MBOSE Class 10 Question Paper 2024 for Maths

Meghalaya Board of School Education

QUESTION
PAPERS

Total No. of Printed Pages—15
X/24/M

2024

MATHEMATICS

( 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 only by the Candidates without Internal
Assessment.

/55 [ 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 total number of factors of a prime number? 1

2. What is the degree of a zero polynomial? 1

3. Write the common difference of the A.P. whose nth term
is 5n + 3. 1

3
4. If A + B = 90° and tan A  , what is the value of cot B ? 1
4

5. At most how many tangents can be drawn parallel to
a given secant of a circle? 1

6. Find the circumference of a circle whose diameter is
22 
35 cm.  Use    1
 7 

X/24/M/55 [ Contd.

( 3 )

7. What is the length of the altitude of an equilateral
triangle of side 2 cm? 1

8. Write the empirical relationship among mean, mode and
median. 1

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

9. Solve the quadratic equation 3x 2  14x  5  0 by
factorization. 2

10. Find the value of

2 cot2 60  3 sin2 30  2 cos2 90 2

11. Find the value of

tan 7 tan 23 tan 67 tan 83 2

12. The line segment joining the points A (4,  5) and B (4, 5)
is divided by the point P such that

AP 2

BP 5
Find the coordinates of P. 2

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( 4 )

13. A (3, 2) and B (–2, 1) are two vertices of a  ABC whose
 5 1 
centroid G has the coordinates  ,  . Find the co-
3 3 
ordinates of the third vertex C of the triangle. 2

14.

In the above figure, in a ABC, D and E are the points
on the sides AB and AC respectively such that DE || BC .
AD 4
If  and AE = 2·4 cm, find AC. 2
DB 7

[ For Visually Handicapped (Blind) Students only,
instead of Question No. 14 given above ]

14. State Basic Proportionality Theorem. 2

15. In the figure below, l is a line intersecting the two
concentric circles, whose common centre is O, at the
points P, Q, R and S, and OM is perpendicular to line l.
Show that PQ = RS. 2

X/24/M/55 [ Contd.

( 5 )

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

15. (a) Define a circle. 1
(b) The length of a tangent from an external point on a
circle is always less than the radius of the circle.
( State whether True or False ) 1

SECTION—C
( Marks : 24 )
( Question Nos. 16 to 23 carry 3 marks each )

16. Using ruler and compass only, draw a line segment of
length 8 cm and divide it internally in the ratio 4 : 5.
(Only traces of constructions are required) 3

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

16. (a) Define scalene triangle. 2
(b) The distance between the parallel lines is always the
same.
( State whether True or False ) 1

17. In the figure below, in a ABC, AD is the bisector
of A , intersecting the side BC at D. If AB = 10 cm,
AC = 6 cm and BC = 12 cm, find BD and DC. 3

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( 6 )

Or
O is the centre of a circle of radius 8 cm. The tangent at
a point A on the circle cuts a line through O at B such
that AB = 15 cm. Find OB. 3

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

17. (a) The greatest side of a _____ triangle is called
hypotenuse.
( Fill in the blank ) 1

(b) The sum of the squares of the sides of a rhombus is
equal to the sum of the squares of its diagonals.
( State whether True or False ) 1

(c) State Midpoint Theorem. 1

18. A circular park, 42 m in diameter, has a path 3·5 m wide
running around it on the outside. Find the cost of
gravelling the path at R 20 per sq. m. (Use   22 ) 3
7

Or
A chord of a circle of radius 14 cm subtends an
angle 60° at the centre. Find the area of the major
sector. (Use   22 ) 3
7

19. If  and  are zeroes of the polynomial 5 x 2  2x  3 , then
prove that
   34
  3
  15

X/24/M/55 [ Contd.

( 7 )

20. Find the largest positive integer which divides 615 and
963, leaving remainder 6 in each case. 3

21. A box contains 20 balls numbered from 1 to 20. A ball
is drawn at random from the box. Find the probability
that the number on the ball is—

(a) an even number;

(b) divisible by 3 or 5. 3

22. Find the sum of all 3-digit natural numbers, which are
multiples of 11. 3

23. Prove that

cosec6   cot6   3 cot2   cosec2   1 3

Or

If cos   sin   2 sin  , prove that cos   sin   2 cos  . 3

SECTION—D
( Marks : 16 )

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

24. A two-digit number is such that the product of its
digits is 14. If 45 is added to the number, the digits
interchange their places. Find the number. 4

X/24/M/55 [ P.T.O.

( 8 )

Or

The present age of a woman is 3 years more than three
times the age of her daughter. Three years later, the
woman’s age will be 10 years more than twice the age of
her daughter. Find their present ages. 4

25. A vertical tower stands on a horizontal plane and is
surmounted by a vertical flag-staff of height 5 metres.
From a point on the plane, the angles of elevation of
the bottom and the top of the flag-staff are 30° and 60°.
Find the height of the tower. 4

Or

Two men are on opposite sides of a tower. The measures
of the angles of elevation of the top of the tower are
30° and 45° respectively. If the height of the tower is
50 metres, find the distance between the two men.
(Use 3  1  732 ) 4

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

25. (a) Define angle of elevation. 2

(b) If the Sun’s altitude decreases, then the length of
shadow of a tower _____.
( Fill in the blank ) 1

(c) The value of cot  is always less than 1.
( State whether True or False ) 1

X/24/M/55 [ Contd.

