MBOSE Class 10 Question Paper 2020 for Mathematics Old Course

Total No. of Printed Pages—16
X/20/M (O)

2020

MATHEMATICS

( Old 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 (Section—F) are to be answered
by Candidates without Internal Assessment marks.

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(v) In Question Nos. 1 to 8 of Section—A and Question
No. 31 Subnos. (a) to (e) 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. A polynomial of degree 2 is called a

(A) linear polynomial

(B) cubic polynomial

(C) biquadratic polynomial

(D) quadratic polynomial

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2. The prime factors of 156 are

(A) 2  32  13

(B) 22  3  13

(C) 2  3  132

(D) 22  32  13

3. The solutions of the equation 2x 2  9x are
2
(A) 0,
9
2
(B) 0,
9
9
(C) 0,
2
9
(D) 0, 
2

a
4. If sin   , then tan  is equal to
a 2  b2
a
(A)
b
b
(B)
a
b
(C)
a 2  b2

a 2  b2
(D)
a

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5. The fourth term of an AP, whose first term (a )  x and
common difference (d )  x  3 is

(A) x + 3

(B) 3x + 6

(C) 4x + 9

(D) 2x + 3

6. The distance between the origin and the point (– 4, 3) is

(A) 5 units

(B) 5 units

(C) 1 units

(D) – 7 units

7. The total surface area of a right circular cylinder of
radius of base r units and height h units is

(A) 2rh square units

(B) 2  r (r  h ) square units

(C) r r 2  h 2 square units

(D) h (R  r )(R  r ) square units

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8. If all the sides of a parallelogram touch a circle, then the
parallelogram is a
(A) rectangle
(B) trapezium
(C) rhombus
(D) All of the above

9. Fill in the blanks : ½+½=1

(a) A line which intersects a circle at two points is called
a _____ of the circle.
(b) If two triangles are equiangular, then their
corresponding sides are _____.

10. Define unimodal of grouped data.

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

11. Find the sum and product of the zeros of quadratic
polynomial 4 3x 2  5x  2 3 .

12. Find the value of P for which the given quadratic
equation 3x 2  10x  P  0 has real roots.
Or
Write the first four terms of the sequence whose nth
term (tn ) is 2n 2  3n  1 .

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13. For A = 30°, verify that

cos2 A
 sin A  cosec A
sin A

14. Prove that

cot (90  )·sin(90  )
1
cos (90  )

Or

Prove that

cos3   sin3  cos3   sin3 
 2
cos   sin  cos   sin 

15. Find the length of the tangent drawn from a point whose
distance from the centre of a circle of radius 8 cm
is 17 cm.

16. In the given figure, PQ || BC , AP = 2·4 cm, AQ = 2 cm,
QC = 3 cm and BC = 6 cm. Find AB.

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

16. Define similar triangles. 2

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

17. Find the LCM and HCF of 29260 and 1482 by applying
the prime factorization method.

18. In a flower bed, there are 23 rose plants in the first row,
21 in the second, 19 in the third and so on. There are
5 rose plants in the last row. How many rows are there
in the flower bed?
Or

Find a fraction that becomes 12 when its numerator and
denominator are both increased by 1. It becomes 14
when its numerator and denominator are both
diminished by 1.

19. Find the coordinate of the point which divides the line
segment joining the points A (1, 3) and B (2, 7) in the
ratio 3 : 4.

20. If x cos   y sin   a and x sin   y cos   b , then prove
that x 2  y 2  a 2  b 2 .
Or
Prove that tan2   cot2   2  sec2 ·cosec2 .

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21. A paper is in the form of a rectangle ABCD in which
AB = 18 cm and BC = 14 cm. A semicircular portion with
BC as diameter is cut off. Find the area of the remaining
paper. (Use   22
7
)

Or

The perimeter of a certain sector of a circle of radius
5·7 m is 27·2 m. Find the area of the sector.

22. The four faces of a regular tetrahedron are marked A, B,
C and D and it is thrown twice.

(a) Write down all the possible outcomes.

(b) How many outcomes are there in all?

(c) How many outcomes are there with both the letters
are same?

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SECTION—D
( Marks : 16 )
( Question Nos. 23 to 26 carry 4 marks each )

23. The sum of the ages of a man and his son is 45 years.
Five years ago, the product of their ages was four times
the man’s age at that time. Find their present ages.

24. Find the value of P for which the points (–1, 3), (2, P ) and
(5, –1) are collinear.
Or
Show that the join of the points (a, a), (–a, –a) and
(a 3, a 3) form an equilateral triangle.

25. The shadow of a tower is three times as long as the
shadow of tower when the sun’s rays met the ground at
an angle of 60°. Find the angle of elevation of the sun at
the time of the longer shadow.
Or

The shadow of a vertical pole is 1 of its height. Find the
3
sun’s altitude.

