Category: CBSE

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 2

                                                        Section A

1.Determine whether the given value of x is a solution of the given quadratic equation or not:
6X² – x – 1 = 0; x =1/2.

2.Find 15th term of the AP with second term 11 and common difference 9.

Download Formula Book for Class 10 Maths and Science CBSE Sample Papers for Class 10 Maths

3.Find the coordinates of the point which divides the line segment joining the points (3, 5) and (7, 9) internally in the ratio 2 : 3.

4.In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the length of the arc.

                                                          Section B

5.Using quadratic formula, solve the following quadratic equation: 2X² – 7x + 3 = 0

6.Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

7.A point P is 18 cm from the centre of a circle. The radius of the circle is 12 cm. Find the length of the tangent drawn to the circle from the point P.

8.In a box, there are 800 bulbs, out of which 20 bulbs are defective. One bulb is taken out at random. Find the probability that the bulb is not defective.

9.The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of these two circles.

10.A rectangular solid metallic cuboid 18 cm x 15 cm x 4.5 cm is melted and recast into solid cubes each of side 3 cm. How many solid cubes can be made?

                                                                     Section C

11.Divide 39 into two parts such that their product is 324.

12.Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

13.Solve for x:(1/ x + 4 )-(1/x-7 )=11/30,  (x not equal to  -4, 7 )

14.Draw a triangle ABC with side BC = 7 cm, B = 45°, A = 105°. Then construct a triangle whose sides are 4/3 times the corresponding sides of triangle ABC.

15. 21 cards are numbered 1, 2, …, 20, 21 and placed in a box. The cards are mixed thoroughly. A card is drawn at random from the box. Find the probability that the number on the card is
(i) an even                                   (ii) a prime number                                      (iii) divisible by 4

16.A box contains 80 discs which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.

17.Find the value of k if the points A(2,3), B(4, k) and C(6, -3) are collinear.

18.Find the value of k, if the point P(2,3) is equidistant from the points A{k, 1) and B(7, k).

19.The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. (Take pi =22/7)

20.A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 14 cm, find the area of material used for making it. (Take pi =22/7)

                                                                  Section D

21. One year ago, a man was 8 times as old as his son. Now, his age is equal to the square of his son’s age in years. Find their present ages.

22. A manufacturer of TV sets produced 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year, find
(i) the production in the first year,     (ii) the production in the 10^th year,
(iii) the total production in 7 years

23.A circle is inscribed in AABC having sides AB = 8 cm, BC = 7 cm and AC = 5 cm. Find AD, BE and CF

24.In figure, given below, XP and XQ are tangents from X to the circle with centre O and ARB is tangent at point R. Prove that XA + AR = XB + BR

25.If O be the centre of a circle and tangents drawn to the circle at the points A and B of the circle intersect each other at P, then prove that angle AOB + angle APB = 180°.

26.An electric pole is 12 m high. A steel wire tied to the top of the pole is affixed at a point on the ground to keep the pole upright. If the wire makes an angle of 60° with the horizontal through the foot of the pole, find the length of the wire. (Take root 3 =73)

27.The angle of elevation of the top of a tower from a point on the ground is 45°. On walking 30 metres towards the tower, the angle of elevation becomes 60°. Find the height of the tower and the original distance from the foot of the tower. (Take root 3 = 1.73)

28.Find the length of the median through the vertex A(5, 1) drawn to the triangle ABC where other two vertices are B(l, 5) and C(-3, -1).

29.Find the area of the shaded region in figure if ABCD is a square of side 20 m and APD and BPC are semicircles. (Take pi =22/7)

If shaded region is used by society for planting trees, then what value is reflected?

30.A solid is in the form of a cone mounted on a right circular cylinder both having same radii of their bases. Base of the cone is placed on the top base of the cylinder. If the radius of the base and height of the cone be 4 cm and 7 cm respectively and the height of the cylindrical part of the solid is 3.5 cm, find the volume of the solid. (Take pi =22/7)

31.A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy. (Take pi =22/7)

Answers

                                                                Section A

1.Determine whether the given value of x is a solution of the given quadratic equation or not: 6X² – x – 1 = 0; x =1/2.
Ans.

2.Find 15th term of the AP with second term 11 and common difference 9.
Ans.

