10th 2022-23 maths model question papers

10th kseeb Mathematics model papers

Here are the model papers on NCERT Mathematics 10 th kseeb board Examinations.

You can download it free. By clicking on links.

1Unsolved Model paper 1

General Instructions to the Candidate :

1. This question Paper consists of objective and subjective types of 38 questions.

2. This question paper has been sealed by reverse jacket. You have to cut on the right side to open the paper at the time of commencement of the examination. Check whether all the pages of the question paper are intact.

3. Follow the instructions given against both the objective and subjective types of questions.h

4. Figures in the right hand margin indicate maximum marks for the questions.

5. The maximum time to answer the paper is given at the top of the question paper. It includes 15 minutes for reading the question paper.

…………………………………………………………………………………………………………………………………………………………………………………...

I. Four choices are given for each of incomplete / statement / questions. Choose the correct answer and write the complete answer along with its letter of alphabet. 8 x 1 = 8

1. In the pair of Linear equations x + y = 9 and x - y = 1 then the value of ‘x’ and ‘y’ are :

A. 5 and 4 B. 4 and 5 C. 6 and 3 D. 3 and 6

2. The nth term of an arithmetic progression is an = 5n + 5 then the 4th term is :

A. 25 B. 9 C. 13 D. 17

3. If the roots of the quadratic equation x2 + 8x + k = 0 are equal, then the value of ‘k’ is :

A. 9 B. 16 C. 8 D. 5

4. The value of sin 60° × cos 30° is :

A. 1/4 B. √3/4 C. 3/4 D. 1/2

5. The distance of the co-ordinate p(4, 3) from the x- axis is :

A. 2 units B. 3 units C. 4 units D. 5 units

6. A straight line intersecting a circle at one points is called :

A. a secant B. a tangent C. radius D. a normal

7. The volume of a cylinder is 300 m3 then the volume of a cone having the same radius and height as that of the cylinder is :

A. 900 m3 B. 600 m3 C. 150 m3 D. 100 m3

8. The surface area of a sphere of radius 7cm is :

A. 154 cm2 B. 308 cm2 C. 616 cm2 D. 770 cm2

II. Answer the following questions in a sentence each. 8 x 1 = 8

9. How many solutions have the pair of linear equations 5x+2y-10=0 and 10x + 4y - 20 = 0?

10. Write the standard form of a pair of linear equation.

11. Find the value of cotθ - tan (900 - θ ).

12. In the figure ∠Q=900 , and PQ=5cm,PR = 25 – X then find length of RQ .

13. Write the co-ordinates of the midpoint of the line segment joining the points A(1 , 1 ) and B (2 , 2 ).

14. Find the median of the scores 10, 12, 14, 16, 18 and 20 ?

15. State BASIC PROPORTIONALITY theorem ?

16. Find the courved surface rea of cone of base radius r and height h.

III. Answer the following questions. 8 x 2 = 16

17. Find the 47th term of an arithmetic progression 1, 3, 5, 7, . . . . . . .

18. Find the sum of first 50 terms of the arithmetic progression 20, 25, 30, . . . . . . using the formula.

Find the sum of the first 30 positive integers multiples of 8.

19. Solve : 6x + y = 30 18x ˗ y = 18

20. Solve by using quadratic formula : 5x2 -12x+4=0.

21. Find the discriminant of the quadratic equation 5x2 ˗8x+4=0 and hence write the nature of roots.

Prove that the quadratic equation x2 +9x˗4=0 has distinct, real roots.

22. Find the distance between the co-ordinate of the points A(0, 0) and B(10, -3).

23. Draw a line segment of AB=7cm and divide it in the ratio 4:3 by geomtrical construction.

24. Find the quadratic polynominal whose sum and product of zeroes are ¼ and -1 respectively

IV. Answer the following questions. 9 x 3 = 27

25. Evaluate : 2tan2 450+ cos2300 –sin2600

Test yourself

The angle of elevation of the top of a tower from a point on the ground, which is 30m away from the foot of the tower is 300. Find the height of the tower.

26. As observed from the top of a 100m high light house from the sea level the angle of depression of two ships are 300 and 450. If one of the ship is exactly behind the other on the same side of the light house, find the distance between the two ships (√3 ≈1.73)

Prove that (cosθ-2〖cos〗^3 θ)/(2〖sin〗^3- sinθ)=cotθ.

