Sample Paper Mathematics CBSE SA 2


Sample papers


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:

(a) 50 degree (b) 40 degree (c) 70 degree (d) 90 degrees

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, 8) 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, 8) 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.

 

CBSE SA 2 Sample Paper / Model Test Paper





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  1. kysquare + 3 – ky = 0, y=0 k 3square + 3 – 3k = 0 9k + 3 – 3k = 0 6k + 3 = 0 6k = -3 k = -3/6 k = -1/2

  2. Sir Iam student of class 10 Sir I want all subject sample paper of your.. PLEASE sir send me all sample papers with answer please sir

  3. If from any point on the common chord of 2 intersecting circles,tangents be drawn to the circles,prove that they r =

  4. SAMPLE PAPER / MODEL TEST PAPER CBSE SA – 2 (II) 2011 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: (a) 50 degree (b) 40 degree (c) 70 degree (d) 90 degrees 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, 8) 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, 8) 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

  5. a=120 d=5 l=360 360 = 120 + (n-1)5 360 – 120 / 5 = n – 1 48 = n-1 Therefore n = 49 sides

  6. hii guyz this a good platform…we can discuss que….if any 1 wanna discuss online que than my id on facebook is juverhhea.kousar1996@gmail.com and many of u r giving board…n some are having their xms b4 24th march….den guys plz gimme copy of ur xm que paper…a sincere request..plz do if possible..

  7. NO … optionc) is correct 8root3m….the ht of the total tree or the ht of the original tree..

  8. let angle APO be theta so sin theta = oppo side divided by adj side therefore r divide by 2r =1 divided by 2 =sin 30 angle BPO = 30 degree since centre lies on the bisector other 2 angles are equal angle oppo to equal sindes are equal

  9. at 1st draw the base BC of 6 cm with the help of scale 2.from point B of 6 cm . 3.divide BC into two parts as we MEdian divide it into 3=3 BD=3 4.from point D cut an arc of 4 cm as AD=4cm the point of intersection of arcs will be A NOw join AB,AC,AD..UR TRIANgLe Is formed..

  10. GIVEN:-pt is tangent with center O and PAB is a secant. CONSTRUCTION:- Join OT and OA,OP and draw OM perpendicular to AB PROOF:- OT is perpendicular to PT since the tangent is perpendicular to the radius of the circle at the pt of contact In right triangle OTP OT*2=OT*2+PT*2(pythagoras th*m) PT*2=OP*2-OT*2 =OM*2=PM*2-OA*2(by pythagoras thorem in triangle OMP .OT=OA) OA*2-AM*2+PM*2-OA*2 (in rt triangle OMA) PM*2-AM*2 (PM+AM)(PM-AM)((a-b)*2=(a+b)(a-b)) PM+AM(PM) PT*2=PB*PA PT*2=PA*PB…. HENCE PROVED.

  11. how do you solve this question- this is a 9th class ka rd sharma se question.chapter- constructions. Q. construct a triangle ABC such that BC=6cm, AB= 6cm, and Median AD=4cm plz email me the steps of construction.- if not the teacher then the 10th students.. plz positively by today evening cuz 2morrow is my test,…. waiting.

  12. the radius of the circle whose circumference is equal to the sum of the two circles with diameter 36cm and 20cm is:

  13. IF u think all this r hard…. then try on this,its an arithmatic progression- find the number of sides in a polygon whose least angle is 120 degree and the common difference is 5 degree.

  14. take it as A(5,7) B(6,6) & C(2,-2) as three ptss on circle. Take O as centre and solve by distance formula OA=OB=OC

  15. IN Triangle abc let the third vertecs be (x,y) ie ,c,the find the distance between AB ,BC,AC ,the equate ,by squaring the you will surely get ans

  16. hi, i want to kno how to do this sum.please help.. find the centre of a circle passing through the pts. (5,7) , (6,6) and (2,-2). also find the radius. hope u tell me soon…..

  17. nth term of AP is 4n-10 1st term = 4*1-10 = -6 2nd term = 4*2-10 = -2 So, 1st term = -6 and common difference = -6+(-2)= -6-2 = -8 Sn = n/2(2a+(n-1)d) = 10/2(2*-6+(10-1)(-2) = 5(-12+(9)(-2) = 5(-12+(-18) = 5(-12-18) = 5*-30 = -150

  18. 2nd and 7th is already answered by navneeta nw 12th question’s ans:the answer to the 12th question is (1,-1),it becums easy if u draw the diagram and look.take the ratio of AB by wich it is divided by the origin and get the point at wich the y axis divide AK (if K Is the third vertex,u’ll get (0,-1))and by section formula u’ll get the coordinates of K the vertex.if any doubts i’ll clear.

  19. the answer to the 12th question is (1,-1),it becums easy if u draw the diagram and look.take the ration of AB by wich it is divided by the origin and get the point at wich the y axis divide AK (if K Is the third vertex,u’ll get (0,-1))and by section formula u’ll get the coordinates of K the vertex.if any doubts i’ll clear.