3.Find the coordinates of the point which divides the line segment joining the points (3, 5) and (7, 9) internally in the ratio 2 : 3.
Ans.

4.In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the length of the arc.
Ans.

                                                          Section B

5.Using quadratic formula, solve the following quadratic equation: 2X² – 7x + 3 = 0
Ans.

6.Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.
Ans.

7.A point P is 18 cm from the centre of a circle. The radius of the circle is 12 cm. Find the length of the tangent drawn to the circle from the point P.
Ans.

8.In a box, there are 800 bulbs, out of which 20 bulbs are defective. One bulb is taken out at random. Find the probability that the bulb is not defective.
Ans.

9.The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of these two circles.
Ans.

10.A rectangular solid metallic cuboid 18 cm x 15 cm x 4.5 cm is melted and recast into solid cubes each of side 3 cm. How many solid cubes can be made?
Ans.

                                                                     Section C

11.Divide 39 into two parts such that their product is 324.
Ans.

12.Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.
Ans.

13.Solve for x:(1/ x + 4 )-(1/x-7 )=11/30,  (x not equal to  -4, 7 )
Ans.

14.Draw a triangle ABC with side BC = 7 cm, B = 45°, A = 105°. Then construct a triangle whose sides are 4/3 times the corresponding sides of triangle ABC.
Ans.

15. 21 cards are numbered 1, 2, …, 20, 21 and placed in a box. The cards are mixed thoroughly. A card is drawn at random from the box. Find the probability that the number on the card is
(i) an even                                   (ii) a prime number                                      (iii) divisible by 4
Ans.

16.A box contains 80 discs which are numbered from 1 to 80. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.
Ans.

17.Find the value of k if the points A(2,3), B(4, k) and C(6, -3) are collinear.
Ans.

18.Find the value of k, if the point P(2,3) is equidistant from the points A{k, 1) and B(7, k).
Ans.

19.The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. (Take pi =22/7)
Ans.

20.A fez, the cap used by the Turks, is shaped like the frustum of a cone. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 14 cm, find the area of material used for making it. (Take pi =22/7)
Ans.

                                                                  Section D

21. One year ago, a man was 8 times as old as his son. Now, his age is equal to the square of his son’s age in years. Find their present ages.
Ans.

22. A manufacturer of TV sets produced 600 units in the third year and 700 units in the 7th year. Assuming that the production increases uniformly by a fixed number every year, find
(i) the production in the first year,     (ii) the production in the 10^th year,
(iii) the total production in 7 years
Ans.

23.A circle is inscribed in AABC having sides AB = 8 cm, BC = 7 cm and AC = 5 cm. Find AD, BE and CF

Ans.

24.In figure, given below, XP and XQ are tangents from X to the circle with centre O and ARB is tangent at point R. Prove that XA + AR = XB + BR

Ans.

25.If O be the centre of a circle and tangents drawn to the circle at the points A and B of the circle intersect each other at P, then prove that angle AOB + angle APB = 180°.

Ans.

26.An electric pole is 12 m high. A steel wire tied to the top of the pole is affixed at a point on the ground to keep the pole upright. If the wire makes an angle of 60° with the horizontal through the foot of the pole, find the length of the wire. (Take root 3 =73)
Ans.

27.The angle of elevation of the top of a tower from a point on the ground is 45°. On walking 30 metres towards the tower, the angle of elevation becomes 60°. Find the height of the tower and the original distance from the foot of the tower. (Take root 3 = 1.73)
Ans.

28.Find the length of the median through the vertex A(5, 1) drawn to the triangle ABC where other two vertices are B(l, 5) and C(-3, -1).
Ans.

29.Find the area of the shaded region in figure if ABCD is a square of side 20 m and APD and BPC are semicircles. (Take pi =22/7)

If shaded region is used by society for planting trees, then what value is reflected?
Ans.

30.A solid is in the form of a cone mounted on a right circular cylinder both having same radii of their bases. Base of the cone is placed on the top base of the cylinder. If the radius of the base and height of the cone be 4 cm and 7 cm respectively and the height of the cylindrical part of the solid is 3.5 cm, find the volume of the solid. (Take pi =22/7)
Ans.

31.A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy. (Take pi =22/7)
Ans.