27. The volume of acube is 64cm3. Find the total surface area of the cube.

28. Prove that “The tangent at any point of a circle is perpendicular to the radius through the point of contact”.

Prove that “The lengths of tangents drawn from an external point to a circle are equal”

29. Construct a triangle of sides 4cm,5cmand 6cm and then a triangle simlar to it, whose sides are 2/3 of the corresponding sides of the first triangle.

30. A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digits. Find the number.

The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is 29/30 Find the original fraction.

31. If 4tan 𝜃 =3 Evaluate (4sinθ-cosθ+1)/(4sinθ+cosθ-1)

Test yourself

If tan 2A = cot (A-180) where 2A is an acute angle. Find the value of A

32. Draw a pair of tangents to a circle of radius 4cm which are inclined to each other at an angle of 700 and write the measure of its length.

33. Calculate the median for the following data

Class interval Frequency (F)

0-20 6

20-40 8

40-60 10

60-80 12

80-100 6

100-120 5

120-140 3

n=50.

Calculate the mode for the following frequency distribution table

Class interval Frequency (F)

5-15 6

15-25 11

25-35 21

35-45 23

45-55 14

55-65 5

n=80

Construct ‘ogive’ for the following distribution C.I 0-3 3-6 6-9 9-12 12-15

F 9 3 5 3 1

V. Answer the following. 4 x 4 = 16 34. Solve the equations graphically 2x – y = 2 4x – y =4

35. An arithmetic progression consists of 37 terms. The sum of the first 3 terms of it is 12 and the sum of its last 3 terms is 318, then find the first and last terms of the progression.

The sum of the first 7 terms of an arithmetic progression is 140 and the sum of the next 7 terms of the same progression is 385 then find the arithmetic progression.

36. Construct a triangle with sides 4cm, 5cm, and 6cm and then another triangle whose sides are 5/3 of the corresponding sides of the first triangle.

37. A wooden article was made by scooping out a hemisphere from one end of a cylinder and a cone from other end as shown in the figure. If the height of cylinder is 40cm, radius is 7cm and height of cone is 24cm, find the volume of wooden article.

VI. Answer the following question : 1 x 5 = 5 38. Prove that “ if two triangles are equiangular , then their corresponding sides are propotional’ and also write the relation between area of these two similar triangle and their corresponding sides.

2Unsolved paper 2

General Instructions to the Candidate :

1. This question Paper consists of objective and subjective types of 38 questions.

3. Follow the instructions given against both the objective and subjective types of questions.

4. Figures in the right hand margin indicate maximum marks for the questions.

5. The maximum time to answer the paper is given at the top of the question paper. It includes 15 minutes for reading the question paper.

I. Four choices are given for each of incomplete / statement / questions. Choose the correct answer and write the complete answer along with its letter of alphabet. 8 x 1 = 8

1. If one of the zeroes of the quadratic polynomial x2 + 3x + k is 2, then the value

of k is

a. 10 b. –10 c.–7 d. –2

2. The total number of factors of a prime number is

a.1 b.0 c. 2 d.3

3. The quadratic polynomial, the sum of whose zeroes is –5 and their product is 6, is

a. x2 + 5x + 6 b.x2 – 5x + 6 c. x2 – 5x – 6 d.–x2 + 5x + 6

4. The value of k for which the system of equations x + y – 4 = 0 and 2x + ky =3 has no solution, is

a.–2 b. ≠2 c.3 d. 2

5. The value of x for which 2x,(x + 10) and ( 3x + 2 ) are the three consecutive terms of an AP, is

a.6 b. –6 c. 18 d.–18

6. The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ – b cos θ), is

a. a2 + b2 b.a2 – b2 c. a2 + b2 d.a2 −b2

7. The value of p, for which the points A(3, 1), B(5, p) and C(7, –5) are collinear, is

a.–2 b.2 c. –1 d.1

8. The surface area of a sphere of radius 7cm is :

A. 154 cm2 B. 308 cm2 C. 616 cm2 D. 770 cm2

II. Answer the following questions in a sentence each. 8 x 1 = 8

9. How many solutions have the pair of linear equations x+2y-10=0 and x + 4y - 20 = 0?

10. Write the standard form of a pair of linear equation.

11. Find the value of cot150 - tan 750.

12. In the given graph, the number of zeros of the polynomial y = p ( x ) is

13. In the figure, O is the centre of a circle, AC is a diameter. If ACB = 50°, then find the measure of BAC .

14. Write the formula to find the total surface area of a right-circular cone whose circular base radius is ‘r’ and slant height is ‘l’.

