Category: CBSE

CBSE Previous Year Question Papers Class 10 Maths SA2 Delhi – 2014

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 and PR are two tangents to a circle with centre O. If ∠QPR = 46°, then calculate ∠QOR.

Solution.

CBSE Sample Papers Class 10 Maths

Question. 2 If two different dice are rolled together, calculate the probability of getting an even number on both dice.
Solution.

Question.3 If the points A(x, 2), B(-3, -4) and C(7, -5) are collinear, then find the value of x.
Solution.

Question.4 Find the number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm.
Solution.

SECTION B
Questions number 5 to 10 carry 2 marks each.
Question.5 Solve the quadratic equation 2x²+ ax – a² = 0 for x.
Solution.

Question.6 The first and the last terms of an AP are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.
Solution.

Question.7 Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.
Solution.

Question.8 If from an external point P of a circle with centre O, two tangents PQ and PR are drawn such that ∠QPR = 120°, prove that 2PQ = PO.
Solution.

Question.9 Rahim tosses two different coins simultaneously. Find the probability of getting at least one tail.
Solution.

Question.10 In Fig. 2, a square OABC is inscribed in a quadrant OPBQ of a cirlce. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)

Solution.

SECTION C
Questions number 11 to 20 carry 3 marks each.
Question.11 Solve the equation

Solution.

Question.12 If the seventh term of an AP is 1/2 and its ninth term is 1/7 find its 63^rd term.
Solution.

Question.13 Draw a right triangle ABC in which AB = 6 cm, BC = 8 cm and ∠B = 90°. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D. Construct tangents from A to this circle.
Solution.

Question.14 If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also find the length of AB.
Solution.

Question.15 Two ships are there in the sea on either side of a light house in such a way that the ships and the light house are in the same straight line. The angles of depression of two ships as observed from the top of the light house are 60° and 45°. If the height of the light house is 200 m, find the distance between the two ships. [Use √3 =1.73]
Solution.

Question.16 If the points A(-2,1), B(a, b) and C(4, -1) are collinear and a – b = 1, find the values of a and b.
Solution.

Question.17 In Fig. 3, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region. [Use π = 3.14 and √3 = 1.73]

Solution.

Question.18 In Fig. 4, PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region. [Use π = 3.14]

Solution.

Question.19 A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km per hour, in how much time will the tank be filled completely?
Solution.

Question.20 A solid metallic right circular cone 20 cm high and whose vertical angle is 60°, is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1/2 cm, find the length of the wire.
Solution.

SECTION D
Questions number 21 to 31 carry 4 marks each.
Question.21 The difference of two natural numbers is 5 and the difference of their reciprocals is1/10 Find the numbers.
Solution.

Question.22 Prove that the length of the tangents drawn from an external point to a circle are equal.
Solution.

Question.23 The angles of elevation and depression of the top and the bottom of a tower from the top of a building, 60 m high, are 30° and 60° respectively. Find the difference between the heights of the building and the tower and the distance between them.
Solution.

Question.24 A bag contains cards numbered from 1 to 49. A card is drawn from the bag at random, after mixing the cards thoroughly. Find the probability that the number on the drawn card is:
(i) an odd number
(ii) a multiple of 5
(iii)a perfect square
(iv) an even prime number
Solution.

Question.25 Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, -3). Also find the value of x.
Solution.

Question.26 Find the values of k for which the quadratic equation (k + 4)x² + (k + l)x + 1 = 0 has equal roots. Also find these roots.
Solution.

Question.27 In an AP of 50 terms, the sum of first 10 terms is 210 and the sum of its last 15 terms is 2565. Find the AP.
Solution.

Question.28 Prove that a parallelogram circumscribing a circle is a rhombus.
Solution.

Question.29 Sushant has a vessel, of the form of an inverted cone, open at the top, of height 11 cm and radius of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm
are put in the vessel due to which 2/5th of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds.
What value has been shown by Sushant?
Solution.

Question.30 From a solid cylinder of height 2.8 cm and diameter 4.2 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= 22/7]
Solution.