CBSE Previous Year Question Papers Class 10 Maths SA2 Delhi 2016

Time allowed: 3 hours                                                                                           Maximum marks: 90

GENERAL INSTRUCTIONS:

1. All questions are compulsory.
2. The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.
3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
4.  Use of calculators is not permitted.

CBSE Sample Papers Class 10 Maths

SET I

SECTION A 
Questions number 1 to 4 carry 1 mark each.
Question .1. From an external point P, tangents PA and PB are drawn to a circle with centre O. If ∠PAB = 50° then find ∠AOB.
Answer.

Question 2. In Fig. 1, AB is a 6 m high pole and CD is a ladder inclined at an angle of 60° to the horizontal and reaches up to a point D of pole. If AD = 2.54 m. Find the length of the ladder. (Use √3 = 1.73)

Answer.

Question 3. Find the 9th term from the end (towards the first term) of the A.P. 5, 9,13, …, 185.
Answer.

Question 4. Cards marked with number 3,4,5,…., 50 are placed in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the selected card bears a perfect square number.
Answer.

SECTION B
Questions number 5 to 10 carry 2 marks each.
Question 5. If x = 2/3 and x = -3 are roots of the quadratic equation ax² + 7x + b = a and b.
Answer.

Question 6. Find the ratio in which y-axis divides the line segment joining the points A(5, -6), and B(-1, -4). Also find the coordinates of the point of division.
Answer.

Question 7. In Fig. 2, a circle is inscribed in a ΔABC, such.that it touches the sides AB, BC and CA at points D, E and F respectively. If the lengths of sides AB, BC and CA are 12 cm, 8 cm and 10 cm respectively, find the lengths of AD, BE and CF.

Answer.

Question 8. The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q (2, -5) and R(-3, 6), find the coordinates of P.
Answer.

Question 9. How many terms of the A.P. 18,16,14,…. be taken so that their sum is zero?
Answer.

Question 10. In Fig. 3, AP and BP are tangents to a circle with centre O, such that AP = 5 cm and ∠APB = 60°. Find the length of chord AB.

Answer.

SECTION C
Questions number 11 to 20 carry 3 marks each.
Question 11. In Fig. 4, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region. [Use π = 22/7 ]

Answer.

Question 12. In Fig. 5, is a decorative block, made up of two solids—a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on .the top has a diameter of 3.5 cm. Find the total surface area of the block. [Use π = 22/7 ]

Answer.

Question 13. In Fig. 6, ABC is a triangle Coordinates of whose vertex A are (0, -1). D and E respectively are the mid-points of the sides AB and AC and their coordinates are (1, 0) and (0, 1) respectively. If F is the mid-point of BC, find the areas of ΔABC and ΔDEF.

Answer.

Question 14. In Fig. 7, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with centre O and radius OP while arc PBQ is a semicircle drawn on PQ as diameter with centre M. If OP = PQ = 10 cm, show that area of shaded region is 25(√3-π /6)cm².

Answer.

Question 15. If the sum of first 7 terms of an A.P is 49 and that of its first 17 terms is 289, find the sum of first n terms of the A.P.
Answer.

Question 16. Solve for x:

Answer.

Question 17. A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread evenly all abound it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.
Answer.

Question 18. The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder.[Use π = 22/7 ]
Answer.

Question 19. The angles of depression of the top and bottom of a 50 m high building from the top of a tower are 45° and 60° respectively. Find the height of the tower and the horizontal distance between the tower and the building. [Use√3 = 1.73]
Answer.

Question 20. In a single throw of a pair of different dice, what is the probability of getting (i) a prime number on each dice? (ii) a total of 9 or 11?
Answer.

SECTION D
Questions number 21 to 31 carry 4 marks each.
Question 21. A passenger, while boarding the plane, slipped from the stairs and got hurt. The pilot took the passenger in the emergency clinic at the airport for treatment. Due to this, the plane got delayed by half an hour. To reach the destination 1500 km away in time, so that the passengers could catch the connecting flight, the speed of the plane was increased by 250 km/hour than the usual speed. Find the usual speed of the plane. What value is depicted in this question?
Answer.


Value: By giving utmost importance to the health and well-being of the passenger the pilot displays the value of compassion. By making up for the time lost due to this delay he displays concern for the passengers’ time and money and shows dedication towards his airline and job.

Question 22. Prove that the lengths of tangents drawn from an external point to a circle are equal. ‘
Answer. See Q. 27 (Theorem), 2011 (I Delhi).