15. If P ( x ) =2x3 + 3x2 -11x +6 , then find the value of P ( 1 ).

16. If one root of the equation ( x + 4 ) ( x + 3 ) = 0 is – 4, then find the another root of the equation.

III. Answer the following questions. 8 x 2 = 16

17. Solve the following pair of linear equations : 2x + 3y = 11

2x – 4y = – 24

18. Find the sum of first 20 terms of arithmetic series 5 + 10 + 15 + ..... using suitable formula.

Find the sum of the first 30 positive integers multiples of 8.

19. Find the value of k of the polynomial P ( x ) = 2x2 − 6x + k , such that the sum of zeros of it is equal to half of the product of their zeros.

20. Find the value of the discriminant of the quadratic equation 2x2 – 5x -1 = 0, and hence write the nature of its roots

21. Prove that cosec A ( 1 – cos A ) ( cosec A + cot A ) = 1.

OR Prove that (tanA-sinA)/(tanA+sinA)= (secA-1)/(secA+1)

22. Find the coordinates of the mid-point of the line segment joining the points ( 2, 3 ) and ( 4, 7 ).

23. Draw a circle of radius 4 cm, and construct a pair of tangents to the circle, such that the angle between the tangents is 60°.

24. Letters of English alphabets A B C D E I are marked on the faces of a cubical die. If this die is rolled once, then find the probability of getting a vowel on its top face.

IV. Answer the following questions. 9 x 3 = 27

25. Prove that √3is an irrational number.

Find L.C.M. of H.C.F. ( 306, 657 ) and 12.

26. As The diagonal of a rectangular playground is 60 m more than the smaller side of the rectangle. If the longer side is 30 m more than the smaller side, find the sides of the playground.

The altitude of a triangle is 6 cm more than its base. If its area is 108 cm2 , find the base and height of the triangle.

27. In the figure, the vertices of Δ ABC are A ( 0, 6 ), B ( 8, 0 ) and C ( 5, 8 ). If CD ⊥ AB, then find the length of altitude CD.

Show that the triangle whose vertices are A ( 8, – 4 ), B ( 9, 5 ) and C ( 0, 4 ) is an isosceles triangle.

28. Prove that “The tangent at any point of a circle is perpendicular to the radius through the point of contact”.

Prove that “The lengths of tangents drawn from an external point to a circle are equal”

29. Construct a triangle of sides 4cm,5cmand 6cm and then a triangle simlar to it, whose sides are 2/3 of the corresponding sides of the first triangle.

30. A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digits. Find the number.

31. If 4tan 𝜃 =3 Evaluate (4sinθ-cosθ+1)/(4sinθ+cosθ-1)

If tan 2A = cot (A-180) where 2A is an acute angle. Find the value of A

32. Draw a pair of tangents to a circle of radius 4cm which are inclined to each other at an angle of 700 and write the measure of its length.

33. Calculate the mode for the following frequency distribution table :

Class-interval Frequency ( f )

0 — 5 8

5 — 10 9

10 — 15 5

15 — 20 3

20 — 25 1

∑ f = 26

Calculate the mode for the following frequency distribution table

Class interval Frequency (F)

5-15 6

15-25 11

25-35 21

35-45 23

45-55 14

55-65 5

n=80

Calculate the mode for the following frequency distribution table :

An insurance policy agent found the following data for distribution of ages of 35 policy holders. Draw a “less than type” ( below ) of ogive for the given data :

Age ( in years ) Number of policy holders

Below 20 2

Below 25 6

Below 30 12

Below 35 16

Below 40 20

Below 45 25

Below 50 35

V. Answer the following. 4 x 4 = 16 34. In the Δ ABD, C is a point on BD such that BC : CD = 1 : 2, and Δ ABC is an equilateral triangle. Then prove that

AD2 = 7AC2 .