Question.31 A peacock is sitting on the top of a pillar, which is 9 m high. From a point 27 m away from the bottom of the pillar, a snake is xoming to its hole at the base of the pillar. Seeing the snake the peacock pounces on it. If their speeds are equal, at what distance from the hole is the snake caught?
Solution.

SET II

Note: Except for the following questions, all the remaining questions have been asked in Set I.
Question.10 The first and last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.
Solution.

Question.18 Solve the equation

Solution.

Question.19 Points A(-l, y) and B(5, 7) lie on a circle with centre 0(2, -3y). Find the values of y. Hence find the radius of the circle.
Solution.

Question.20 If the points P(-3,9), Q(a, b) and R(4, -5) are collinear and a + b – 1, find the values of a and b.
Solution.

Question.27 The difference of two natural numbers is 3 and the difference of their reciprocals is
Find the numbers.
Solution.

Question.28 Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Solution.

Question.29. All the black face cards are removed from a pack of 52 playing cards. The remaining cards are well shuffled and then a card is drawn at random. Find the probability of getting a:
(i) face card
(ii) red card
(iii) black card
(iv) king
Solution.

Question.30 Find the values of k for which the quadratic equation (3k + l)x + 2(k + l)x + 1 = 0 has equal roots. Also find the roots.
Solution.

SET III

Note: Except for the following questions, all the remaining questions have been asked in Set I and Set II.
Question.10 The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
Solution.

Question.18 If the points A(-l, -4), B(b, c) and C(5, -1) are collinear and 2b + c = 4, find the values of b and c.
Solution.

Question.19 If the point P(2, 2) is equidistant from the points A(-2, k) and B(-2k, -3), find k. Also find the length of AP.
Solution.

Question.20 Solve the equation

Solution.

Question.27 Find the value of p for which the quadratic equation (2p + l) x²– (7p + 2) x + (7p – 3) = 0 has equal roots. Also find these roots.
Solution.

Question.28 Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is :
(i) an odd number
(ii) a perfect square number
(iii) divisible by 5
(iv) a prime number less than 20
Solution.

Question.29 Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.
Solution.

Question.30 The difference of two natural numbers is 5 and the difference of their reciprocals is 5/14. Find the numbers.
Solution.

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

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

                                                                      Section A

2.Find the number of three-digit natural numbers which are divisible by 11.

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

3.Find the distance between the points (o cos 35°, 0) and (0, a cos 55°).

4.A square is inscribed in a circle. What is the ratio of the areas of the circle and the square?

                                                                     Section B

5.A polygon of n sides has n(n-3)/2 diagonals. How many sides has a polygon with 54 diagonals?

6.The sum of first six terms of an AP is 42. The ratio of its 10th term to its 30th term is 1 : 3. Calculate the first term of the AP.

7.If d1 , d₂ (d₂ > d1) be the diameters of two concentric circles and c be the length of a chord of a circle which is tangent to the other circle, prove that d2² = c² + d1².

8.4 face cards of black colour are lost from the pack of 52 playing cards. The remaining cards are well-shuffled and then a card is drawn from them. Find the probability the drawn card is a face card of red colour.

9.Find the area of the largest triangle that can be inscribed in semicircle of radius 14 cm.

10.Volumes of two cubes are in the ratio 8 : 125. What is the ratio of their surface areas?

                                                                                Section C

11.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.

13.Show that the sum of first 20 even natural numbers is 21/20 times the sum of first 20 odd natural numbers.

14.Let ABC be a right triangle in which AB = 3 cm, BC = 4 cm and B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

15.Two dice are rolled once. Find two probability of getting such numbers on two dice, whose product is a prime number.

16.At a fete, cards bearing numbers 1 to 400, one on each card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card bears a number which is a perfect square of an even number, the player wins prize.       ‘
(i) What is the probability that the first player wins a prize?
(ii) The second player wins prize, if the first has not won

17.Point R divides the line segment joining the points P(3, 2) and Q(6, -7) such that PR/PQ = 1/3. If R lies on the line 3x – 4y + k = 0, find the value of k.

