Category: CBSE

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 9

                                                               Section A

1.If 2 is a root of the equation x² + bx + 12 = 0 and the equation has equal roots, find the value of b.

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

4.If the perimeter and the area of a circle are numerically equal, then find the radius of the circle.

                                                                 Section B

5.If sin a and cos a are the roots of the equation ax² + bx + c = 0, then prove that a² + 2ac = b².

6.Determine k so that 3k – 3, 2k² – 5k + 7 and Ak + 2 are the three consecutive terms of an AP.

7.In figure, two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that triangle APB = 2 triangle OAB.

8.Ace, Jack and queen of diamonds are removed from a deck of 52 playing cards. One card is selected from the reamaining cards. Find the probability of getting a card of diamond.

9.In given figure, PQR is a triangle right angled at P, with PQ = 21 cm and PR = 42 cm with the vertices P, Q and R as centres, arcs are drawn each of radius 10 cm. Find the area of the shaded region. (Use pi = 3.14)

10.A cone and a sphere have equal radii and equal volume. What is the ratio of the diameter of the sphere to the height of the cone?
  Section C
11.At t minutes past 2 p.m. the time needed by the minutes hand of a clock to show 3 p.m. was found to be 3 minutes less than t²/4 minutes. Find t.

12.Solve for x :6X2 – 6(a + b)x + (4/3 a²+10/3ab+4/3 b²)= 0

13.The sum of n terms of an AP whose first term is 6 and common difference is 40 is equal to the sum of 2n terms of another AP whose first term is 40 and common difference is 6. Find n.

14.Draw a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of 45°.

15.Cards bearing numbers 1, 4, 7, 10,….58 are kept in a bag. A card is drawn at random from the bag. Find
the probability of getting a card bearing
(i)a prime number less than 18.
(ii)a number divisible by 4.

16.Six cards – ace, jack, queen, king, ten and nine of spade are well shuffled with their face downwards. One card is then picked up at random.
(i) What is the probability that the card is an ace?
(ii) If the ace is drawn and put aside, what is the probability that the second card picked up is
(a) a jack,(b) an ace.
.
17.If P is a point lying on the line segment QR, joining Q(-l, -1) and R(4, -1) such that PQ = 3/7 QR, then find the coordinates of P.

18.For what value of k, (k > 0) the area of triangle with vertices (k, 1), (3k, 1) and (2, 4) is 6 sq. units.

19.A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 154 cm. If bucket ascends in 2 minutes 56 seconds with a uniform speed of 2.2 m/s, then calculate the number of
complete revolutions the wheel makes in raising the bucket. (Use pi = 22/7)

20.A solid cone of base radius 30 cm is cut into two parts through the mid-point of its height by a plane parallel to its base. Find the ratio of the volumes of the two parts of the cone.

                                                                 Section D
21.A man bought a certain number of toys for Rs 180; he kept one for his own use and sold the rest for one rupee each more than he gave for them, besides getting his own toy for nothing he made a profit of Rs 10. Find the number of toys.

22.A ladder has rungs 50 cm apart. The rungs decrease uniformly in length from 90 cm at the bottom to 50 cm at the top. If top and bottom rungs are 5 m apart, what is the length of the wood required for the rungs?

23.ABC is a right-angled triangle, right angled at A. A circle is inscribed in it. The lengths of two sides containing the right angle are 24 cm and 10 cm. Find the radius of the incircle.

24.In figure the common tangent, AB and CD to two circles with centres O and O’ intersect at E.Prove that the points O, E and O’ are collinear.

25.In the given figure, the diameters of two wheels have measures 4 cm and 2 cm. Determine the lengths of the belts AD and BC that pass around the wheels if it is given that belts cross each other at right angles.

26.A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed, 6 seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

27. A fire in a building B is reported on telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of 60° to the road and Q observes that it is at an angle of 45° to the road. ‘
(a) Which station should send its team and how much will this team have to travel?
(b) What according to you, are the values displayed by the teams at fire stations P and Q?

28.The opposite angular points of a square are (2, 0) and (5, 1). Find the remaining points.

29.In the given figure, three circles of radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius R cm. Find the value of R and the area of the shaded region.

30.The area of the base of a cone is 770 cm2 and the curved surface area is 814 cm2. Find the volume of the cone.

31.An agricultural field is in the form of a rectangle of length 20 m and width 14 m. A pit 6 m long, 3 m wide and 2.5 m deep is dug in the corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field. Find the extent to which the level of the field has been raised.

Answers

                                                                Section A

1.If 2 is a root of the equation x² + bx + 12 = 0 and the equation has equal roots, find the value of b.
Ans.

Ans.

Ans.