35. Prove that “the lengths of tangents drawn from an external point to a circle are equal”.

36. AB and CD are the arcs of two concentric circles with centre O of radius 21 cm and 7 cm respectively. If AOB = 30° as shown in the figure, find the area of the shaded region.

37. In the figure, ABCD is a square, and two semicircles touch each other externally at P. The length of each semicircular arc is equal to 11 cm. Find the area of the shaded region.

VI. Answer the following question : 1 x 5 = 5 38. Prove that “if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio ( or proportion ) and hence the two triangles are similar”.

Test yourself

3Unsolved paper 3

General Instructions to the Candidate :

1. This question Paper consists of objective and subjective types of 38 questions.

3. Follow the instructions given against both the objective and subjective types of questions.

4. Figures in the right hand margin indicate maximum marks for the questions.

5. The maximum time to answer the paper is given at the top of the question paper. It includes 15 minutes for reading the question paper.

I. Four choices are given for each of incomplete / statement / questions. Choose the correct answer and write the complete answer along with its letter of alphabet. 8 x 1 = 8

1 The sum of first 20 natural numbers is

A. 142 B. 210 C. 254 D. 310.

2. The total number of factors of a prime number is

a.1 b.0 c. 2 d.3

3 If the mean of 5 scores is 6, then the sum of all the scores is

(A) 11 (B) 26 (C) 30 (D) 42.

4. The value of k for which the system of equations x + y – 4 = 0 and 2x + ky =3 has no solution, is

a.–2 b. ≠2 c.3 d. 2

5. The value of x for which 2x,(x + 10) and ( 3x + 2 ) are the three consecutive terms of an AP, is

a.6 b. –6 c. 18 d.–18

6. If p ( x ) = 2x2 − 3x + 5, then the value of p ( – 1 ) is

(A) 4 (B) 6 C) 8 (D) 10.

7. The value of p, for which the points A(3, 1), B(5, p) and C(7, –5) are collinear, is

a.–2 b.2 c. –1 d.1

8. The distance of the point P ( 3, 4 ) from y-axis is

(A) 3 units (B) 4 units (C) 5 units D) 7 units

II. Answer the following questions in a sentence each. 8 x 1 = 8

9. Write the H.C.F. of any two prime numbers.

10. If cos x = 24/25 , then what is the value of sec x ?

11 Define concentric circles.

12. In the given graph, the number of zeros of the polynomial y = p ( x ) is

13. In ABC, if AB2 + BC2 = AC2 , then name the right angle.

14. Write the formula to find the total surface area of a right-circular cone whose circular base radius is ‘r’ and slant height is ‘l’.

15. The area of the base of a right circular cone is 100 cm2 and height is 3 cm. Find its volume.

16. If one root of the equation ( x + 4 ) ( x + 3 ) = 0 is – 4, then find the another root of the equation.

III. Answer the following questions. 8 x 2 = 16

17. Classify the following situations as examples of Permutations and Combinations :

i) Arranging 6 different books on a shelf

ii) Selecting 2 black balls from a bag containing 3 red and 4 black balls

iii) Forming a committee of 4 members from a group of 12 persons

iv) Forming 3-digit numbers using 1, 4, 5 and 7.

18. If 8, x – 1, 16 are in Arithmetic Progression, then find the value of x.

19. Find the remainder obtained when p ( x ) = 2x3 – 5x + 6 is divided by g ( x ) = ( x – 2 ) using Remainder theorem.

20. In the given figure in Δ ABC, XY || BC. If BX = 7 cm, AX = 5 cm and AC = 18 cm, then find CY

21 Prove that : ( 1 − cos θ)2 ( 1 + cotθ )2 + tan2θ = sec .

22. Find the distance of the point P ( 5, 12 ) from the origin.

23. Draw a circle of radius 3 cm. Construct a pair of tangents to it such that the angle between them is 60°.

24. The length of a rectangular field is three times its breadth. If the area of the field is 192 m2 , then find its breadth.

IV. Answer the following questions. 9 x 3 = 27

25. The fourth term of an Arithmetic Progression is 6 more than its second term. If the eighth term is 26, then find the Arithmetic Progression.

26. The total runs scored by two cricket players A and B in 15 matches are 1050 and 900 with standard deviations 5·6 and 3·0 respectively. i) Who is better run getter ? ii) Find who is more consistent in performance.