Question 23. Draw two concentric circles of radii 3 cm and 5 cm. Construct a tangent to smaller circle from a point on the larger circle. Also measure its length.
Answer.

Question 24. In Fig. 8, O is the centre of a circle of radius 5 cm. T is a point such that OT 13 cm and OT intersects circle at E. If AB is a tangent to the circle at E, find the length of AB, where TP and TQ are two tangents to the circle.

Answer.

Question 25. Find x in terms of a, b and c:

Answer.

Question 26. A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of elevation of the bird is 45°. The bird flies away horizontally in such a way that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30°. Find the speed of flying of the bird. (Take √3 = 1.732)
Answer.

Question 27. A thief runs with a uniform speed of 100 m/minute. After one minute a policeman runs after the thief to catch him. He goes with a speed of 100 m/minute in the first minute and increases his speed by 10 m/ minute every succeeding minute. After how many minutes the policeman will catch the thief.
Answer.

Question 28. Prove that the area of a triangle with vertices (f, t. – 2), (f + 2/ f + 2) and (f + 3, f) is independent of f.
Answer.

Question 29. A game of chance consists of spinning an arrow on a circular board, divided into 8 equal parts, which comes to rest pointing at one of the numbers 1, 2, 3, …., 8 (Fig. 9), which are equally likely outcomes. What is the probability that the arrow will point at (i) an odd number (ii) a number greater than 3 (iii) a number less than 9.

Answer.

Question 30. An elastic belt is placed around the rim of a pulley of radius 5 cm. (Fig. 10) From one point C on the belt, the elastic belt is pulled directly away from the centre O of the pulley until it is at P, 10 cm from the point O. Find the length of the belt that is still in contact with the pulley. Also find the shaded area. Use (π = 3.14 and √3 = 1.73)

Answer.

Question 31. A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm³. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. (Use π= 3.14)
Answer.

SET II

Note: Except for the following questions, all the remaining questions have been asked in Set I.
Question 10. How many terms of the A.P. 27, 24, 21, … should be taken so that their sum is zero?
Answer.

Question 18. Solve for x:

Answer.

Question 19. Two different dice are thrown together. Find the probability of:
(i) getting a number greater than 3 on each die
(ii) getting a total of 6 or 7 of the numbers on two dice
Answer.

Question 20. A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm2. Find the volume of the cone. (Use π = 3.14)
Answer.

Question 28. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are 60° and 30° respectively. Find the height of the tower.
Answer.

Question 29. Construct a triangle ABC in which BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct another triangle whose sides are 3/4 times the corresponding sides of ∆ABC.
Answer.

Question 30. The perimeter of a right triangle is 60 cm. Its hypotenuse is 25 cm. Find the area of the triangle.
Answer.

Question 31. A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/ minute every succeeding minute. After how many minutes, the policeman will catch the thief?
Answer.

SET III

Note: Except for the following questions, all the remaining questions have been asked in Set I and Set II.
Question 10. How many terms of the A.P. 65, 60, 55, … be taken so that their sum is zero?
Answer.

Question 18. A box consists of 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. Ramesh, a shopkeeper will buy only those shirts which are good but ‘Kewal’ another shopkeeper will not buy shirts with major defects. A shirt is taken out of the box at random. What is the probability that
(i) Ramesh will buy the selected shirt?
(ii) ‘Kewal’ will buy the selected shirt?
Answer.

Question 19. Solve the following quadratic equation for x:

Answer.

Question 20. A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the toy. [Use π = 22/7]
Answer.

Question 28. The sum of three numbers in A.P. is 12 and sum of their cubes is 288. Find the numbers.
Answer.

Question 29. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Answer. See Q. 27, 2012 (I Delhi).

Question 30. The time taken by a person to cover 150 km was 2 1/2 hours more than the time taken in the return journey. If he returned at a speed of 10 km/hour more than the speed while going, find the speed per hour in-each direction.
Answer.

Question 31. Draw a triangle ABC with BC = 7 cm, ∠B -=45° and ∠A = 105°. Then construct a triangle whose sides are 4/5 times the corresponding sides of ΔABC.
Answer.