4.If the perimeter and the area of a circle are numerically equal, then find the radius of the circle.
Ans.

                                                                 Section B

5.If sin a and cos a are the roots of the equation ax² + bx + c = 0, then prove that a² + 2ac = b².
Ans.

6.Determine k so that 3k – 3, 2k² – 5k + 7 and Ak + 2 are the three consecutive terms of an AP.
Ans.

7.In figure, two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that triangle APB = 2 triangle OAB.

Ans.

8.Ace, Jack and queen of diamonds are removed from a deck of 52 playing cards. One card is selected from the reamaining cards. Find the probability of getting a card of diamond.
Ans.

9.In given figure, PQR is a triangle right angled at P, with PQ = 21 cm and PR = 42 cm with the vertices P, Q and R as centres, arcs are drawn each of radius 10 cm. Find the area of the shaded region. (Use pi = 3.14)

Ans.

10.A cone and a sphere have equal radii and equal volume. What is the ratio of the diameter of the sphere to the height of the cone?
Ans.

                                                                              Section C
11.At t minutes past 2 p.m. the time needed by the minutes hand of a clock to show 3 p.m. was found to be 3 minutes less than t²/4 minutes. Find t.
Ans.

12.Solve for x :6X2 – 6(a + b)x + ((4/3) a²+(10/3)ab+(4/3) b²)= 0
Ans.

13.The sum of n terms of an AP whose first term is 6 and common difference is 40 is equal to the sum of 2n terms of another AP whose first term is 40 and common difference is 6. Find n.
Ans.

14.Draw a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of 45°.
Ans.

15.Cards bearing numbers 1, 4, 7, 10,….58 are kept in a bag. A card is drawn at random from the bag. Find
the probability of getting a card bearing
(i)a prime number less than 18.
(ii)a number divisible by 4.
Ans.

16.Six cards – ace, jack, queen, king, ten and nine of spade are well shuffled with their face downwards. One card is then picked up at random.
(i) What is the probability that the card is an ace?
(ii) If the ace is drawn and put aside, what is the probability that the second card picked up is
(a) a jack,(b) an ace.
Ans.

17.If P is a point lying on the line segment QR, joining Q(-l, -1) and R(4, -1) such that PQ = 3/7 QR, then find the coordinates of P.
Ans.

18.For what value of k, (k > 0) the area of triangle with vertices (k, 1), (3k, 1) and (2, 4) is 6 sq. units.
Ans.

19.A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 154 cm. If bucket ascends in 2 minutes 56 seconds with a uniform speed of 2.2 m/s, then calculate the number of complete revolutions the wheel makes in raising the bucket. (Use pi = 22/7)
Ans.

20.A solid cone of base radius 30 cm is cut into two parts through the mid-point of its height by a plane parallel to its base. Find the ratio of the volumes of the two parts of the cone.
Ans.

                                                                 Section D
21.A man bought a certain number of toys for Rs 180; he kept one for his own use and sold the rest for one rupee each more than he gave for them, besides getting his own toy for nothing he made a profit of Rs 10. Find the number of toys.
Ans.

22.A ladder has rungs 50 cm apart. The rungs decrease uniformly in length from 90 cm at the bottom to 50 cm at the top. If top and bottom rungs are 5 m apart, what is the length of the wood required for the rungs?
Ans.

23.ABC is a right-angled triangle, right angled at A. A circle is inscribed in it. The lengths of two sides containing the right angle are 24 cm and 10 cm. Find the radius of the in circle.
Ans.

24.In figure the common tangent, AB and CD to two circles with centres O and O’ intersect at E.Prove that the points O, E and O’ are collinear.

Ans.

25.In the given figure, the diameters of two wheels have measures 4 cm and 2 cm. Determine the lengths of the belts AD and BC that pass around the wheels if it is given that belts cross each other at right angles.

Ans.

26.A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed, 6 seconds later the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.
Ans.

27. A fire in a building B is reported on telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of 60° to the road and Q observes that it is at an angle of 45° to the road. ‘
(a) Which station should send its team and how much will this team have to travel?
(b) What according to you, are the values displayed by the teams at fire stations P and Q?
Ans.

28.The opposite angular points of a square are (2, 0) and (5, 1). Find the remaining points.
Ans.

29.In the given figure, three circles of radius 2 cm touch one another externally. These circles are circumscribed by a circle of radius R cm. Find the value of R and the area of the shaded region.

Ans.

30.The area of the base of a cone is 770 cm2 and the curved surface area is 814 cm2. Find the volume of the cone.
Ans.

31.An agricultural field is in the form of a rectangle of length 20 m and width 14 m. A pit 6 m long, 3 m wide and 2.5 m deep is dug in the corner of the field and the earth taken out of the pit is spread uniformly over the remaining area of the field. Find the extent to which the level of the field has been raised.
Ans.

