MBOSE Class 10 Question Paper 2020 for Mathematics New Course

Total No. of Printed Pages—12
X/20/M (N)

2020

MATHEMATICS

( New Course )

( FOR CANDIDATES WITH INTERNAL ASSESSMENT )

Full Marks : 80
Pass Marks : 24

( FOR CANDIDATES WITHOUT INTERNAL ASSESSMENT )

Full Marks : 100
Pass Marks : 30

Time : 3 hours

( FOR ALL CATEGORIES OF CANDIDATES )

General Instructions :

(i) This Question Paper comprises 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 all candidates.

(iv) Question Nos. 31 and 32 of Section—F are to
be answered by Candidates without Internal
Assessment.

/58 [ P.T.O.

( 2 )

(v) In question on construction, the drawing should be
neat and exactly as per the given measurements.
(vi) Questions, which are meant for Visually Handicapped
(Blind) Students, should be answered by them only.
(vii) Use of Calculator/Mobile Phone is not permitted.

SECTION—A
( Marks : 8 )
( Question Nos. 1 to 8 carry 1 mark each )

1. What is the sum of exponents of prime factors in the
prime factorization of 98 ? 1

2. Find the zeroes of the polynomial 49x 2  64 . 1

1 1 3
3. For the AP , , , 1, ...., write the first term and
4 2 4
common difference. Also, write the fifth term. 1

4. If the altitudes of two similar triangles are in the ratio
2 : 3, what is the ratio of their areas? 1

5. Evaluate :
cos2 42  sin2 48 1

6. Find the distance between two parallel tangents of a
circle of radius 8 cm. 1

7. If the diameter of a semi-circular protractor is 14 cm,
then find its perimeter. (Use   22
7
) 1

8. If P (E )  0·05 , what is the probability of ‘not E’ ? 1

X/20/M (N)/58 [ Contd.

( 3 )

SECTION—B
( Marks : 14 )
( Question Nos. 9 to 15 carry 2 marks each )

9. Find the value of k for which the quadratic equation
3x 2  5x  2k  0 has real and equal roots. 2

10. Find the value of x ( 0  x  90 ) in
sin 2x  sin 60 cos 30  cos 60 sin 30 2

1  sin 
11. Prove that  ( sec   tan  )2. 2
1  sin 

12. The line segment joining A(–2, 9) and B (6, 3) is a diameter
of a circle with centre C. Find the coordinates of C. 2

13. Two vertices of a triangle are (3, –5) and (–7, 4). If its
centroid is (2, –1), find the third vertex. 2

14. The perimeters of two similar triangles are 25 cm and
15 cm respectively. If one side of the first triangle is 9 cm,
what is the corresponding side of the other triangle? 2

15. PQ and PT are tangents to a circle with centre O and
radius 5 cm. If PQ = 12 cm, then prove that the perimeter
of the quadrilateral PQOT is 34 cm. 2

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 15 given above ]

15. (a) Define a quadrilateral. 1
(b) A tangent to a circle is perpendicular to the radius
through the point of contact.
( State whether True or False ) 1

X/20/M (N)/58 [ P.T.O.

( 4 )

SECTION—C
( Marks : 24 )
( Question Nos. 16 to 23 carry 3 marks each )
16. Using ruler and compass only, construct a circle of
radius 3·5 cm and also construct two tangents from a
point P outside the circle at a distance of 6 cm from its
centre. (Only traces of construction are required) 3
[ For Visually Handicapped (Blind) Students only,
instead of Question No. 16 given above ]
16. (a) Define radius of a circle. 1
(b) In a triangle, if the square of one side is equal to the
sum of the squares of the other two sides, then the
angle opposite to the first side is a right angle.
( State whether True or False ) 1
(c) A line which intersects a circle in two distinct points
is called the _____ of the circle.
( Fill in the blank ) 1

17.  ABC is an isosceles triangle with AB  AC  13 cm.
The length of the altitude from A on BC is 5 cm.
Find BC. 3
Or
In the adjoining figure, PS and PT are tangents to
the circle drawn from an external point P. CD is a third
tangent touching the circle at Q. If PT = 10 cm and
CQ = 2 cm, find the perimeter of PCD : 3

X/20/M (N)/58 [ Contd.

( 5 )

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 17 given in Page No. 4 ]

17. (a) State Pythagoras theorem. 2

(b) If a line divides any two sides of a triangle in the
_____ ratio, then the line is parallel to the third side.
( Fill in the blank ) 1

18. An arc of length 20 cm subtends an angle of 144° at
the centre of a circle. Find the radius of the circle. 3

Or

A drain cover is made from a circular metal plate of
radius 14 cm having 21 holes each of diameter 0·5 cm.
Find the area of the remaining plate. (Use   22
7
) 3

19. A bag contains 6 red balls and some blue balls. If the
probability of drawing a blue ball is twice that of red ball,
find the number of blue balls in the bag. 3

20. Find the smallest number which when increased by
11 is exactly divisible by 15, 20 and 54. 3

21. If the zeroes of the quadratic polynomial
2
p(x )  3x  (2k  1) x  5 are equal in magnitude but
opposite in sign, then find the value of k. 3

22. How many terms of the AP 18, 16, 14, ... should be
taken so that their sum is zero? 3

X/20/M (N)/58 [ P.T.O.