27. If one root of the equation 2x + px + q = 0 is 3 times the other, then prove that 3p2 = 16 q.

Solve by using formula : ( 2m + 3 ) ( 3m – 2 ) + 2 = 0.

28 Prove that “if two circles touch each other externally, then the centres and the point of contact are collinear”.

29. Construct a triangle of sides 4cm,5cmand 6cm and then a triangle simlar to it, whose sides are 2/3 of the corresponding sides of the first triangle.

30. In an equilateral triangle ABC, AN ⊥ BC. Prove that AN2 = BN2.

In Δ ABC, AB = AC and D is any point on BC as shown in the figure. Prove that AB2 – AD2 = BD . DC.

31 The angle of elevation of the top of a vertical pole from a point on a horizontal ground is 30°. On walking 5 m towards the pole the angle of elevation is found to be 45°. Find the height of the pole.

32. Construct a pair of tangent to two circles of radii 4 cm and 2 cm whose centres are 9 cm apart..

33. Calculate the mode for the following frequency distribution table :

Class-interval Frequency ( f )

0 — 5 8

5 — 10 9

10 — 15 5

15 — 20 3

20 — 25 1

∑ f = 26

Calculate the mode for the following frequency distribution table

Class interval Frequency (F)

5-15 6

15-25 11

25-35 21

35-45 23

45-55 14

55-65 5

n=80

Calculate the mode for the following frequency distribution table :

An insurance policy agent found the following data for distribution of ages of 35 policy holders. Draw a “less than type” ( below ) of ogive for the given data :

Age ( in years ) Number of policy holders

Below 20 2

Below 25 6

Below 30 12

Below 35 16

Below 40 20

Below 45 25

Below 50 35

V. Answer the following. 4 x 4 = 16 34. Find the solution of the following pair of linear equations by the graphical method.

2x + y = 8

x + y = 5

35. An aircraft flying parallel to the ground in the sky from the point A through the point B is observed, the angle of elevation of aircraft at A from a point on the level ground is 60°, after 10 seconds it is observed that the angle of elevation of aircraft at B is found to be 30° from the same point. Find at what height the aircraft is flying, if the velocity of aircraft is 648 km/hr. ( Use 3 = 1·73 ) ‘

36. Prove that “if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio ( or proportion ) and hence the two triangles are similar”.

37. A medicine capsule is in the shape of a cylinder with hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

VI. Answer the following question : 1 x 5 = 5 38. The common difference of two different arithmetic progressions are equal. The first term of the first progression is 3 more than the first term of second progression. If the 7th term of first progression is 28 and 8th term of second progression is 29, then find the both different arithmetic progressions.

General Instructions to the Candidate :

1. This question Paper consists of objective and subjective types of 38 questions.

3. Follow the instructions given against both the objective and subjective types of questions.

4. Figures in the right hand margin indicate maximum marks for the questions.

5. The maximum time to answer the paper is given at the top of the question paper. It includes 15 minutes for reading the question paper.

I. Four choices are given for each of incomplete / statement / questions. Choose the correct answer and write the complete answer along with its letter of alphabet. 8 x 1 = 8

1. If the pair of Linear equations x + 2y = 3 and 2x + 4y = k are coincide then the value of ‘k’ is :

A. 3 B. 6 C. -3 D. -6

2. The nth term of an arithmetic progression is an = 4n + 5 then the 3rd term is :

A. 5 B. 9 C. 13 D. 17

3. If the roots of the quadratic equation x2 + 6x + k = 0 are equal, then the value of ‘k’ is :

A. 9 B. -9 C. 8 D. 5

4. The value of sin 60° × cos 30° is :

A. 1 4 B. 3 4 C. 3 4 D. 1 2

5. The distance of the co-ordinate p(4, 3) from the x- axis is :

A. 2 units B. 3 units C. 4 units D. 5 units

6. A straight line intersecting a circle at two points is called :

A. a secant B. a tangent C. radius D. a normal

7. The volume of a cylinder is 300 m3 then the volume of a cone having the same radius and height as that of the cylinder is :