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

25. (a) What is the angle of elevation? 2

(b) sin A  cos (90  A ) ( State True or False ) 1

(c) cot2   1  _____. ( Fill in the blank ) 1

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26. Using ruler and compass only, construct a circle and
a diameter of the circle and also construct tangents at
both the end points of the diameter. (Only traces of
construction are required)

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

26. (a) Define tangent of a circle. 1
(b) The diameter of a circle is a chord which passes
through the centre of the circle.
( State True or False ) 1
(c) The tangent at any point of a circle is _____ to the
radius through the point of contact.
( Fill in the blank ) 1
(d) The sum of all angles of a triangle is (three right
angles/two right angles).
( Choose the correct option ) 1

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

27. Solve the following system of linear equations
graphically :
x  2y  7
2x  y  4

Shade the area bounded by these two lines and the
y-axis. (Plot at least three points for each graph)

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[ For Visually Handicapped (Blind) Students only,
instead of Question No. 27 given in Page No. 10 ]

27. Solve the following system of linear equations : 6

3x  4y  6
3x  y  9

28. Prove that if a line is drawn parallel to one side of a
triangle to intersect the other two sides in distinct points,
then the other two sides are divided in the same ratio.
Using the above, do the following :

In the above  ABC , if a line intersects AB at X and
AC at Y, and if AX = 2·4 cm, XB = 4·2 cm, AY = 6 cm,
YC = 10·5 cm, then find whether XY is parallel to BC
or not.

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

28. (a) Define isosceles triangle. 1

(b) Define scalene triangle. 1

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(c) The sum of any two sides of a triangle must be less
than the third side.
( State True or False ) 1

(d) State Pythagoras theorem. 2

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

29. A right-angled triangle, whose sides forming the right
angle are 15 cm and 20 cm, is made to revolve about its
hypotenuse. Find the volume of the double cone
so formed. (Use  = 3·14)
Or

Find the volume and total surface area of the hemisphere
of radius 3·5 cm. (Use   22 )
7

30. Find the value of f if the mean of the following
distribution is 21 :

Class interval 0–8 8–16 16–24 24–32 32–40
Frequency 5 9 10 f +2 8

Or

Calculate the mode of the following frequency
distribution :
above above above above above above above
Marks
25 35 45 55 65 75 85

No. of students 52 47 37 17 8 2 0

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SECTION—F
( Marks : 20 )
[ For Candidates without Internal Assessment ]

31. Answer the following as directed (any eight) : 1×8=8
(a) A natural number which has exactly two factors i.e.,
1 and the number itself is known as

(A) even number

(B) rational number

(C) prime number

(D) irrational number
( Choose the correct option )

(b) Which of the following is a polynomial?

3 1 2
(A) x 5   x 4
x 3

1
(B) 7x 4  x  2x 
3

1
(C) x 2  2
x

1 3
(D) 1  5x  2x 2  x
6
( Choose the correct option )

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(c) The discriminant of the quadratic equation
k 2x 2  kx  1  0 is

(A) 3k 2

(B) 3k 2

(C) 5k 2

(D) 5k 2
( Choose the correct option )

(d) The perimeter of a circle of radius r is given by

(A) 2r

(B) r 2

(C) r

2
(D) 2r
( Choose the correct option )

(e) The point (0, –2) lies on the

(A) x-axis

(B) y-axis

(C) 1st quadrant

(D) 2nd quadrant
( Choose the correct option )

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(f) A _____ of a circle is the figure bounded by a chord
and an arc of the circle cut off by the chord.
( Fill in the blank )

(g) Probability is the science that measures _____.
( Fill in the blank )

(h) If A = 30° and B = 60°, then find the value of
sin (A + B ).

(i) What is an ogive?

(j) Find the volume of the cuboid 1 cm thick, 2 cm wide
and 3 cm long.

(k) The _____ of the sun is simply the angle of elevation
of the sun.
( Fill in the blank )

(l) Find the perimeter of an equilateral triangle whose
side is 10 cm.

cot 40
(m) Find the value of .
tan 50

(n) Find t8 in the A.P. 4, 1, – 2, ... .

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

(a) Find a quadratic polynomial whose sum and product
of its zeros are respectively 2 and – 8.

(b) Solve x 2  5x  6  0 by factorization method.

(c) Find the common difference of the A.P. 119, 136,
153, 170, ... and write the next two terms.

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(d) Divide the polynomial p (x )  6x 2  x  15 by
g (x )  2x  3 and find the quotient and remainder.

(e) Find the distance between the points (4, 7) and
(–4, –7).

(f) Find the mean of the first ten whole numbers.

(g) Prove that 2 cos2 30  1  cos 60 .

(h) A coin is tossed twice. List all the possible outcomes
using H for head and T for tail.

(i) The lengths of the diagonals of a rhombus are 24 cm
and 10 cm. Find each side of the rhombus.

(j) Find the centroid of the triangle whose vertices are
(4, –8), (–9, 7) and (8, 13).

  

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