( 6 )

23. Prove that
tan10 tan 25 tan 45 tan 65 tan 80  1 3

Or
Eliminate ‘  ’ for the equations :
x  sin   cos 
and y  sin   cos  3

SECTION—D
( Marks : 16 )

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

24. Divide 16 into two parts such that twice the square of
the larger part exceeds the square of the smaller part
by 164. 4
Or
A two-digit number is 4 times the sum of its digits.
If 18 is added to the number, the digits are reversed.
Find the number. 4

25. From the top of a building 60 m high, the angles of
depression of the top and bottom of a tower are observed
to be 30° and 60°. Find the height of the tower. 4
Or
The angle of elevation of the top of a tree from a point A
on the ground is 60°. On walking 20 m away from its
base, to a point B, the angle of elevation changes to 30°.
Find the height of the tree. (Use 3  1·732 ) 4

X/20/M (N)/58 [ Contd.

( 7 )

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 25 given in Page No. 6 ]

25. (a) Express cos 65  tan65 in terms of angles between
0° and 30°. 2
(b) Write the value of cosec2(90   )  tan2 . 2

26. Find the ratio in which the point P (6, a ) divides the
join of A (3,  1) and B (8 , 9). Also, find the value of a. 4

27. Prove that the lengths of tangents drawn from an
external point to a circle are equal. 4

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 27 given above ]
27. (a) Define a circle. 2
(b) Two triangles are similar, if their corresponding
sides are _____.
( Fill in the blank ) 1
(c) The greatest side of a right-angled triangle is called
hypotenuse.
( State whether True or False ) 1

SECTION—E
( Marks : 18 )
( Question Nos. 28 to 30 carry 6 marks each )
28. Solve the following system of linear equations graphically :
3x  y  11  0
x  y 1  0
Also, find the area bounded by these lines and y-axis.
(Plot at least three points for each graph) 6

X/20/M (N)/58 [ P.T.O.

( 8 )

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 28 given in Page No. 7 ]

28. Solve the following system of linear equations : 6

x y  3
4x  3y  26

29. A wooden toy is made by scooping out a hemisphere of
same radius from each end of a solid cylinder. If the
height of the cylinder is 10 cm, and its base is of radius
3·5 cm, find the volume of wood in the toy. (Use   22 7
) 6

Or

The difference between the outer and inner curved
surface areas of a hollow right circular cylinder 14 cm
long is 88 cm2. If the volume of metal used in making the
cylinder is 176 cm3, find the outer and inner diameters
of the cylinder. (Use   22
7
) 6

30. The mean of the following frequency distribution is 62·8
and the sum of all frequencies is 50. Find the missing
frequencies f 1 and f 2 : 6
Class Interval 0–20 20–40 40–60 60–80 80–100 100–120
Frequency 7 f1 12 f2 7 8

Or
Find the median of the following distribution : 6
Class Interval 0–10 10–20 20–30 30–40 40–50 50–60
Frequency 3 6 8 15 10 8

X/20/M (N)/58 [ Contd.

( 9 )

SECTION—F
( Marks : 20 )
[ For Candidates without Internal Assessment ]
31. Answer the following as directed (any eight) : 1×8=8
(a) The prime factors of 408 are
(A) 23  3  17
(B) 23  32  17
(C) 23  3  172
3 3
(D) 2  3  17
( Choose the correct option )
(b) The sum of the zeroes of the polynomial
p(x )  5x 2  2x  3 is
2
(A)
5
3
(B) 
5
3
(C)
5
2
(D) 
5
( Choose the correct option )

(c) The system of equations 2x  5y  17 and
5 x  3y  14 has
(A) unique solution
(B) infinitely many solutions
(C) no solution
(D) None of the above
( Choose the correct option )

X/20/M (N)/58 [ P.T.O.

( 10 )

(d) The discriminant of the quadratic equation
x 2  8x  16  0 is

(A) –1

(B) 0

(C) 1

(D) 2
( Choose the correct option )

(e) Is the following an AP ?
3, 3, 3, 3, ......

(f) What is the area of an equilateral triangle of side ‘a’ ?

(g) If the area of a triangle is _____ square units, then
its vertices are collinear.
( Fill in the blank )

(h) Solve for  , 0    90 , if 2cos   1.

(i) 1  cosec2  cot2  .
( State whether True or False )

(j) Define a tangent to a circle.

(k) Find the area of a circle of radius 10·5 cm.
(Use   22
7
)

X/20/M (N)/58 [ Contd.

( 11 )

(l) Write the formula for the area of a sector of angle 
of a circle of radius ‘r ’.

(m) Find the distance between the points (5, 8) and (–3, 2).

(n) Find the probability of getting a head when a coin is
tossed once.

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

(a) The HCF of two numbers is 16 and their product
is 3072. Find their LCM.

(b) Find a quadratic polynomial whose zeroes are –5
and –7.

(c) Solve the quadratic equation x 2  3x  18  0 by
factorization.

(d) What is the 19th term of the sequence defined
n (n  2)
by an  ?
n 3

(e) Find the coordinates of the centroid of the triangle
whose vertices are (–3, 0), (5, –2), (–8, 5).

(f) Evaluate :
sin2 30  sin2 45  sin2 60

(g) The circumference of a circle is 39·6 cm. Find its
radius. (Use   22
7
)

X/20/M (N)/58 [ P.T.O.

( 12 )

(h) If sec   tan   m and sec   tan   n , prove that
mn  1 .

5
(i) Find the value of k for which the given value x  
2 3
is a solution of the equation 3x  kx  5  0 .

(j) Find two consecutive natural numbers whose
product is 20.

  

X/20/M (N)/58 20K—