A. 900 m3 B. 600 m3 C. 150 m3 D. 100 m3

8. The surface area of a sphere of radius 7cm is :

A. 154 cm2 B. 308 cm2 C. 616 cm2 D. 770 cm2

II. Answer the following questions in a sentence each. 8 x 1 = 8

9. How many solutions have the pair of linear equations 2x+3y-9=0 and 4x + 6y - 18 = 0?

10. Write the standard form of a quadratic equation.

11. Find the value of tanθ - cot (900 - θ ).

12. In the figure ∠B=900 , ∠A = ∠C and BC=10cm, then find the value of tan 450 .

13. Write the co-ordinates of the midpoint of the line segment joining the points A(x1 , y1 ) and B (x2 , y2 ).

14. Find the median of the scores 5, 8, 14, 16, 19 and 20 ?

15. State ‘Thale’s theorem ?

16. Write the formula to find the curved surface area of the frustum of a cone as shown in the figure?

III. Answer the following questions. 8 x 2 = 16

17. Find the 25th term of an arithmetic progression 2, 6, 10, 14, . . . . . . .

18. Find the sum of first 20 terms of the arithmetic progression 3, 8, 13, . . . . . . using the formula.

Find the sum of the first 30 positive integers divisible by 6.

19. Solve : 3x + y = 15 2x ˗ y = 5

20. Solve by using quadratic formula : x2 -3x+1=0.

21. Find the discriminant of the quadratic equation 2x2 ˗6x+3=0 and hence write the nature of roots.

Prove that the quadratic equation x2 +ax˗4=0 has distinct, real roots.

22. Find the distance between the co-ordinate of the points A(2, 3) and B(10, -3).

23. Draw a line segment of AB=8cm and divide it in the ratio 3:2 by geomtrical construction.

24. In the figure given below find the value of sinθ and cos∝ ?

IV. Answer the following questions. 9 x 3 = 27

25. The sum of two natural numbers is 9 and the sum of their reciprocals is 9/20. Find the numbers.

The perimeter and area of a rectangular play ground are 80m and 384m2 respectively. Find the length and breadth of the play ground.

26. Prove that Sinθ/(1-cosθ)+ cosθ/(1-tanθ)=sinθ+cosθ.

Prove that (cosθ-2〖cos〗^3 θ)/(2〖sin〗^3- sinθ)=cotθ.

27. From a point on the ground, the angles of elevation of the top and bottom of a transmission tower fixed at the top of a 20m high building are 600 and 450 respectively. Find the height of the transmission tower.

28. Find the value of ‘k’. If the co-ordinates of the points A(2, -2), B(-4, 2) and C(-7, k) are collinear.

29. Calculate the ‘mean’ for the frequency distribution table given below, by direct method.

Find the ‘mode’ of the frequency distribution table given below.

30. The following table gives the production yield per hectare of wheat of 100 farms of a village. Draw a ‘more than type ogive’ for the given data.

31. Prove that “the tangent at any point of a circle is perpendicular to the radius through the point of contact”.

32. Draw a pair of tangents to a circle of radius 4cm which are inclined to each other at an angle of 700 and write the measure of its length.

33. A right circular metalic cone of height 20cm and base radius 5cm is melted and recast into a solid sphere. Find the radius of the sphere.

A solid sphere of radius 3cm is melted and reformed by stretching it into a cylindrical shaped wire of length 9m. Find the radius of the wire.

V. Answer the following. 4 x 4 = 16 34. Find the solution of the following pair of linear equations by the graphical method. 2x + y = 10 x + y = 6

35. An arithmetic progression consists of 37 terms. The sum of the first 3 terms of it is 12 and the sum of its last 3 terms is 318, then find the first and last terms of the progression.

The sum of the first 7 terms of an arithmetic progression is 140 and the sum of the next 7 terms of the same progression is 385 then find the arithmetic progression.

36. Construct a triangle with sides 4cm, 5cm, and 6cm and then another triangle whose sides are 5/3 of the corresponding sides of the first triangle.

37. A toy is made in the shape of a cylinder with one hemisphere stuck to one end and a cone to the other end, as shown in the figure, the length of the cylindrical part of the toy is 20cm and its diameter is 10cm. If the slant height of the cone is 13cm. Find the surface area of the toy

VI. Answer the following question : 1 x 5 = 5 38. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Model Mathematics paper 7