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 13

                                                                             SECTION A

1.The sum of the ages of two friends is 20. Four years ago, the product of their ages in years was 48. Is it possible to determine their present ages?

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

3. In the given figure, AB, AC and AD are tangents to the circles with centre O and O’. If AD = 10 cm, find AB

4.The probability of getting a defective pen from a lot of 500 pens is 1/25 Find the number of defective pensin the lot.

                                                             SECTION B
5.For what value of k, given equation has real and equal roots: (k – l)x² – 2(k – l)x +1 = 0?

6.In the given figure, there are two concentric circles with centre O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP

7.Which term of the Arithmetic Progression 3, 10, 17,… will be 84 more than its 13th term?

8.Prove that tangents drawn at the ends of a diameter of a circle are parallel.

9.Find the value of k, if the distance between the points (2, k) and (4, 3) is 8.

10.Find the coordinates of a point P which lies on the line segment joining the points A (-2, 0) and B(0, 8)such that AP = 1/4 AB.

                                                                  SECTION C

12.A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

13.On the first day of the strike of doctors in a hospital, the attendance at its OPD was 1040 patients. As the strike continues, the attendance declined by 80 patients every day. Find from which day of the strike the OPD would have no patient.

14.A juice seller serves his customers using a glass as shown in figure. The inner diameter of the cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical raised portion which reduces the capacity of the glass. If the height of the glass is 10 cm, find the apparent capacity of the glass and its actual capacity. (Use n = 3.14)

16.A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 4.2 cm and height of the cone is 8 cm. The solid is placed in a cylindrical tub full of water in such a way that whole solid is submerged in the water. If the radius of the cylinder is 10 cm and its height is 19.6 cm, find the volume of water left in the cylindrical tub. (Use pi =22/7)

17.An equilateral triangle has two vertices at the points (3, 4) and (- 2, 3). Find the coordinates of the third vertex.

18.A hemispherical bowl of internal radius of 30 cm contains a liquid. The liquid is to be filled into cylindrical shaped bottles of diameter 10 cm and height 12 cm. How many bottles are necessary to empty the bowl, if 10% of the liquid is wasted during the process of filling the bottles?

19.The diameter of internal and external surfaces of a hollow spherical vessel are 6 cm and 10 cm respectively.If it is melted and recast into a solid cylinder of height 2~ cm, find the diameter of the cylinder.

20.In the given figure, the shape of the top of a table in a restaurant is that of a sector of a circle with centre O and BOD = 90°, if BO = OD = 60 cm find :
(i)the area of the top of the table
(ii)the perimeter of the table top. (Take pi =3.14)

                                                                  SECTION D

21.Students of class ‘X’ collected Rs 9000. They wanted to divide it equally among a certain number of students residing in slum areas. When they started distributing the amount, 20 more students from nearby slum also joined. Now each student got Rs 160 less.
(a)Find the original number of students living in the slum.
(b)Which value is depicted by students of class X?

22.A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, … . What is the total length of such a spiral made up of thirteen consecutive semicircle?(taken pi=22/7)

23.O is the centre of a circle. PA and PB are tangents to the circle from a point P. Prove that (i) PAOB is a cyclic quadrilateral (ii) PO is the bisector of angle APB (iii) angle OAB = angle OPA.

24.QR is a tangent at Q. PR || AQ, where AQ is a chord through A and P is the centre of the circle with the end point of the diameter AB. Prove that BR is tangent at B.

25.Cards numbered 2, 3, 4, 26 are put in a box and mixed thoroughly. One person draws a card from the box. Find the probability that number on the card is (i) even (ii) prime (iii) a perfect square (iv) divisible by 2 or 5.

26.The angle of elevation of a cloud from a point 200 m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud above the lake.

27.Draw a right triangle in which the sides (other than hypotenuse) are of lengths 6 cm and 8 cm. Then construct another triangle whose sides are 4/3 times the corresponding sides of the given triangle.

28.A(6, 1), B(8, 2) and C(9, 4) are three vertices of a parallelogram ABCD. If E is the mid-point of DC, find the area of triangle ADE.

30.A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Find the cost of the canvas of the tent at the rate of Rs 500 per m². Also, find the volume of air enclosed in the tent.

31.The area of an equilateral triangle is 17320.5 cm². With each vertex of the triangle as centre, a circle is described with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circle.

CBSE Sample Papers for Class 10 SA2 Maths Solved 2016 Set 12

                                                                 Section A

2.Find the length of the shadow of a tree 18 m long when the Sun’s angle of elevation is 45°.

