SAMPLE PAPER / MODEL TEST PAPER CBSE SA – 2 (II) 2012 SUBJECT – MATHEMATICS SECTION-A Question number 1 to 10 carry 1 mark each. For each of the question 1-10, four alternative choices have been provided of which only one is correct. You have to select the correct choice. 1. The sum of the first 15 multiples of 8 is: (a) 920 (b) 860 (c) 900 (d) 960 2. A target PQ at a point P of a circle of radius 5 meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is: (a) 12 cm (b) 13 cm (c) 8.5 cm (d) root 119 cm 3. If y =3 is a root of the quadratic equation ky square + 3 – ky = 0, then the value of k is: (a) ½ (b) -1/2 (c) 2 (d) -2 4. A girl calculates that the probability of her winning the first prize in a lottery is 0. 08. If 6000 tickets are sold, how many tickets has she bought? (a) 40 cm (b) 240 cm (c) 480 cm (d) 750 5. A tree breaks due to storm and broken part bends so that the top of the tree touches the ground making an angle of 30 degree with ground. If the distance between the foot of the tree to the
Transcript
SAMPLE PAPER / MODEL TEST PAPER
CBSE SA – 2 (II) 2012
SUBJECT – MATHEMATICS
SECTION-A
Question number 1 to 10 carry 1 mark each. For each of the question 1-10, four alternative choices have been provided of which only one is correct. You have to select the correct choice.
1. The sum of the first 15 multiples of 8 is:
(a) 920 (b) 860 (c) 900 (d) 960
2. A target PQ at a point P of a circle of radius 5 meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is:
(a) 12 cm (b) 13 cm (c) 8.5 cm (d) root 119 cm
3. If y =3 is a root of the quadratic equation ky square + 3 – ky = 0, then the value of k is:
(a) ½ (b) -1/2 (c) 2 (d) -2
4. A girl calculates that the probability of her winning the first prize in a lottery is 0. 08. If 6000 tickets are sold, how many tickets has she bought?
(a) 40 cm (b) 240 cm (c) 480 cm (d) 750
5. A tree breaks due to storm and broken part bends so that the top of the tree touches the ground making an angle of 30 degree with ground. If the distance between the foot of the tree to the point where the top touches the ground is 8 m then the height of the tree is:
(a) 8/3 cm (b) 3/8cm (c) 8 root 3 m (d) 8/ root 3 m
6. A point P is 13 cm from the centre of a circle. Radius of the circle is drawn from P to the circle is:
(a) 10 (b) 11 (c) 12 (d) 13
7. If tangents PA and PB from a point P to a circle with centre with O are inclined to each other at angle of 80 degree, angle POA is:
8. The circular ends of a bucket are of radii 35 cm and 14 cm and height of the bucket is 40 cm. Find the volume.
(a) 50080 cm cub (b) 80080 cm cub (c) 70080 cm cub (d) 60080 cm cub
9. In two concentric circle, the length of tangent to inner circle is 8 cm. Find the radius of outer circle, if the radius of inner circle is 3 cm.
(a) 5 cm (b) 4 cm (c) 3 cm (d) 2 cm
10. The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is:
(i) 56 cm (ii) 42 cm (iii) 28 cm (iv) 16 cm
SECTION – B
11. Two players, Sangeeta and Reshma, play a tennis match. It is known that the probability of Sangeeta winning the match is 0. 62. What is the probability of Reshma winning the match?
Or
In a lottery there are 20 prizes and 30 blanks. Find the probability of getting a prize
12. An equilateral triangle has two vertices at the points (1, 1) and (-1, -1), Find the coordinates of the third vertex.
13. Find the roots of the quadratic equation 1/ x – 3 – 1/x + 5 = 1/6; x does not equal 3, -5.
14. If 9th term of an A.P. is zero prove that its 29th term is double the 19th tern.
15. Prove that parallelogram circumscribing a circle is a rhombus.
16. a road which is 7 m wide surrounds a circular park whose circumference is 352 m.
Find the area of the road.
17. A drinking glass is in the shape of a frustum of a cone of height 14 cm. the diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. (Use PI = 22/7)
18. Find the coordinates of the points which divide the line segment joining A ( -2, 2) and B ( 2, into four equal parts.
SECTION – C
19. A chord of a circle of radius 15 cm subtends an angle of 60 degree at the centre. Find the area of the corresponding minor and major segments of the circle.
(User PI = 3. 14 and root 3 = 1.73)
20. Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.