CBSE Previous Year Question Papers CBSE Previous Year Question Papers Class 10 Maths

CBSE Previous Year Question Papers Class 10 Maths SA2 Delhi – 2011

Time allowed: 3 hours                                                                                           Maximum marks: 90

GENERAL INSTRUCTIONS:

1. All questions are compulsory.
2. The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.
3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
4.  Use of calculators is not permitted.

SET I

SECTION A
Questions number 1 to 4 carry 1 mark each.
Question.1 In Fig. 1, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB = 100°, then calculate ∠BAT.

Solution.

CBSE Sample Papers Class 10 Maths

Question.2. In Fig. 2, PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then calculate ∠OAB.

Solution.

Question.3. A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then calculate the rise of water level (in cm).
Solution.

Question.4. In which quadrant the point P that divides the line segment joining the points A(2, – 5) and B(5, 2) in the ratio 2 : 3 lies?
Solution.

SECTION B
Questions number 5 to 10 carry 2 marks each.
Question.5. The angles of a triangle are in A.P., the least being half the greatest. Find the angles.
Solution.

Question.6. Three vertices of a parallelogram taken in order are (- 1, 0), (3, 1) and (2, 2) respectively. Find the coordinates of fourth vertex.
Solution.

Question.7. Find the value of p so that the quadratic equation px(x – 3) + 9 = 0 has two equal roots.
Solution.

Question.8. Find whether – 150 is a term of the A.P. 17,12, 7, 2, … ?
Solution.

Question.9. Two concentric circles are of radii 7 cm and r cm respectively, where r >7. A chord of the larger circle, of length 48 cm, touches the smaller circle. Find the value of r.
Solution.

Question.10. Draw a line segment of length 6 cm. Using compasses and ruler, find a point P on it which divides it in the ratio 3 : 4.
Solution.

SECTION C
Questions number 11 to 20 carry 3 marks each.
Question.11 In Fig. 3, APB and CQD are semi-circles of diameter 7 cm each, while ARC and BSD are semi-circles of diameter 14 cm each.
Find the perimeter of the shaded region. [Use π = 22/7 ]

Or
Find the area of a quadrant of a circle, where the circumference of circle is 44 cm.
[Use π = 22/7 ]
Solution.

Question.12 Two cubes, each of side 4 cm are joined end to end. Find the surface area of the resulting cuboid.
Solution.

Question.13 Find that value(s) of x for which the distance between the points P(x, 4) and Q(9,10) is 10 units.
Solution.

Question.14 A coin is tossed two times. Find the probability of getting at least one head.
Solution.

Question.15 Find the roots of the following quadratic equation: 2 √3 x² – 5x + -√3 = 0
Solution.

Question.16 Find the value of the middle term of the following A.P.: – 6, – 2, 2, …, 58.
Or
Determine the A.P. whose fourth term is 18 and the difference of the ninth term from the fifteenth term is 30.
Solution.

Question.17 In Fig. 4, a triangle ABC is drawn to circumscribe a circle of radius 2 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 4 cm and 3 cm respectively. If area of ΔABC = 21 cm², then find the lengths of sides AB and AC.

Solution.

Question.18 Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60°. Then construct a triangle whose sides are y times the corresponding sides of ΔABC.

Solution.

Question.19 Find the area of the major segment APB, in Fig. 5, of a circle of radius 35 cm and ∠AOB = 90°. [Use π = 22/7 ]

Solution.

Question.20 The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r< 14 cm)
the volume of bucket is 5390 cm3, then find the value of r. [Use π= 22/7 ]
Solution.

SECTION D
Questions number 21 to 31 carry 4 marks each.
Question.21 A survey has been done on 100 people out of which 20 use bicycles, 50 use motorbikes and 30 use cars to travel from one place to another. Find the probability of persons who use bicycles, motorbikes and cars respectively?
Which mode of transport do you think is better and why?
Solution.

Question.22 A game consists of tossing a coin 3 times and noting its outcome each time. Hanif wins if he gets three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.
Or
From the top of a tower 100 m high, a man observes two cars on the opposite sides of the tower with angles of depression 30° and 45° respectively. Find the distance between the cars. [Use √3 = 1.73]
Solution.
The possible out comes on tossing a coin 3 times are,

Question.23 If (3, 3), (6, y), (x, 7) and (5, 6) are the vertices of a parallelogram taken in order, find the values of x and y.
Solution.