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3.If two tangents inclined at an angle of 120° are drawn to a circle of radius 5 cm, then find the length of each tangent.

4.A pair of die is thrown. Find the probability of getting sum of numbers which is perfect square and divisible by 5.

                                                           Section B

5.Solve for x: a/x-a+b/x-b——— -2; x not equal to a.b

6.Which term of the AP: 125, 121, 117, … is 1st negative term?

7.In the given figure, PQR is the tangent to a circle at Q whose centre is O. AB is a chord parallel to PR and BOR = 60°. Find triangle AQB.

8.In the given figure, AC is diameter of the circle with centre O. PAQ is the tangent to the circle at A. If AB || CD and ZBAQ = 65°, find triangle DCA.

9.Find a relation between x and y if area of the triangle formed by the points (x, y), (1, 2) and (7,0) is 5 sq units.

10.If the point P(2, 1) lies on the line segment joining the points A(4,2) and B(8,4) then find AP/AB

                                                            Section C
12.The sum of fourth and the ninth terms of an AP is 46 and their product is 465. Find the sum of first 10 terms of this AP.

13.The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

14.In figure ABC is a right angled triangle right angled at A. Semicircles are drawn on AB, AC and BC as diameters. If AB = 6 cm, AC = 8 cm, find the area of the shaded region.

15.A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in figure. The height of the entire rocket is 52 cm while the height of the conical part is 12 cm. The base of the conical portion has a diameter of 10 cm, while the base diameter of the cylindrical portion is 6 cm. If the conical portion is to be painted, red and the cylindrical portion green, find the area of the rocket painted with each of these colours. (Take, pi = 3.14)

16.A building is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to 2/3 of the total height of the building. Find the surface area of the building, if it contains 2816/21 of air.

17.Solid sphere of diameter 12 cm are dropped into a cylindrical vessel containing some water and are fully submerged. If the diameter of the vessel is 36 cm and the water rises by 80 cm, find the number of solid spheres dropped in the water.

18.The height of a cone is 60 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume is 1/27 of the volume of the given cone, at what height above the base is the section made?

19.ABCD is a rectangle formed by the points A(-l, -1), B(-l, 4), C(5, 4) and D(5, -1). P, Q, R and S are the mid-points of AB, BC, CD and AD respectively. Is the quadrilateral PQRS is a square or rhombus? Justify your answer.

20.What is the probability that an year will have 53 Tuesdays?

                                                                Section D
21.A swimming pool is filled with three pipes with uniform flow of water. The first two pipes operating simultaneously fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool 5 hrs faster than the third pipe and 4 hrs slower than the third pipe. Find the time required by each pipe to fill the pool separately.

22.If the roots of the quadratic equation: p(q – r)x2 + q(r – p)x + r(p – q) = 0 are equal, show that:1/p+ 1/r = 2/q

23.A contractor employed 150 workers to finish a piece of work in a certain fixed number of days. On the first day, all 150 workers worked. He dropped four workers on the second day, four more workers were dropped on the third day and so on. In this way work got finished in 8 more days. Find the number of days in which work was to be completed originally.

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

26. A contractor was awarded to construct a vertical pillar at a horizontal distance of 200 m from a fixed point. It was decided that angle of elevation of the top of the complete pillar from that point to be 60°. Contractor
finished the job by making a pillar such that the angle of elevation of its top was 45°.
(i) Find the height of the pillar to be increased as per the terms of contract.
(ii) Contractor demands full payment for this work
(a) Is he justified?
(b) Which ‘value’ is he lacking?

27.Draw a right triangle ABC in which AB = 5 cm, BC = 7 cm, B = 90°. Through B, draw BD perpendicular AC. Then draw a circle passing through B, C and D. Construct a pair of tangents to this circle from A.

28.Water is pumped from a sump (an underground tank) to an overhead tank in the shape of cylinder. Sump is in the shape of a cuboid of dimensions 4mx3mx2m. The overhead tank has radius 60 cm and height 80 cm. Find the height of water left in the sump after the overhead tank has been completely filled with water from the sump (assume sump was completely filled before water was pumped to overhead tank). Also compare the capacity of tank with that of sump. (Take pi = 3.14)

29.The area of an equilateral AABC is 17320.5 cm². With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of side of the triangle. Find the area of the triangle which is uncommon with circles. (Take pi = 3.14, root 3= 1.73205)

30.Find the coordinates of the point equidistant from three given points A(5, 1), B(-3, -7) and (7, -1).

31.At a fete, cards bearing numbers 1 to 1000, one number on one card are put in a box. Each player select one card at random and that card is not replaced. If the selected card has a perfect square greater than 500, the player wins a prize. What is the probability that: (0 the first player wins a prize? (//) second player wins a prize, if the first has won?