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MATHEM ATICS - 2012 MODEL QUESTION PAPERS

HASSAN DISTRICT MATHEMATICS TEACHERS’ CUB URL: http://hassanmathsclub.blogspot.com http://freeganita.com/ & www.eshale.org/qkosha/

DEPARTMENT OF PUBLIC INSTRUCTION

HASSAN

C.K.S GIRLS’ HIGH SCHOOL K.R. PURAM HASSAN X: Standard M Α ┼∏ ∋ M Α ┼ ⊥ CS Marks: 100 Time :3 hrs I. Choose the most appropriate answer for the following questions; 20*1=20 1. The shaded region of the Venn diagram represents --------A. A B. B C. AUB D. B – A

Ans . . . . . . . . . . . . . . . . . . . 2. The Demorgan’s law is ------B. ( A ∩ B) 1 = A 1 ∩ B 1 A. ( AUB) 1 = A 1 U B 1 C. ( AUB) 1 = A 1 ∩ B 1 D. A 1 U B 1 = A 1 ∩ B 1

Ans . . . . . . . . . . . . . . . . . . . 3. If Tn = 3 n 2 – 2 and Tn = 25, then ‘n’ = ----A. ± 3 B. 27 C. 23 D. 5

Ans . . . . . . . . . . . . . . . . . . . 4. If 9 , x + 1 and 25 are in G.P, then ‘x’ = ---A. 15 B. 14 C. 5 D. 3

Ans . . . . . . . . . . . . . . . . . . . 5. In an A.P if T20 = 10 and T10 = 20. then ‘d’ = ----A. 10 B. 20 C. 1 D. – 1

Ans . . . . . . . . . . . . . . . . . . . 6. The correct relationship between n

A. n Pr = n C r

B. n Pr =

Cr r!

n

n

Pr and

C r is n

C.

n

Pr =

Pr D. r!

n n

pr = r! Cr

Ans . . . . . . . . . . . . . . . . . . . 7. If ‘A’ is a square matrix , then A – A 1 is A. Zero matrix B. Identity matrix C. symmetric matrix D. Skew symmetric matrix

Ans . . . . . . . . . . . . . . . . . . . 1

3 + x

8. If A = is a symmetric matrix , then ‘x’ = --1 2 x − 1 A. 0 B. 4 C. 2 D. 1

Ans . . . . . . . . . . . . . . . . . . . 9. The product of 2 and 3 3 is --A. 6 B. 3 6 C. 6 36

D. 6 72

Ans . . . . . . . . . . . . . . . . . . . 10. The rationalizing factor of 2m − 3n is ------A. 2m − 3n B. 2m + 3n C. 2 m − 3 n D. 2 m + 3 n

Ans . . . . . . . . . . . . . . . . . . .

1

11. If

∑ x = 0 , then

x 2 + y 2 – z 2 + 2 xy = -----

x, y, z

A. 2yz

C. x 2 + y 2 + 2xy – z 2

B. 0

D. ( x + y ) 2 + z 2

Ans . . . . . . . . . . . . . . . . . . . 12. If

∑a

2

2 ∑ ab = 9 , then a+b+c = ----

= 16 and

a ,b,c

A. 0

a ,b , c

B. 25

C. 5

D. 144

Ans . . . . . . . . . . . . . . . . . . . 13. Which of the following expressions is a cyclical symmetric? A. a+b+c B. a – b – c C. a 2 – b 2 – c 2 D. a 3 – b 3 – c 3

Ans . . . . . . . . . . . . . . . . . . . 14. The H.C.F and L.C.M of two expressions are 15ab and 75 a 2 b 3 c 2 respectively. If one expression is 25 a 3 b 3 c2 , then the other expression is ---A. 45 a B. 45 b C. 45 ac D. 5 a

Ans . . . . . . . . . . . . . . . . . . . 15. If l 2 = h 2 + r 2 , then ‘r’ = A.

l2 h2

B.