Question.24 If two vertices of an’equilateral triangle are (3, 0) and (6, 0), find the third vertex.
Or
Find the value of k, if the points P(5, 4), Q(7, k) and R(9, – 2) are collinear.
Solution.

Question.25 A motor boat whose speed is 20 km/h in still water, takes 1 hour more to go 48 km
upstream than to return downstream to the same spot. Find the speed of the stream.
Or
Find the roots of the equation 1/x+4- 1/x-7 = 11/30,x ≠ -4,7
Solution.

Question.26 If the sum of first 4 terms of an A.P. is 40 and that of first 14 terms is 280, find the sum of its first n terms.
Or
Find the sum of the first 30 positive integers divisible by 6.
Solution.

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

Question.28 In Fig. 6, arcs are drawn by taking vertices A, B and C of an equilateral triangle ABC of side 14 cm as centres to intersect the sides BC, CA and AB at their respective mid-points D, E and F. Find the area of the shaded region.
[Use π = 22/7 and√3 =1.73]

Solution.

Question.29 From a solid cylinder whose height is 15 cm and diameter 16 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. [Take π = 3.14] :
Solution.

Question.30 Two poles of equal heights are standing opposite to each other on either side of the road, which is 100 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles.
Solution.

Question.31 Two pipes running together can fill a cistern in 3  1/13  minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.
Solution.

SET II

Note: Except for the following questions, all the remaining questions have been asked in Set 1.

Question.5 Which term of the progression 4, 9,14,19,… is 109?
Solution.

Q.6 Find a relation between x and y such that the point P(x, y) is equidistant from the points A (2, 5) and B (-3, 7).
Solution.

Question.13 Find the value of k so that the quadratic equation kx (3x – 10) + 25 = 0, has two equal roots.
Solution.

Q.14. A coin is tossed two times. Find the probability of getting not more than one head.
Solution.

Question.23 Draw a triangle ABC with side BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct a
triangle whose sides are 3/5 times the corresponding sides of AABC.
Solution.

Question.24 If P(2, 4) is equidistant from Q(7, 0) and R(x, 9), find the values of x. Also find the distance PQ
Solution.

Question.28 From a point on the ground, the angles of elevation of the bottom and top of a transmission tower fixed at the top of a 10 m high building are 30° and 60° respectively. Find the height of the tower.
Solution.

Question.29 Find the area of the shaded region in Fig. 7, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD, where the length of each side of square is 14 cm.
[Use π = 22/7 ]

Solution.

Question.30 A toy is in the shape of a solid cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 21 cm and 40 cm respectively, and the height of cone is 15 cm, then find the total surface area of the toy. [π = 3.14, be taken]
Solution.

SET III

Note: Except for the following questions, all the remaining questions have been asked in Set I and Set II.

Question.5 Find the roots of 4x²+ 3x + 5 = 0 by the method of completing the squares.
Solution.

Question.6 Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2, 7).
Solution.

Question.7 A coin is tossed two times. Find the probability of getting both heads or both tails.
Solution.

Question.8 Find the value of m so that the quadratic equation mx(5x – 6) + 9 = 0 has two equal roots.
Solution.

Question.23 Draw a triangle PQR such that PQ = 5 cm, ∠P = 120° and PR = 6 cm. Construct another
triangle whose sides are 3/4 times the corresponding sides of APQR.
Solution.

Question.24 Find the point of y-axis which is equidistant from the points (- 5, – 2) and (3, 2).
Solution.

Question. 25 From a solid cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm
and radius 6 cm is hollowed out. Find the total surface area of the remaining solid.
[Use π = 22/7 ]
Solution.

Question.26 The length and breadth of a rectangular piece of paper are 28 cm and 14 cm respectively. A semi-circular portion is cut off from the breadth’s side and a semi-circular portion is added on length’s side, as shown in Fig. 8. Find the area of the shaded
region. [Use π = 22/7 ]

Solution.

Question.31 From the top of a 15 m high building, the angle of elevation of tire top of a cable tower is 60° and the angle of depression of its foot is 30°. Determine the height of the tower.
Solution.

CBSE Previous Year Question Papers CBSE Previous Year Question Papers Class 10 Maths

Download Solved CBSE Sample Papers for Class 10 Maths Paper 1 2019 PDF to understand the pattern of questions asks in the board exam. Know about the important topics and questions to be prepared for CBSE Class 10 Maths board exam and Score More marks. Here we have given Maths Sample Paper for Class 10 Solved Set 1.

