(State True or False)

(f) State Pythagoras theorem.

(g) Find the distance between the origin and the point (-4 , 0).

(h) Find the prime factors of 3600.

(i) The value of cos 82°- sin 8° is _____. (Fill in the blank)

(j) Define a circle.

(k) If r is the radius of a sphere, then its volume is _____.
(Fill in the blank)

(l) What is the mode of the data 0, 1, 5, 3, 2, 5, 7, 1, 5?

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( 15 )

(m) In which quadrant or axis does the point (-4 , 0) lie?

(n) A polynomial of degree 4 is called a _____ polynomial.
(Fill in the blank)

32. Answer any six from the following : 2×6=12

(a) Find the HCF and LCM of 16 and 24 by prime
factorisation method.

(b) Find the sum and the product of the zeroes of x 2 - 5x + 6.

(c) Divide 6x 2 - 31x + 40 by 2x - 5 and write down the
quotient and remainder.

(d) For A = 30°, verify that

cos2 A
+ sin A = cosecA
sin A

(e) Find the coordinates of the mid-point of the line segment
æ3 3ö æ2 1ö
joining the points ç , - ÷ and ç , - ÷.
è2 4ø è3 3ø

(f) Prove that sin 39° sec 51° + cos 47° cosec43° = 2

(g) Find the radius of a circle whose circumference is 352 m
(use p = 22).
7

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(h) Find the curved surface area of a right-circular cylinder of
radius 3·5 cm and height 10 cm (use p = 22).
7

(i) Determine the length of the diagonal of a square whose
side is 50 cm.

(j) Solve the quadratic equation x 2 + 9x + 14 = 0 by
factorization.

HHH

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