l 2 + h2

C. ± l 2 − h 2

D. h 2 − l 2

Ans . . . . . . . . . . . . . . . . . . . 16. If a straight line intersect the parabolic graph at the points P ( 2,3 ) and Q ( - 1 , 3 ) , then the roots of the equation are ----A. 2 and 3 B. – 1 and 5 C. 3 and 5 D. 2 and – 1

Ans . . . . . . . . . . . . . . . . . . . 17. The quadratic equation whose roots are 2 ± 3 is -------B. x 2 – 4 x + 1 = 0 A. x 2 + 4 x + 1 = 0 2 C. x + x – 4 = 0 D. x 2 – x – 4 = 0

Ans . . . . . . . . . . . . . . . . . . . 18. Which one the following is not a Pythagorean triplets? A. 3, 4, 5 B. 8, 16, 20 C. 5, 12, 13 D. 7, 24 , 25

Ans . . . . . . . . . . . . . . . . . . . 19. The matrix of the given network is --------0 1 0 A. 0 1 1 B. 0 1 0

0 1 0 1 2 1 C. 0 1 0

0 2 1 2 0 1 D. 1 1 0

0 2 0 2 0 1 0 1 0

Ans . . . . . . . . . . . . . . . . . . . 20. In the adjoining figure the correct relation is A. AP x AB = AQ x AC B. AP x AC = AQ x AB C. AP x AQ = AC x AB D. AP x PQ = BC x AC

Ans . . . . . . . . . . . . . . . . . . .

2

II. Fill in the blanks

10*1=10 1 2 3 , , . . . . . . . . . . is ---------2 3 4

21. The nth term of the sequence

22. The relation between Standard deviation and C.V is ----23. The Indian Mathematician who explained earlier the proof of Pythagoras theorem, using similar triangles was-----------24. Regular polyhedron are also called ------------- solids 25. If the centres of the circles lie on the same side of the common tangent, then the tangent is called a ----------26. The value of 3 ⊕ 8 10 is --------27. If ∆ < o, then the nature of the root is ----28. The positive root of ( 2 x – 3 ) ( 5x + 2 ) = 0 is --------29. The value of ∑ x( y − z ) is ---------x, y, z

30. The curved surface area of cylindrical water tank is -----Answer the following questions 18*2=36 31. How many terms are there in A.P 4 , - 1 , - 6………. (- 106)?

32. There are 24 factories which prepare pens or pencils, 18 factories prepare pens and 8 factories prepare both pens and pencils, then how many factories prepare only pencils?

3

33. Find the sum to infinite terms of the series 3 +9+27+--------

34. In how many ways 2 Kannada and 2 English books can be arranged such that two Kannada books are not together?

35. The S.D and C.V of some scores are 1.8 and 1.5 respectively. Find the arithmetic mean

4

1 − 2 , Find A x A1 5

36. If A = 3

37. The product of two expressions is (x 2 – 9) ( x + 5) ( x + 2 ) and their H.C.F is ( x – 3 ). Find their L.C.M

3

3

3

b +c c + a a +b 38. If a+b+c=0, then prove that + + =-3 a b c

5

39. Simplify by rationalizing the denominator

40. If K =

5 3+ 2

−

2 3− 2

1 mv2, then solve for ‘v’ and find the value of ‘v’ 2

when K = 100 and m = 2

41. Factories 2 ( a 2 – 1 ) = a ( 1 – a )

6

42. Find the sum and product of the roots of the equation 2x2+5xâ€“8=0

43. Construct Cayleyâ€™s table for Z3 under addition modulo 3

44. Construct a tangent to a circle of radius 3 cm from an external point at a distance of 5 cm away from the centre

7

45. Verify Euler’s formula for square based pyramid

2 1 0 46. Draw the network for the matrix 1 4 1 0 1 2

47. Draw a plan by using the data and scale given below ( Scale 20 m =1 cm)

80 to D 50 to E

To D (in meteres) 180 120 60 20 From A

8

70 to B

48. Calculate the total surface area of a cone of radius 6 m and slant height 8 m.

49. In the first square there are one coin of Rs 5, in the second square two coins of Rs. 5, in the third four coins and so on, then how many coins are there in the tenth square? Calculate its value. 6*3=18

9

50. Divide Rs 20 into two parts such that sum of their reciprocal is

4 15

51. Find the L.C.M of x 3 – 2 x 2 – 13 x – 10 and x 3 – x 2 – 10 x - 8.

10

52. From 5 gentlemen and 3 ladies a committee of 4 is to be formed. In how many ways can this be done so that each committee contains at least 2 ladies?