Board – Central Board of Secondary Education, cbse.nic.in
Subject – CBSE Class 10 Mathematics
Year of Examination – 2019.

Solved CBSE Sample Papers for Class 10 Maths Paper 1

CBSE Sample Papers

We hope the Solved CBSE Sample Papers for Class 10 Maths Paper 1, help you. If you have any query regarding CBSE Sample Papers for Class 10 Maths Solved Paper 1, drop a comment below and we will get back to you at the earliest.

CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi 2016

Time allowed: 3 hours                                                                                           Maximum marks: 90

GENERAL INSTRUCTIONS:

1. All questions are compulsory.
2. The Question Taper consists of 31 questions divided into four Sections A, B. C. and D.
3. Section A contains 4 questions of 1 mark each. Section B contains 6 questions of 2 marks each, Section C contains 10 questions of 3 marks each and Section D contains 11 questions of 4 marks each.
4.  Use of calculators is not permitted.

 

SET I

SECTION A
Questions number 1 to 4 carry 1 mark each.
Question 1. In Fig. 1, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°. Find ∠PCA.

Answer.

CBSE Sample Papers Class 10 Maths

Question 2. For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms of an A.P.?
Answer.

Question 3. A ladder, leaning against a wall, makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder.
Answer.

Question 4. A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen.
Answer.

SECTION B
Questions number 5 to 10 carry 2 marks each.
Question 5. If -5 is a root of the quadratic equation 2x²+ px – 15 = 0 and the quadratic equation p(x² + x) + k = 0 has equal roots, find the value of k.
Answer.

Question 6. Let P and Q be the points of trisection of the line segment joining the points A (2, -2) and B (-7, 4) such that P is nearer to A. Find the coordinates of P and Q.
Answer.

Question 7. In Fig. 2, a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that: AB + CD = BC + DA.

Answer.

Question 8. Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right angled isosceles triangle.
Answer.

Question 9. The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.
Answer.

Question 10. In Fig. 3, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP = 2r, show that ∠OTS = ∠OST = 30°.

Answer.

SECTION C
Questions number 11 to 20 carry 3 marks each.
Question 11. In Fig. 4, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. (Take π = 3.14)

Answer.

Question 12. In Fig. 5, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are 2.1 m and 3 m respectively and the slant height of conical part is 2.8 m, find the cost of canvas needed to make the tent if the canvas is available at the rate of Rs 500/sq. metre. (Use π = 22/7 )

Answer.

Question 13. If the point P(x, y) is equidistant from the points A (a + b,b – a) and B(a -b,a + b), prove that bx = ay.
Answer.

Question 14. In Fig. 6, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC = 40°. (Use π= 22/7 )

Answer.

Question 15. If the ratio of the sum of first n terms of two A.P’s is (7n + 1) : (4n + 27), find the ratio of their m^th terms.
Answer.

Question 16. Solve for x:

Answer.

Question 17. A conical vessel, with bash radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (Use π= 22/7)
Answer.

Question 18. A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 3 (5/9) cm. Find the diameter of the cylindrical vessel.
Answer.

Question 19. A man standing on the deck of a ship, which is 10 m above water level, observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of hill as 30°. Find the distance of the hill from the ship and the height of the hill.
Answer.

Question 20. Three different coins are tossed together. Find the probability of getting (i) exactly two heads (ii) at least two heads (ii) at least two tails.
Answer.

SECTION D
Questions number 21 to 31 carry 4 marks each.
Question 21. Due to heavy floods in a State, thousands were rendered homeless. 50 schools collectively offered to the State Government to provide place and the canvas for 1,500 tents to be fixed by the Government and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs Rs 120 per sq. m, find the amount shared by each school to set up the tents. What value is generated by the above problem? (Use π= 22/7)
Answer.


Value: By helping the flood victims the schools are showing concern for humanity.

Question 22. Prove that the lengths of the tangents drawn from an external point to a circle are equal.
Answer. Theorem. See Q. 27, 2011 (1 Delhi).

Question 23. Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60° to each other.
Answer. See Q. 13, 2013 (I O.D.).