21. Find the roots of the quadratic equation:
x+3/x+2 = 3x – 7 / 2x – 3; x does not equal -2, 3/2
Or
The sum of two numbers is 17 and the sum of their squares is 157. Find the numbers.
22. The first and the last term of A.P. are 4 and 81 respectively. If the common difference is 7, how many terms are there in the A.P. and what is their sum?
23. If A (x , 3 ), B ( 3, 0 ) , ( 0, -4 ) and D ( 4, y ) are the vertices of a rhombus, taken in order. Find the value of x and y.
24. Prove that the lengths of tangents drawn from an external point to a circle are equal.
Or
ABC is a right triangle right angled at B, such that BC = 6 cm and AB = 8 CM, find the radius of its in circle.
25. Find the area of square , if coordinates of its vertices are ( 1, 2) , ( 6 , 3), ( 5, and ( 0, 7) taken in order.
26. A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. find the total surface area of the toy.
27. A bunch of 10 books contains 3 books on Mathematics, 2 books on Physics and the remaining are on
Chemistry. One book is selected at random. Find the probability that:
(i) it is a chemistry book (b) it is a physics book.
28. The angle 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 complementary. Prove that the height of the tower is 6 m.
29. A triangle ABC is drawn to circumscribe a circle of radius 4 cm, such that the segments BD and DC into which BC is divided by the point of contact D are of length 8 cm and 6 cm respectively. Find the sides AB and AC.
30. The angle of elevation of a cloud from a point 60 m above a lake is 30 degree and the angle of depression of n the reflection of the could is 60 degree. Find the height of cloud.
31. Sum of the areas of two squares is 468 m square .If the difference of their perimeters is 24 m, find the sides of the two squares.
32. A right triangle, whose sides are 15 cm and 20 m is made to revolve about its hypotenuse. Find the volume and the surface area of the double one so formed. (Take PI = 3.14)
33. A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is 14/3 m and the diameter of hemisphere is 3.5 m. calculate the volume and the internal surface area of the internal surface area of the solid.
34. A metallic right circular cone 45 cm high and whose vertical angle is 60 degree is cut into two parts in the ratio 1 : 2 from the vertex of the cone by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1 cm, find the length of the wire.
MODEL TEST PAPER / SAMPLE PAPER
SUBJECT MATHEMATICS
CBSE SA – 2
2011
SECTION-A
Question numbers 1 to 10 contain 1 mark each. For each of the questions 1 – 10, four alternative choices have been given of which only one is correct. You have to select the correct choice.
1. The circumference of two circles are in the ratio 2: 3 then the ratio of the areas is:
(a) 2 : 4 (b) 2 : 9 (c) 4 : 9 (d) 4 : 6
2. A silver rod of diameter 2 cm and length 12 cm is drawn into a thin wire of length 24 m of uniform thickness, and then the thickness of the wire is:
(a) 0. 183 (b) 0.173 (c) 0.186 (d) 0.175
3. In two concentric circles, the length of tangent to inner circle is 8cm. Find the radius of outer circle, if the radius of inner circle is 3 cm.
(a) 5 cm (b) 4 cm (c) 3 cm (d) 2 cm
4. A point P is 13 cm from the centre of a circle. Find the length of the tangent drawn to the circle from the point P, if the radius of the circle is 5 cm.
(a) 12 cm (b) 10 cm (c) 8cm (d) 6 cm
5. If PA and PB are tangents from a point playing outside the circle such that PA = 10cm and angle APB, then the length of chord AB is:
(a) 5 cm (b) 4 cm (c) 3 cm (d) 2 cm
6. If 17th term of an A.P. exceeds its 9th term by 64, then the difference is:
(a) 8 (b) 6 (c) 4 (d) 12
7. One coin is tossed three times. The probability of getting 2 heads and 1 heads and 1 tail is:
(a) 1/8 (b) 2/5 (c) 3/8 (d) ¼
8. A vertical stick 20 m long casts a shadow 16 m long. At the same time a tower casts a shadow 48 m long. Then the height of the tower is:
(a)40 m (b) 32 m (c) 96 m (d) 60 m
9. A cone is divided into two parts by drawing a plane through mid – point of its axis, parallel to its base. The ratio of volumes of two parts is:
(a) 2: 3 (b) 1: 2 (c) 1: 3 (d) 1: 7
10. From a point Q , the length of the tangent to a circle is 24cm and the distance of Q from the centre is 25cm. The radius of the circle is:
(a) 7 cm (b) 12 cm (c) 15 cm (d) 24.5 cm
SECTION – B
11. For what value of P, are 2p -1, 7 and 3p three consecutive terms of an A.P.?
12. The length of the minute hand of a clock is 14 cm. Find the area swept out by the minute hand in 1 hour.
13. Find the roots of the quadratic equation 3x – 8/x = 2 ; x does not equal 0
14. If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.
15. A letter is drawn at random form the word ‘MATHEMATICS’. Find the probability of drawing each of the different letters in the given word.