18.The opposite angular points of a square are (1, 0) and (4, 1). Find the coordinates of remaining two vertices of the square.

19.A round table cover has six equal designs as shown in figure. If the radius of the cover is 56 cm, find the cost of making the design at the rate of Rs 5 per cm².(use root 3=1.7, pi=22/7)

20.The total surface area of solid cylinder is 924 cm². If the curved surface area is — of its~total surface area,find its radius and height. (Use pi=22/7)

 Section D
21.One-fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.

22.If /nth term of an AP is 1/n and nth term is 1/m, show that the sum of mn terms is 1/2(mn + 1).

23.A quadrilateral ABCD is drawn so that D = 90°, BC = 38 cm and CD = 25 cm. A circle is inscribed in the quadrilateral and it touches the sides AB, BC, CD and DA at P, Q, R and S respectively. If BP = 27 cm, find the radius of the inscribed circle.

24.In figure, O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle
at E, find the length of AB.

25.Two circles with centres O and O’ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ.

26.The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud from the surface of the lake.

28.If P and Q are two points whose coordinates are (at², 2at) and((a/t²),(-2a/t)) respectively and S is the point(a,0).show that 1/SP+1/SQ is independent of t.

29.For the inaugration of an Eco-club to the school, badges were given to teachers. Seema made these badges in the shape of an equilateral triangle with a circle of radius root 3 cm inscribed in it as shown in the figure [pi = 3.14]
(a)Find the area of the shaded portion.
(b)Which value is depicted?

30. A godown building is in the form as shown in the figure.
The vertical cross section parallel to the width side of the building is a rectangle of dimensions 7 m x 3 m, mounted by semicircle of radius 3.5 m. The inner measurements of the cuboidal portion of the building are 10 m x 7 m x 3 m. Find the interior surface excluding the floor.

31. An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar, if one cubic cm of iron weighs 10 g. [Use pi = 22/7]

Answers

                                                                   Section A

Ans.

2.Find the number of three-digit natural numbers which are divisible by 11.
Ans.

3.Find the distance between the points (o cos 35°, 0) and (0, a cos 55°).
Ans.

4.A square is inscribed in a circle. What is the ratio of the areas of the circle and the square?
Ans.

                                                                     Section B

5.A polygon of n sides has n(n-3)/2 diagonals. How many sides has a polygon with 54 diagonals?
Ans.

6.The sum of first six terms of an AP is 42. The ratio of its 10th term to its 30th term is 1 : 3. Calculate the first term of the AP.
Ans.

7.If d1 , d₂ (d₂ > d1) be the diameters of two concentric circles and c be the length of a chord of a circle which is tangent to the other circle, prove that d2² = c² + d1².
Ans.

8.4 face cards of black colour are lost from the pack of 52 playing cards. The remaining cards are well-shuffled and then a card is drawn from them. Find the probability the drawn card is a face card of red colour.
Ans.

9.Find the area of the largest triangle that can be inscribed in semicircle of radius 14 cm.
Ans.

10.Volumes of two cubes are in the ratio 8 : 125. What is the ratio of their surface areas?
Ans.

                                                                                Section C

11.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.
Ans.

Ans.

13.Show that the sum of first 20 even natural numbers is 21/20 times the sum of first 20 odd natural numbers.
Ans.

14.Let ABC be a right triangle in which AB = 3 cm, BC = 4 cm and B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.
Ans.

15.Two dice are rolled once. Find two probability of getting such numbers on two dice, whose product is a prime number.
Ans.

16.At a fete, cards bearing numbers 1 to 400, one on each card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card bears a number which is a perfect square of an even number, the player wins prize.       ‘
(i) What is the probability that the first player wins a prize?
(ii) The second player wins prize, if the first has not won
Ans.

17.Point R divides the line segment joining the points P(3, 2) and Q(6, -7) such that PR/PQ = 1/3. If R lies on the line 3x – 4y + k = 0, find the value of k.
Ans.

18.The opposite angular points of a square are (1, 0) and (4, 1). Find the coordinates of remaining two vertices of the square.
Ans.