  20. i think this question is in complete. A tangent is a line not a line segment. So it can not have a fixed length. if m correct……..!!!!

  21. The angle of elevation of the top of a tower standing on a horizontal plane A is @. After walking a distance “d” towards the foot of the tower the angle of elevation is found to be #. What is the height of the tower? (a)d/(cot@+cot#) (b)d/(cot@-cot#) (c)d/(tan#-tan@) (d)d/(tan#+tan@)

  22. i guess that the options of the fifth questions are not right. the height of the tree still standing would be 8/root3 but the total height of the tree would be 8(2+1/root3)m.. that 12th question is not reaching anywhere. my brother says the question is wrong. the coordintes of the third points are (1,1) when i calculate.. is it wrong, i mean my answer? if it is… pls reply to my comment…

  23. (a-3d)(a-d)(a+d)(a+3d) let these be the 4 numbs.. and (a-3d)(a+3d)_ 7 (a-d)(a+d) – 15 now cross multiple n solve it ull get the AP…

  24. the queston no; r 32, 33, 34 plz itssssssssss reallyyyyyyyyy urgenttttttt plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

  25. they should also give us solutions so that we can check that we have done or solved question is correct or not.

  26. 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.

  27. we have to put 1,2,3… in place of n. Then we will get an AP like if n=1 4*1-10=-6 4*2-10=-2 we will get sum of first 10 terms. n=10, a=-6, d=4

  28. Easy questions!!! Well try out this Suppose in a figure PT is a tangent and PAB is a sectant Prove that PT*2 = PA X PB

  29. dear sir/madam, could you please post all the sample papers so that it would be easir to attempt my exams??i need the sa2 cbse sample papers for class ten.please send it as soon as possible.thankyou

  30. 1) 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. 2)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)

  31. i want to know that whether only this kind of sample paper will come in exam or more difficult than that?

  32. i want to know that whether othis kind of sample paper will come in exam or more difficult than that?

  33. sir, why the statistics chapter made .what is the reason behind this chapter. thanks for helping us by providing these sample papers earlier. your,obediently deepak sikarwar morar(gwalior)

  34. 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.

  35. Two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that ∠APB = 2 ∠OAB

  36. in two concentric circle with centre O.PQ is the diameter of outer circle and QS is the tangent line to the inner circle touching it in R and outer circle in S. find the length of PR if radius of to circle are 13cm and 8cm

  37. 12. An equilateral triangle has two vertices at the points (1, 1) and (-1, -1), Find the coordinates of the third vertex.

  38. 1. If PA and PB are two tangents drawn to a circle with centre O.Let OP meets the point P in circle at Q. Join OA and AQ. Then, angle OAP = 90 degree (OA is perpendicular to AP) Thus, Q is midpoint of hypotenuse OP of triangle OAP So, Q is equidistance from O, A and P Therefore, QA=OQ=OP=r Thus, OA=OQ=QA=r Therefore, triangle AOQ is equilateral So, angle AOQ=60 degree and angle APO=30 degree Angle APB=2 angle APO =2*30 degree =60 degree Also, PA=PB angle PAB=angle PBA=60 degree Hence, the triangle ABP is equilateral 2.Given-PQ and RS are two parallel tangents to a circle with centre O and AB is tangent to a circle at a point C, intersecting PQ and RS at A and B respectively. To Prove- angle AOB=90 degree Proof- Since PA and PB are tangents to a circle at P and R respectively and POR is a diameter of the circle, we have angle OPA= 90 degree and angle ORB=90 degree angle OPA+angle ORB=180 degree PAis parellel to RB We know that tangents to a circle from an external point are equally inclined to the line segment joining this point to the circle. therefore, angle 2=angle 1(angle PAO=angle2 and angle OAB=angle1) and angle 4=angle 3 (angleABO=angle3 and angleROB=angle4) Now,PA is parallel to RB and AB is a transversal. Therefore, angle PAB+angleRBA=180 degree (angle1+angle2)+(angle3+angle4)=180degree 2angle1+2angle3=180degree 2(angle1+angle3)=180degree angle1+angle3=90degree From triangle AOB,we have angle AOB+angle1+angle3=180degree angleAOB+90degree=180degree angleAOB=90degree proved.

  39. divide 32 into four parts such that they r in A.P & the ratio of product of first term & fourth term = product of second & third terms is equal to7/15.

  40. dear sir/madam, could you please post all the sample papers so that it would be easir to attempt my exams??i need the sa2 cbse sample papers for class ten.please send it as soon as possible.thankyou zainab

  41. i think these papers are more eazy. Will u give surity that this kind of paper will come in exam………

  42. 1.From a point p,two tangents PA & PB are drawn to a circle with centre O. If OP= diameter of the circle show that triangle ABP is equilateral. 2.Prove that the intercept of the tangent between two parallel tangents to a circle subtends a right angle at the center ?

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