16. How many balls each of radius 1 cm can be made from a solid sphere of lead of radius 8cm?
17. It is known that a box of 500 electric tubes contains 15defective electric tubes. One tube is taken out at this box. What is the probability that is a non – defective electric tube?
18. Find the coordinates of the points P,Q and R which divided the line segment joining A (5 , 4) and B (11 , 6) into four equal parts.
SECTION – C
19. The sum of two natural numbers is 8. Determine the numbers, if sum of their reciprocal is 8/15.
20. Draw a right triangle ABC in which AC = AB = 4.5 cm and angle = 90 degree. Draw a triangle similar to triangle to ABC with its sides equal to 5/4th of the corresponding sides of angle ABC.
21. Prove that the tangents drawn at the ends of a chord of circle make equal angles with the chord.
22. In an A.P. the sum of first ten is – 150 and the sum of its next ten terms is – 550.
23. PA and PB are two tangents from an exterior point P to a circle of radius 5 m. If length of the chord AB is 8 cm, then find the length of the tangent.
24. Three cows are tethered with 10 m long rope at the three corners of a triangular field having sides 42 mm 20 m and 34 m. Find the area of the plot which can be grazed by the cows, also find the area of the remaining field (unglazed).
25. The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is ¼. The probability of selecting a blue ball at random from the same jar is 1/3. If this jar contains 10 orange balls, then what is the total number of balls in the jar?
26. If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a) , then prove that x + y = a + b.
27. The internal and external diameters of a hollow hemispherical shell are 6cm and 10cm respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.
28. The line segment joining the points A (2, 1) and B (5, is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given 2x – y+ k = 0, find the value of k.
Or
A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle the angle of elevation of the top of the light house from 60degree to 45 degree. Find the speed of the boat.
SELECTION-D
29. If the radii of the ends of a bucket 45 cm high, are 28 cm and 7 cm. Find the capacity of bucket.
30. The side of a square exceeds the side of another square by 4 cm and the sum of the areas of the two squares is 400 sq. cm. Find the dimensions of the squares.
31. The speed of a boat in still water is 11 km/ h. It can go 12 km upstream and return downstream to the original point in 2 hours and 45 minutes. Find the speed of the stream.
32. An iron sphere of radius ‘a’ unites is immerse completely in water contained in a right circular cone of semi – vertical angle 30 degree , water is drained off from the cone till its surface touches the sphere. Find the volume of water remaining in the cone.
33. The sum of first 8terms of an arithmetic progression is 156. The ratio of its 12th tern to its 68th
is 1: 5 Calculate the first term and the fifteenth term.
34. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
SAMPLE PAPER/MODEL TEST PAPER
SUBJECT – MATH 10TH CBSE SA 2 2011
Section - A
1. The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 300 with horizontal, then the length of the wire is:
(a) 8 m (b) 6 cm (c) 10 m (d) 12 m
2. If the equation 9×2 + 6kx + 4 = 0 has equal, then the roots are both equal to:
(a) ±3 (b) ±3/2 (c) ± 2/3 (d)0
3. If three coins are tossed simultaneously, then the probability of getting at least two heads, is:
(a) ¼ (b) ½ (c) 3/8 (d) 1/3
4. If in an A.P., Sn = n2p and Sm = m2p, where Sr , denotes the sum of r terms of the A.P., then Sp is equal to:
(a) mnp (b) p3 (c) ½ p3 (d) (m + n) p2
5. From the point Q the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of circle is:
(a) 15 cm (b) 24.5 cm (c) 7 cm (d) 24.5 cm
6. In a single throw of a die, the probability of getting a multiple of 3 is:
(a) 2/3 (b) 1/3 (c) ½ (d) 1/6
7. If the sun of n terms of an A.P. is 3n2 + 5n, then which of its terms is 164?
(a) 27th (b) 28th (c) 26th (d) none of these
8. If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these is 273, then the third term is:
(a) 9 (b) 17 (c) 13 (d) 21
9. If TP and TQ are two tangents to a circle with centre O, so that ∟POQ = 1100, then ∟PTQ is equal to:
(a) 900 (b) 700 (c) 600 (d) 800
10. The length of the tangent from point A at a circle, of radius 3 cm. The distance of a from the centre of circle is:
(a) 25 cm (b) 7 cm (c) 5 cm (d) √7 cm
Selection – B
11. A car has wheels which are 80 cm in diameter. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km/h.
12. A dice that the points (4, 3), (5, 1) and (1, 9) are collinder.
(a) a multiple of there
(b) an even prime number
13. In an A.P., the sum of first n terms is 3n2/2 + 5n/2. Find its 25th term.
14. A right circular cone of height 8.4 cm and the radius of its base is 2.1 cm. It melted and recast.
15. Solve for x:
1/x + 1 + 2/ x + 2 = 4 / x + 4
16. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
17. If the point C ( -1, 2) divides the line segment AB in the ration 3 : 4, where the co – ordinates of A are (2, 5). Find the co – ordinates of B.
18. The 5th term of an Arithmetic Progression (A .P.) is 26 and the 10th term is 51. Determne the 15th term of A.P.
18. Find the area of the quadrilateral whose vertices taken in order are A( -5, -3), B( -4, -6), C( 2, – 1) and D (1, 2)
Section – C
19. A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag. Find the probability of getting.
(a) neither a green ball nor a red ball.
(b) a white ball or a green ball.
20. How many times will the wheel of a car rotate in a journey of 88 km if it is known that the diameter of the wheel is 56 cm ? [Take π = 22/7]
21.A gulabjamun when completely ready for eating contains sugar syrup to about 30% of its volume. Find approximately how much syrup would be found in 45 gulabjaImun shaped like a cylinder with two hemispherical ends, if the complete length of each of gulabjamuns is 5 cm and its diameter is 2.8 cm.
22. A square park has each side of 100 m. At each corner of the park, there is a flowerbed in the form of a quadrant of radius 14 m as shown in the figure given below. Find the area of the remaining.
23. A train covers a distance of 90 km at a uniform speed. Had if the speed been 15 km/hour more, it would have taken 30 minutes less for the journey. Find the original speed of the train.
24. Construct a triangle with side 5 cm and 7 cm and then another triangle whose sides are 7/5 times of corresponding sides of first triangle.
25. A vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height m. From a point on the plane the angle of elevation of the bottom and top of the flagstaff are respectively 300 and 600 find the height of the tower.
26. From a point P outside a circle with centre O, tangents PA and PB are drawn. Prove that
(a) OP is the perpendicular bisector of AB.
(b) ∟AOP = ∟BOP
27. If the points (10, 5), (8, 4) and (6, 6) are mid points of the side of a triangle. Find its vertices.
28. Cards being numbers 3 to 19 are put in a box and mixed thoroughly. A card is drawn from the box at random, find the probability that the number on the card drawn is:
(a) divisible by 2 and 3 both.
(b) even.
Section – D
29. A horse is tied to a peg at one corner to a square shaped grass field of side 15 m by means of a 5 m long rope. Find:
(a) the increases in grazing area if a rope were 10 m long instead of 5 m. (Use π = 3.14)
(b) the area of the field in which the horse can graze.
30. Marbles of diameter 1.4 cm are dropped into a cylinder beaker, of diameter 7 cm, containing some water. Find the number of marbles that should be dropped into the beakers so that the water level rises by 5.6 cm.
31. From the top of a building 60 m high, the angles of depression of the top and bottom of a vertical lamp post are observed to be 300 and 600 respectively. Find.
(a) The height of lamp post.
(b) The horizontal distance between the building and the lamp post.
32. A manufacturer of T.V. sets produced 6,000 units in third year and 7,000 units in the seventh year. Assuming the production uniformly increases by a fixed number every year. Find:
(a) the production in 10th year.
(b) the production in first year.
(c) the total production in 7 years.
33. A container made up of a metal sheet is the form of a frustum of a cone of height 16 cm from of a frustum of a cone of height 16 cm with radii of its lower and upper ends are 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs. 20 per litre and the cost of the metal used if it costs. Rs. 10 per 100 cm2.