19.A round table cover has six equal designs as shown in figure. If the radius of the cover is 56 cm, find the cost of making the design at the rate of Rs 5 per cm².(use root 3=1.7, pi=22/7)

Ans.

20.The total surface area of solid cylinder is 924 cm². If the curved surface area is 2/3 of it’s total surface area,find its radius and height. (Use pi=22/7)
Ans.

                                                                                  Section D
21.One-fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels.
Ans.

22.If /nth term of an AP is 1/n and nth term is 1/m, show that the sum of mn terms is 1/2(mn + 1).
Ans.

23.A quadrilateral ABCD is drawn so that D = 90°, BC = 38 cm and CD = 25 cm. A circle is inscribed in the quadrilateral and it touches the sides AB, BC, CD and DA at P, Q, R and S respectively. If BP = 27 cm, find the radius of the inscribed circle.

Ans.

24.In figure, O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle
at E, find the length of AB.

Ans.

25.Two circles with centres O and O’ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ.
Ans.

26.The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud from the surface of the lake
Ans.

Ans.

28.If P and Q are two points whose coordinates are (at², 2at) and((a/t²),(-2a/t)) respectively and S is the point(a,0).show that 1/SP+1/SQ is independent of t.
Ans.

29.For the inaugration of an Eco-club to the school, badges were given to teachers. Seema made these badges in the shape of an equilateral triangle with a circle of radius root 3 cm inscribed in it as shown in the figure [pi = 3.14]
(a)Find the area of the shaded portion.
(b)Which value is depicted?

Ans.

30. A godown building is in the form as shown in the figure.
The vertical cross section parallel to the width side of the building is a rectangle of dimensions 7 m x 3 m, mounted by semicircle of radius 3.5 m. The inner measurements of the cuboidal portion of the building are 10 m x 7 m x 3 m. Find the interior surface excluding the floor.

Ans.

31. An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar, if one cubic cm of iron weighs 10 g. [Use pi = 22/7]
Ans.

(Download Questions PDF)

CBSE Previous Year Question Papers Class 10 Maths SA2 Outside Delhi 2015

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. If the quadratic equation px²– 2-√5 px + 15 = 0 has two equal roots, then find the value of p.
Answer.

CBSE Sample Papers Class 10 Maths

Question.2. In Figure 1, a tower AB is 20 m high and BC, its shadow on the ground, is 20-√3 m long. Find the Sun’s altitude.

Answer.

Question.3. Two different dices are tossed together. Find the probability that the product of the two numbers on the top of the dice is 6.
Answer.

Question.4. In Figure 2, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT = 60°, find ∠PRQ.

Answer.

SECTION B
Questions number 5 to 10 carry 2 marks each.
Question.5. In Figure 3, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120°, then prove that OR = PR + RQ.

Answer.

Question.6. In Figure 4, a triangle ABC is drawn to circumscribe a circle of radius 3 cm, such that the segments BD and DC are respectively of lengths 6 cm and 9 cm. If the area of ∆ABC is 54 cm², then find the lengths of sides AB and AC.

Answer.

Question.7. Solve the following quadratic equation for x:

Answer.

Question.8. In an AP, if S₅+ S₇ = 167 and S₁₀ = 235, then find the AP, where Sn denotes the sum of its first n terms.
Answer.

Question.9. The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right triangle, right-angled at B. Find the value of p.
Answer.

Question.10. Find the relation between x and y if the points A(x, y), B(-5, 7) and C(-4, 5) are collinear.
Answer.

SECTION C
Questions number 11 to 20 carry 3 marks each.
Question.11. The 14th term of an AP is twice its 8th term. If its 6th term is -8, then find the sum of its first 20 terms.
Answer.

Question.12. Solve for x:

Answer.

Question.13. The angle of elevation of an aeroplane from a point A on the ground is 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the aeroplane is flying at a constant height of 1500 √3 m, find the speed of the plane in km/hr.
Answer.

Question.14. If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = 3/5 AB, where P lies on the line segment AB.
Answer.

