# Tamilnadu Board Class 10 Math Sample Papers 2011

## Tamilnadu Board Sample Papers 2011 for Class 10 Math

Tamil Nadu State Broard Mathemathics - Class X

(Sample Paper)

Time Allowed : 2 ½ hours Maximum Marks : 100

Instructions :

1.This question paper consists of four Parts, Read the note carefully under each Part before answering them.

2.Write legibly. The rough work should be shown at the bottom of the pages of the answer-book.

3.Only the logarithmic and trigonometric tables issued at the centre should be used.

Part - A ( Marks : 20 )

Note :

Answer any ten from the fifteen questions.

Show all the steps.

Each question carries two marks. (10 × 2 = 20)

1.Find the sum of the first eight terms of the G.P. 2, 4, 8.............

2.Define Parallelogram:

3.A cylindrical pillar is 3.5 m in diameter and 20 m high. Find the cost of painting its curved surface at the rate of Rs. 20 per square metre.

4.If A = { a, b, c, d, e, f, g, h } , B = { a, b, e, f} and C = { a, c, e, g, h } find A − (B ∪ C).

5.Given A = { 1, 2, 3, 4, 5 } , B = { 3, 6, 8 }. List the elements for the following relations from A to B

is less than

is greater than.

6.When x + 2 divides 4x3 + 5x2 + px−2 without remainder. find p.

7.Determine the nature of the roots of the equation x2−2x+5 = 0.

8.Define critical path and project duration.

9.How far is a chord of length 12 cm away from the centre of a circle of radius 10 cm ?

10.In the figure, AB is the diameter of a circle, ∠ BAC = 42°. find ∠ ACD.

11.Find the point which divides the line segment joining the points (−1,2) and ( 4, − 5 ) internally in the ratio 2 : 3.

12.If the straight line 7x − 5y = k passes through the point (1,1), what is k ?

13.Use trigonometric tables, to find the value of sin 60° 42′ + cos 42° 20′.

14.The least score of a cricket player of the school team is 5 runs in a series of ten matches. If his range of scores is 87, find his highest score in the series.

15.If three coins are tossed, then what is the chance of getting exactly one head ?

Part - C ( Marks : 45 )

Note :

This Part contains ten questions each with two alternatives.

Answer any nine questions.

Choose either of the alternatives in each question.

Steps and diagrams should be shown.

Each question carries five marks. (9 × 5 = 45)

16.Find the sum of all multiples of 9 between 400 and 600.

Or

A rubber ball dropped from a height of 50 m rebounds at every impact from the floor to a height half of that from which it has fallen. Find the total distance described, by the time it comes to rest.

17.An ice-cream cone has a hemispherical top. If the height of the cone is 9 cm and base radius is 3 cm, find the volume of the ice-cream in the ice-cream cone,

Or

Three solid spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

18.Verify the de Morgan's law A−(B ∩ C ) = ( A − 6 ) ∪ ( A − C ) using Venn Diagram.

Or

if A = { 1, 2, 3, 4 } and B = { 9, 13, 17, 21 } and if function A → B is defined by f(x) = 4x + 5, represent f as (i) set of ordered pairs (ii) an arrow diagram (iii) a graph (iv) a table.

19.In Δ ABC, m ∠ C is 20° greater than m ∠ A. The sum of m ∠ A and m ∠ C is twice m ∠ B. Find the three angles.

Or

Factorlse : x3 + 13x2 + 32x + 20.

20.Find the values of a and b if 25x4 − 40x3 − 34x2 + ax + b is a perfect square.

Or

If α and β are the roots of x2 + 8x − 12 = 0. find

α - β

α2 + β2

21.Maximise :Z = 30x + 20y

subject to :2x + y ≤ 800,

x + 2y ≤ 1000,

x ≥ 0, y ≥ 0.

Or

A small maintenance project consists of the following jobs whose activities and duration are given below :

Activity 1 − 2 1 − 3 2 − 3 2 − 4 3 − 4 3 − 5 4 − 5

Duration in days 20 25 10 12 5 8 10

Draw the network diagram

Find the critical path and project duration.

22.Prove the converse of, “The perpendicular drawn from the centre of a circle to a chord bisects the chord,”

Or

P and Q are the points on the sides CA and CB respectively of a Δ ABC right angled at C. Prove that AQ2 + BP2 = AB2 + PQ2.

23.Show that ( 9, 0 ), ( 1, 4 ) and ( 11, − 1 ) are collinear.

Or

Find the equation of the perpendicular-bisector of the line Joining the points A( 1, 7) and B (−3, 3).

24.If sin 6 = cos 9 where 6 is an acute angle, find the value of

OR

The angles of depression of the top and the bottom of a 12 m tall building from the top of a tower are 45° and 60° respectively. Find the height of the tower.

25.The marks obtained by 10 students in a class test out of 100 marks are 62, 49. 71, 75, 33, 41, 100, 88, 50, 31. Calculate the standard deviation of the marks.

Or

Two dice are rolled once. Find the probability of getting an even number.

Part - C ( Marks : 20 )

Note :

This part contains two questions, each with alternatives.

Answer both the questions choosing cither of the alternatives under each question.

Each question carries ten marks. (2 × 10 = 20)

26.Construct a triangle ABC such that BC = 7 cm, m ∠ A = 60° and altitude from A to BC is 4 5 cm.

Or

Take a point P at a distance of 7 cm from the centre of a circle of radius 3 cm and from P draw two tangents PA and PB to the circle. Verify the lengths of the tangents by algebraic calculation.

27.Draw the graph of y = 2x2 + x − 6 and hence find the roots of 2x2 + x − 10 − 0.