34. The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of 66 km per hour?
SAMPLE PAPER/MODEL TEST PAPER
SUBJECT – MATH CBSE 10TH SA 2 2011
Section – A
1. If the radius of a circle is diminished by 10%, then its area is diminished by:
(a) 20 % (b) 19 % (c) 36% (d) 10 %
2. The volumes of two spheres one is the ratio 64: 27. The ratio of their surface areas is:
(a) 1 : 2 (b) 9 : 16 (c) 16 : 9 (d) 2 : 3
3. The number of quadratic equation having real roots and which do not change by squaring their roots is:
(a) 2 (b) 1 (c) 3 (d) 4
4. If points (1, 2), (-5, 6) and (α, 2) are collinear, then α =
(a) 7 (b) 2 (c) -2 (d) -3
5. The area of the in circle of an equilateral triangle of sides 42 cm is:
(a) 321 cm2 (b) 924 cm2 (c) 472 cm2 (d) 22√3 cm2
6. If four sides of a quadrilateral ABCD are tangential to a circle, then:
(a) AB +CD = BC + AD (b) AC + AD+ = BC +DB
(c) AC + AD = AC + CD (d) AB + CD = AC + BC
7. The length of the tangent drawn from a point 8 cm away from the centre of a circle radius 6 cm is:
(a) 10 cm (b) 5 cm (c) √7 cm (d) 2 √7 cm
8. The number of quadratic equations having real roots and which do not change by squaring their roots is:
(a) 1 (b) 2 (c) 3 (d) 4
9. If 7th terms of an A.P. be 34 and 64, respectively, then its 18th term is:
(a) 88 (b) 89 (c) 87 (d) 90
10. The ratio of the length of a rod and its shadow is 1: √ 3. The angle of elevation of the sum is:
11. Find the area of a quadrant of a circle whose circumference is 22 is.
12. A pair of dice thrown once. Find the probability of getting the same number of each dice.
13. Find the circumference and area of a circle of radius 8.4 cm.
14. Two cube each of 10n cm edge are joined end to end. Find the surface area of resulting cuboid.
15. If the points A (4, 3) and B (x, 5) are on the circle with the centre O (2, 3), find the value of x.
16. Find the common difference and write the next three terms of the A.P. 3, -2, -7, -12.
17. Find the value of (α – 12) x2 + 2 (α – 12) x + 2 = 0 has equal roots.
18. A point P is 13 cm from the centre of the circle. The length of the tangent drawn to the circle is 12.
Section – C
19. An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from her eyes is 45 degree. What is the height of the tower?
20. The base radius and height of a right of a right circular solid cone are 2 cm and 8 cm respectively. It is melted and recast into spheres of diameter 2 cm each. Find the number of spheres so formed.
21. One card is drawn from a well shuffeled deck of 52 playing cards. Find the probability of getting:
(a) a black king or a red queen
(b) a non – face card
22. The co – ordinates of the mid – point of the line joining the points (2p +1, 4) and
(5, q – 1) are (2p, q), Find the values of p and q.
23. A chord AB of a circle of radius 10 cm makes a right angle at the centre of the circle. Find the area of the major and minor segments. (Take PI = 3.14)
24. In an A.P. the first term is 8, nth term is 33 and sum to first n terms is 123, find n and d.
25. Construct a triangle ABC in which CA = 6 cm, AB = 5 cm and angle BAC = 45 degree then construct a triangle similar to the given triangle whose are 6/5 of the corresponding side of the triangle.
26. The vertices of a triangle are (-1, 3), (1, 1); and (5, 1). Find the length of medians through vertices (-1, 3) and (5, 1).
27. The perimeter of an isosceles triangle is 32 cm. If each equal side is 5/6 times the base. Find the area of the triangle.
28. The sum of 5th and 9th term of an A.P. is 72 and the sum of 7th and 12th terms is 97.
Find the A.P.
Section – D
29. A gulabjamun when completely ready for eating contains sugar syrup up to about 30 % of its volume. Find approximately how much syrup would be found is 45 gulabjamuns shaped like a cylinder with two hemispherical ends, if the complete length of each of gulabjamun is 5cm and its diameter is 2.8 cm.
30. Two tangents TP or TQ are drawn to a circle with centre O from an external point T.
Prove that
∟PTQ = 2∟OPQ
31. The sum of n, 2n, 3n terms of an AP are S1, S2, S3 respectively. Prove that
S3 = 3 (S2 – S1).
32. The angle of depression of the top and bottom of an 8 m tall building from the top of a multistoreyed building are 30 degree and 45 degree respectively. Find the height of the multi storeyed building and the distance between the two buildings.
33. In a flight of 600 km, a air craft slowed donor due to bad weather, its average speed of the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. Find the duration of flight.
34. A chord of circle of radius 12 cm subtends an angle of 120 degree at the centre. Find the area of the corresponding segment of circle. (PI = 3.14 and √3 = 1.73)