Question.15. The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is 1/4. The probability of selecting a blue ball at random from the same jar is 1/3 . If the jar contains 10 orange balls, find the total number of balls in the jar.
Answer.

Question.16. Find the area of the minor segment of a circle of radius 14 cm, when its central angle is 60°. Also find the area of the corresponding major segment. [Use π = 22/7 ]
Answer.

Question.17. Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m, and the canvas to be used costs Rs 100 per sq. m, find the amount, the associations will have to pay. [Use π = 22/7 ] What values are shown by these associations?
Answer.


Values: Helping the flood victims and showing concern for humanity.

Question.18. A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of the each bottle, if 10% liquid is wasted in this transfer.
Answer.

Question.19. A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs 5 per 100 sq. cm. [Use π= 3.14]
Answer.

Question.20. 504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area. [Use π = 22/7 ]
Answer.

SECTION D
Questions number 21 to 31 carry 4 marks each.
Question.21. The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.
Answer.

Question.22. Find the 60th term of the AP 8,10,12,…, if it has a total of 60 terms and hence find the sum of its last 10 terms.
Answer.

Question.23. A train travels at a certain average speed for a distance of 54 km and then travels a . distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?
Answer.

Question.24. Prove that the lengths of the tangents drawn from an external point to a circle are equal.
Answer. See Q. 27,2012 (I Outside Delhi).

Question.25. Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.
Answer.

Question.26. Construct a ∆ABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°. Construct another ∆AB’C’ similar to ∆ABC with base AB’ = 8 cm.
Answer.

Question.27. At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30°. The angle of depression of the reflection of the cloud in the lake, at A is 60°. Find the distance of the cloud from A.
Answer.

Question.28. A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is
(i) a card of spade or an ace. (ii) a black king.
(iii) neither a jack nor a king. (iv) either a king or a queen.
Answer.

Question.29. Find the values of k so. that the area of the triangle with vertices (1, -1), (-4, 2k) and (-k, -5) is 24 sq. units.
Answer.

Question.30. In Figure 5, PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flower beds (shaded parts).

Answer.

Question.31. From each end of a solid metal cylinder, metal was scooped out in hemispherical form of same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm. The rest of the cylinder is melted and converted into a cylindrical wire of 1.4 cm thickness. Find the length of the wire. [Use π = 22/7 ]
Answer.

SET II

Note: Except for the following questions, all the remaining questions have been asked in Set-I.
Question.10. If A(4, 3), B(-l, y) and C(3, 4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.
Answer.

Question.18. All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if the area of the circle is 1256 cm2. [Use π= 3.14]
Answer.

Question.19. Solve for x:

Answer.

Question.20. The 16th term of an AP is five times its third term. If its 10th term is 41, then find the sum of its first fifteen terms.
Answer.

Question.28. A bus travels at a certain average speed for a distance of 75 km and then travels a distance of 90 km at an average speed of 10 km/h more than the first speed. If it takes 3 hours to complete the total journey, find its first speed.
Answer.

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

Question.30. Construct a right triangle ABC with AB = 6 cm, BC = 8 cm and ∠B = 90°. Draw BD, the perpendicular from B on AC. Draw the circle through B, C and D and construct the tangents from A to this circle.
Answer. See Q. 13, 2014 (I Delhi).

Question.31. Find the values of k so that the area of the triangle with vertices (k + 1, 1), (4, -3) and (7, -k) is 6 sq. units.
Answer.

SET III

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

Answer.

Question.18. The 13^th term of an AP is four times its 3^rd term. If its fifth term is 16, then find the sum of its first ten terms.
Answer.

Question.19. Find the coordinates of a point P on the line segment joining A(1, 2) and B(6, 7) such that AP=2/5 AB.
Answer.

Question.20. A bag contains, white, black and red balls only. A ball is drawn at random from the bag. If the probability of getting a white ball is 3/10 and that of a black ball is 2/5, then find the probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.
Answer.

Question.28. A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.
Answer.