Or

Draw the graph of xy = 12, x, y > 0. Use the graph to find y when x = 5 and x when y = 8.

(Sample Paper)

Time Allowed : 2 ½ hours Maximum Marks : 100

Instructions :

1.This question paper consists of four Parts, Read the note carefully under each Part before answering them.

2.Write legibly. The rough work should be shown at the bottom of the pages of the answer-book.

3.Only the logarithmic and trigonometric tables issued at the centre should be used.

Part - A ( Marks : 20 )

Note :

Answer any ten from the fifteen questions.

Show all the steps.

Each question carries two marks. (10 × 2 = 20)

1.Find the sum of the first eight terms of the G.P. 2, 4, 8.............

2.Define Parallelogram:

3.A cylindrical pillar is 3.5 m in diameter and 20 m high. Find the cost of painting its curved surface at the rate of Rs. 20 per square metre.

4.If A = { a, b, c, d, e, f, g, h } , B = { a, b, e, f} and C = { a, c, e, g, h } find A − (B ∪ C).

5.Given A = { 1, 2, 3, 4, 5 } , B = { 3, 6, 8 }. List the elements for the following relations from A to B

is less than

is greater than.

6.When x + 2 divides 4x3 + 5x2 + px−2 without remainder. find p.

7.Determine the nature of the roots of the equation x2−2x+5 = 0.

8.Define critical path and project duration.

9.How far is a chord of length 12 cm away from the centre of a circle of radius 10 cm ?

10.In the figure, AB is the diameter of a circle, ∠ BAC = 42°. find ∠ ACD.

11.Find the point which divides the line segment joining the points (−1,2) and ( 4, − 5 ) internally in the ratio 2 : 3.

12.If the straight line 7x − 5y = k passes through the point (1,1), what is k ?

13.Use trigonometric tables, to find the value of sin 60° 42′ + cos 42° 20′.

14.The least score of a cricket player of the school team is 5 runs in a series of ten matches. If his range of scores is 87, find his highest score in the series.

15.If three coins are tossed, then what is the chance of getting exactly one head ?

Part - C ( Marks : 45 )

Note :

This Part contains ten questions each with two alternatives.

Answer any nine questions.

Choose either of the alternatives in each question.

Steps and diagrams should be shown.

Each question carries five marks. (9 × 5 = 45)

16.Find the sum of all multiples of 9 between 400 and 600.

Or

A rubber ball dropped from a height of 50 m rebounds at every impact from the floor to a height half of that from which it has fallen. Find the total distance described, by the time it comes to rest.

17.An ice-cream cone has a hemispherical top. If the height of the cone is 9 cm and base radius is 3 cm, find the volume of the ice-cream in the ice-cream cone,

Or

Three solid spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

18.Verify the de Morgan's law A−(B ∩ C ) = ( A − 6 ) ∪ ( A − C ) using Venn Diagram.

Or

if A = { 1, 2, 3, 4 } and B = { 9, 13, 17, 21 } and if function A → B is defined by f(x) = 4x + 5, represent f as (i) set of ordered pairs (ii) an arrow diagram (iii) a graph (iv) a table.

19.In Δ ABC, m ∠ C is 20° greater than m ∠ A. The sum of m ∠ A and m ∠ C is twice m ∠ B. Find the three angles.

Or

Factorlse : x3 + 13x2 + 32x + 20.

20.Find the values of a and b if 25x4 − 40x3 − 34x2 + ax + b is a perfect square.

Or

If α and β are the roots of x2 + 8x − 12 = 0. find

α - β

α2 + β2

21.Maximise :Z = 30x + 20y

subject to :2x + y ≤ 800,

x + 2y ≤ 1000,

x ≥ 0, y ≥ 0.

Or

A small maintenance project consists of the following jobs whose activities and duration are given below :

Activity 1 − 2 1 − 3 2 − 3 2 − 4 3 − 4 3 − 5 4 − 5

Duration in days 20 25 10 12 5 8 10

Draw the network diagram

Find the critical path and project duration.

22.Prove the converse of, “The perpendicular drawn from the centre of a circle to a chord bisects the chord,”

Or

P and Q are the points on the sides CA and CB respectively of a Δ ABC right angled at C. Prove that AQ2 + BP2 = AB2 + PQ2.

23.Show that ( 9, 0 ), ( 1, 4 ) and ( 11, − 1 ) are collinear.

Or

Find the equation of the perpendicular-bisector of the line Joining the points A( 1, 7) and B (−3, 3).

24.If sin 6 = cos 9 where 6 is an acute angle, find the value of

OR

The angles of depression of the top and the bottom of a 12 m tall building from the top of a tower are 45° and 60° respectively. Find the height of the tower.

25.The marks obtained by 10 students in a class test out of 100 marks are 62, 49. 71, 75, 33, 41, 100, 88, 50, 31. Calculate the standard deviation of the marks.

Or

Two dice are rolled once. Find the probability of getting an even number.

Part - C ( Marks : 20 )

Note :

This part contains two questions, each with alternatives.

Answer both the questions choosing cither of the alternatives under each question.

Each question carries ten marks. (2 × 10 = 20)

26.Construct a triangle ABC such that BC = 7 cm, m ∠ A = 60° and altitude from A to BC is 4 5 cm.

Or

Take a point P at a distance of 7 cm from the centre of a circle of radius 3 cm and from P draw two tangents PA and PB to the circle. Verify the lengths of the tangents by algebraic calculation.

27.Draw the graph of y = 2x2 + x − 6 and hence find the roots of 2x2 + x − 10 − 0.

Or

Draw the graph of xy = 12, x, y > 0. Use the graph to find y when x = 5 and x when y = 8.

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