Question 24. In Fig. 7, two equal circles, with centres O and O’, touch each other at X. OO’ produced meets the circle with centre O’ at A. AC is tangent to the circle with centre O, at the point C. O’D is perpendicular to AC. Find the value of DO’/CO.

Answer. Given: two equal circles, with centres O and O’, touch each other at point X. OO’ is produced to meet the circle with centre O’ at A. AC is tangent to the circle with centre O, at the point C. O’D is perpendicular to AC.

Question 25. Solve for x:

Answer.

Question 26. The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60°. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of tower is 45°. Find the height of the tower PQ and the distance PX. (Use √3= 1.73)
Answer.

Question 27. The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses preceding the house numbered X is equal to sum of the numbers of houses following X.
Answer.

Question 28. In Fig. 8, the vertices of ∆ABC are A(4, 6), B(l, 5) and C(7, 2). A line segment DE is drawn to intersect the sides AB and AC at D and E respectively such that AD/AB= AE/AC= 1/3 .Calculate the area of ∆ADE and Calculate the area compare it with area of ∆ABC.

Answer.

Question 29. A number x is selected at random from the numbers 1, 2, 3 and 4. Another number y is selected at random from the numbers 1, 4, 9 and 16. Find the probability that product of x and y is less than 16.
Answer.

Question 30. In Fig. 9, is shown a sector OAP of a circle with centre O, containing ∠θ. AB is perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is r :


Answer.

Question 31. A motor boat whose speed is 24 km/h in still water takes 1 hr more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream.
Answer.

SET II

Note:Except for the following questions, all the remaining questions have been asked in Set-I.
Question 10.Solve for x:

Answer.

Question 18. The digits of a positive number of three digits are in A.P. and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number.
Answer.

Question 19. If the roots of the quadratic equation (a – b)x² + (b – c)x + (c – a) = 0 are equal, prove that 2a = b + c.
Answer.

Question 20. From a pack of 52 playing cards, Jacks, Queens and Kings of red colour are removed. From the remaining, a card is drawn at random. Find the probability that drawn card is: (i) a black King (ii) a card of red colour (iii) a card of black colour
Answer.

Question 28. Draw an isosceles ∆ABC in which BC = 5.5 cm and altitude AL = 3 cm. Then construct another triangle whose sides are 3/4 of the corresponding sides of ∆ABC.
Answer.

Question 29. Prove that the tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.
Answer. Theorem. See Q. 25, 2011 (I Outside Delhi).

Question 30. As observed from the top of a light house, 100 m high above sea level, the angles of depression of a ship, sailing directly towards it, changes from 30° to 60°. Find the distance travelled by the ship during the period of observation. (Use √3 = 1.73)
Answer.

Question 31. A rectangular park is to be designed whose breadth is 3 m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude 12 m. Find the length and breadth of the rectangular park.
Answer.

SET III

Note: Except for the following questions, all the remaining questions have been asked in Set-I and Set II.
Question 10. Solve for x:

Answer.

Question 18. There are 100 cards in a bag on which numbers from 1 to 100 are written. A card is taken out from the bag at random. Find the probability that the number on the selected card (i) is divisible by 9 and is a perfect square (ii) is a prime number greater than 80.
Answer.

Question 19. Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Find the numbers.
Answer.

Question 20. The sums of first n terms of three arithmetic progressions are S₁, S₂ and S₃ respectively. The first term of each A.P. is 1 and their common differences are 1, 2 and 3 respectively. Prove that S₁+ S₃ = 2S₂.
Answer.

Question 28. Two pipes running together can fill a tank in 11 (1/9) minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
Answer.

Question 29. From a point on the ground, the angle of elevation of the top of a tower is observed to be 60°. From a point 40 m vertically above the first point of observation, the angle of elevation of the top of the tower is 30°. Find the height of the tower and its horizontal distance from the point of observation.
Answer.

Question 30. Draw a triangle with sides 5 cm, 6 cm and 7 cm. Then draw another triangle whose sides are 4/5 of the corresponding sides of first triangle.
Answer.

Question 31. A number x is selected at random from the numbers 1, 4, 9, 16 and another number y is selected at random from the numbers 1, 2, 3, 4. Find the probability that the value of xy is more than 16.
Answer.

CBSE Previous Year Question Papers CBSE Previous Year Question Papers Class 10 Maths