Question.29. An Arithmetic Progressions, 12,19,… has 50 terms. Find its last term. Hence find the sum of its last 15 terms.
Answer.

Question.30. Construct a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60°. Now construct another triangle whose sides are 5/7 times the corresponding sides of ∆ABC.
Answer. See Q. 18, 2011 (I Delhi).

Question.31. Find the values of k for which the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k – 1, 5k) are collinear.
Answer.

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

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set

                                                               Section A

1.Simplify the following equation and identify whether this equation is quadratic or not:

(x – 2) (x + 2)=12.

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

3. Find the distance between the points A(8, – 2) and B(3, – 6).

4.Find the area of a sector of a circle when the radius of the circle is 21 cm and angle of the sector is 60°.

(Take = 22/7) 

                                                                            Section B

5.Find the roots of the following quadratic equation by using the method of factorization:

6X² – 13x -5 = 0.

6. How many terms of the AP 9, 17, 25, ….    must be taken to give a sum of 636?

7. The length of a tangent from a point A,    at a distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

 8. A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the    probability that    she takes out

(i) an orange flavoured candy?    (ii) a lemon flavoured candy?

9. A paper is in form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A semi-circular portion with BC as diameter   is cut  off. Find the area of    the    remaining    part.    (Take  =  22/7)

10. Two cubes each    of side 10 cm are joined end    to    end. Find    the    surface    area    of the resulting rectangular shaped solid.

                                                                             Section C

11.    Solve for x: (1/x-2)+(2/x-1)=6/x   (x not equal to 0,1,2)

12.  The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.

13. Determine the value of p for which the quadratic equation px² – 24x + 16 = 0 has equal roots.

14.Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

15. One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting

(i) a king of red colour (ii) a face card    (iii) the queen of diamonds

16. A lot consists of 220 ball pens out of which 22 are defective. Sunita will buy a pen if it is good but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that

(i) she will buy it?    (ii) she will not buy it?

17. Find the area of the triangle whose vertices are (1, – 1), (- 4, 6) and (3, – 5).

18.Find the value of x for which the distance between the points P(2, – 3) and Q(x, 5) is 10 units.

19.From a circular sheet of 10 cm radius, a disc of radius 3 cm is cut out and the portion of the sheet left behind is painted at the rate of ? 0.35 per cm². Find the cost of painting the sheet. (Take n = -~)

20.The radii of the ends of a frustum of a right circular cone are 5 cm and 8 cm and its lateral height

(slant height) is 5 cm. Find the volume of the frustum. (Take = 22/7)

21.The perimeter of a rectangular piece of land is 130 m and its area is 1000 m². Determine its dimensions.

22.A sum of ? 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ? 20 less than its preceding prize, find the value of each of the prizes. What value is reflected by giving cash prizes to students?

23.Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.

24.Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

25.The tangent at any point of a circle is perpendicular to the radius through the point of contact. Prove it.

26.A ladder is placed against a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 8 m away from the foot of the wall and the ladder is making an angle of 30° with the level of the ground. Determine the height of the wall. (Take  = 1.732)

27.A vertical tower stands on the plane ground and is surmounted by a flagstaff of height 5 m. From a point on the ground, the angle of elevation of the bottom of the flagstaff is 45° and that of the top of the flagstaff is 60°. Find the height of the tower. (Take  = 1.732)

28.Prove that the points A(- 3, 0), B(l, – 3) and C(4, 1) are the vertices of an isosceles right-angled triangle.

29.From each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in fig. Find the area of the remaining portion of the  square.
(Take = 22/7)

30.A solid is in the form of a right circular cylinder mounted on a solid hemisphere of radius  14 cm. The radius of the base of the cylindrical part is 14 cm and the vertical height of the    complete solid is 28 cm. Find the volume of the solid. (Take = 22/7)

31.A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap? (Take  = 22/7)

Answers

                                                          Section A

1.Simplify the following equation and identify whether this equation is quadratic or not:
(x – 2) (x + 2)=12.
Ans.

2.Write the AP with given first term a and common difference d for the following: a = 17,
d = – 6.
Ans.