( 9 )

26. If the points A(x, y), B (–5, 7) and C (– 4, 5) are collinear,
then show that 2x  y  3  0 . 4

27. Prove that the ratio of the areas of two similar triangles
is equal to the ratio of the squares of their corresponding
sides. 4

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

27. (a) Define similar polygons. 2

(b) If two triangles are equiangular, then the ratio of
the corresponding sides is the _____ as the ratio of
the corresponding medians.
( Fill in the blank ) 1

(c) If a line divides any two sides of a triangle in the
same ratio, then the line must be parallel to the
third side.
( 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 :
2x  3y  6  0
4x  y  16  0
Find the area of the triangle formed by the lines and
the x-axis. (Plot at least three points for each graph) 6

X/24/M/55 [ P.T.O.

( 10 )

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

28. Solve the following system of linear equations : 6

2x  3y  13
7x  2y  20

29. A military tent of height 8·25 m is in the form of a right
circular cylinder of base diameter 30 m and height 5·5 m
surmounted by a right circular cone of same base radius.
Find the length of the canvas used in making the tent, if
the breadth of the canvas is 1·5 m. (Use   22 ) 6
7
Or
The internal and external diameters of a hollow
hemispherical shell are 6 cm and 10 cm respectively. It is
melted and recast into a solid cone of base diameter
14 cm. Find the height of the cone so formed. 6

30. The mean of the following frequency distribution is 57·6
and the sum of the observations 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 8 5

Or
Find the median of the following frequency distribution : 6

Class interval 5–10 10–15 15–20 20–25 25–30 30–35 35–40 40–45

Frequency 5 6 15 10 5 4 2 2

X/24/M/55 [ Contd.

( 11 )

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

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

(a) The prime factors of 4050 is

(A) 2  33  5

(B) 2  34  5

(C) 2  34  53

4 2
(D) 2  3  5
( Choose the correct option )

(b) The sum of the zeroes of the polynomial 2x 2  3x  9
is

3
(A)
2

3
(B)
2

9
(C)
2

9
(D)
2
( Choose the correct option )

X/24/M/55 [ P.T.O.

( 12 )

(c) If a pair of linear equations a1x  b1y  c1  0 and
a2x  b2y  c 2  0 represents parallel lines, then

a1 b1
(A) 
a2 b2

a1 b1 c1
(B)  
a2 b2 c2

a1 b1 c1
(C)  
a2 b2 c 2

(D) None of the above
( Choose the correct option )

(d) The nth term of the A.P. with first term ‘a’ and
common difference ‘d’ is given by

(A) 2a  (n  1) d

(B) a  2(n  1) d

 n 1
(C) a   d
 2 

(D) a  (n  1)d
( Choose the correct option )

(e) A polynomial having _____ terms is called binomial.
( Fill in the blank )

X/24/M/55 [ Contd.

( 13 )

(f) The quantity b2 – 4ac for a quadratic equation
ax 2  bx  c  0 is called its discriminant.
( State whether True or False )

(g) Evaluate :

tan 20
cot 70

(h) Write the formula of the volume of a sphere of radius
r units.

(i) The _____ value of data is called mode.
( Fill in the blank )

(j) Find the class mark of class 0 – 20.

(k) The sum of two irrational numbers is an irrational
number.
( State whether True or False )

(l) Write the value of cosec 2 (90  )  tan2  .

(m) Define prime number.

(n) The common point of a tangent to a circle and the
circle is called as _____.
( Fill in the blank )

X/24/M/55 [ P.T.O.

( 14 )

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

(a) If the product of two numbers is 540 and their HCF
is 30, find their LCM.

(b) Find a quadratic polynomial whose sum and product
of its zeroes are 8 and 7 respectively.
3

(c) Find the coordinates of the midpoint of the line
segment joining the points P (2, 8) and Q (6,  4) .

(d) Write the nature of the roots of the quadratic
equation 3x 2  5x  2  0 .

(e) Find the common difference of the A.P.
50, 58, 66, 74, 
and write the next two terms.

(f) If 3 sin   cos  , find the acute angle .

(g) A box contains 3 blue, 2 white and 4 red marbles.
If a marble is drawn at random from the box, what
is the probability that it will not be a white marble?

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

X/24/M/55 [ Contd.

( 15 )

(i) Find the 20th term of the A.P. given by

21, 16, 11, 6, 1, – 4, – 9, 

(j) State Pythagoras Theorem.

(k) If A = 60° and B = 30°, verify that

sin( A  B )  sin A  cos B  cos A  sin B

  

X/24/M/55 24K—58370

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