3. Find the distance between the points A(8, – 2) and B(3, – 6).
Ans.

4.Find the area of a sector of a circle when the radius of the circle is 21 cm and angle of the sector is 60°.
(Take = 22/7) 
Ans.

                                                                            Section B

5.Find the roots of the following quadratic equation by using the method of factorization:
6X² – 13x -5 = 0.
Ans.

6. How many terms of the AP 9, 17, 25, ….    must be taken to give a sum of 636?
Ans.

7. The length of a tangent from a point A,    at a distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
Ans.

 8. A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the    probability that    she takes out
(i) an orange flavoured candy?    (ii) a lemon flavoured candy?
Ans.

9. A paper is in form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A semi-circular portion with BC as diameter   is cut  off. Find the area of    the    remaining    part.    (Take  =  22/7)
Ans.

10. Two cubes each    of side 10 cm are joined end    to    end. Find    the    surface    area    of the resulting rectangular shaped solid.
Ans.

                                                                             Section C

11.    Solve for x: (1/x-2)+(2/x-1)=6/x   (x not equal to 0,1,2)
Ans.

12.  The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Ans.

13. Determine the value of p for which the quadratic equation px² – 24x + 16 = 0 has equal roots.
Ans.

14.Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
Ans.

15. One card is drawn from a well shuffled deck of 52 cards. Find the probability of getting
(i) a king of red colour (ii) a face card    (iii) the queen of diamonds
Ans.

16. A lot consists of 220 ball pens out of which 22 are defective. Sunita will buy a pen if it is good but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that
(i) she will buy it?    (ii) she will not buy it?
Ans.

17. Find the area of the triangle whose vertices are (1, – 1), (- 4, 6) and (3, – 5).
Ans.

18.Find the value of x for which the distance between the points P(2, – 3) and Q(x, 5) is 10 units.
Ans.

19.From a circular sheet of 10 cm radius, a disc of radius 3 cm is cut out and the portion of the sheet left behind is painted at the rate of ? 0.35 per cm². Find the cost of painting the sheet. (Take n = 22/7)
Ans.

20.The radii of the ends of a frustum of a right circular cone are 5 cm and 8 cm and its lateral height (slant height) is 5 cm. Find the volume of the frustum. (Take = 22/7)
Ans.

21.The perimeter of a rectangular piece of land is 130 m and its area is 1000 m². Determine its dimensions.
Ans.

22.A sum of ? 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ? 20 less than its preceding prize, find the value of each of the prizes. What value is reflected by giving cash prizes to students?
Ans.

23.Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.
Ans.

24.Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Ans.

25.The tangent at any point of a circle is perpendicular to the radius through the point of contact. Prove it.
Ans.

26.A ladder is placed against a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 8 m away from the foot of the wall and the ladder is making an angle of 30° with the level of the ground. Determine the height of the wall. (Take  = 1.732)
Ans.

27.A vertical tower stands on the plane ground and is surmounted by a flagstaff of height 5 m. From a point on the ground, the angle of elevation of the bottom of the flagstaff is 45° and that of the top of the flagstaff is 60°. Find the height of the tower. (Take  = 1.732)
Ans.

28.Prove that the points A(- 3, 0), B(l, – 3) and C(4, 1) are the vertices of an isosceles right-angled triangle.
Ans.

29.From each corner of a square of side 4 cm, a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in fig. Find the area of the remaining portion of the  square.
(Take = 22/7)

Ans.

30.A solid is in the form of a right circular cylinder mounted on a solid hemisphere of radius  14 cm. The radius of the base of the cylindrical part is 14 cm and the vertical height of the    complete solid is 28 cm. Find the volume of the solid. (Take = 22/7)
Ans.

31.A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap? (Take  = 22/7)
Ans.

Download Solved CBSE Sample Papers for Class 10 Maths Set 4 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 4.

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

You can also Download NCERT Solutions for Class 10 Maths to help you to revise complete Syllabus and score more marks in your examinations.

Solved CBSE Sample Papers for Class 10 Maths Set 4

CBSE Sample Papers

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