53. In the adj. fig If AB = AC = 4 6 cm, then calculate the radius of the circle

11

54. The length and breadth of a rectangle are 20 cm and 14 cm respectively when it is revolved on the side 14 cm. Name the solid formed and find its volume.

55. Calculate the S.D for the following scores C-1 5-9 10-14 15-19 20-24 25-29

F 2 4 8 5 1 N= 20

12

4*4=16

56. Solve x 2 + x – 2 = 0 graphically 57. Prove that the “Areas of the similar triangles are proportional to square of their corresponding sides”.

13

58. Construct Transverse common tangents to two circles of radii 4 cm and 2.5 cm, whose centres are 10 cm apart.

14

D.D.P.I HASSAN X: Standard

M Α ┼∏ ∋ M Α ┼ ⊥ CS

Marks: 100 Model paper – 2 Time : 3 hours I. Choose the most appropriate answer for the following questions;

20*1=20 1. If U = { 1,2,3,4,5,6,7} and A = { 3,4,5} then (A1)1 = ------------A. { 1,2,6,7} B. { 3,4,5,6}C. { 3,4,5} D. { U } 2. The c.d of an A.P is -----A. T2 + T 1 B. T 1 – T 2 C. T 1 + T 3 D. T 3 – T 2 3 2

1 0

3. If A = and I = 0 1 , then I A = --------1 4 2 3

4.

5.

6.

7.

3 2

2 3

3 1

A. B. C. 4 1 D. 2 4 1 4 1 4 n The value of P 3 is --A. n ( n – 1 ) ( n – 2 ) B. n ( n + 1 ) ( n – 2 ) C. n ( n – 1 ) ( n + 2 ) D. n ( n – 1 ) ( n – 2 )( n – 3 ) If the A.M of some scores is 60 and their standard deviation is 6, then CV = -A. 360 B. 10 C. 100 D. 60 2 The L.C.M and H.C.F of 2 a b and 6 a c are A. 2a and 6abc 2 B. 6 a b c 2 and 2 a C. 6ab and 2 a D. 2 a 2 and 6 a c 2 If ∑ a = 0 , then a ,b , c

A. a b c = 0 B. a = 0 C. a +b+ c = 0 D. a-b-c =0 8. The expression x 2 + y 2 + z 2 – x – y – z can be written using notation as A. ∑ x 2 + x B. ∑ x 2 − x C. ∑ x 2 + x D. ∑ x 2 + y x, y, z

x, y,z

x, y, z

9. If a+ b+ c =0, then ( b + c ) ( b + a ) =---A. ac B. – a c C. b + c D. b 2 + ac 10. The rationalizing factor of 5 a - 3 b is --A. 5a + 3 b B. 5 a + b C. 5 a + 3 b D. a + b 11. Which of the following is not a pure quadratic equation? A. x2+2=6 B. 2m 2 = 72 C. 3 a 2 = 4 3 D. m (m – 1) = 0 12. The roots of the equation ( m +3 ) ( m – 2 ) = 0 are A. ( 3, - 2 ) B. ( - 3 , 2 ) C. ( 3, 2) D. ( - 3 , - 2 ) 13. The roots of a quadratic equation are real and equal if A. ∆ < 0 B. ∆ >0 c. ∆ ≥ 0 D. ∆ = 0

1

∑

14. The length of the chord passing through the centre of a the circle of radius 4 cm is ------------ cm A. 2 B. 8 C. 4 D. 16 15. The angle subtended in the segment ACB is ------------A. Acute angle B. Obtuse angle C. Right angle D. straight angle 16. Two concentric circles are of radii 13 cm and 5 cm , then the length of the chord of the outer circle which touches the inner circle is ----- cm A. 13 B. 5 C. 8 D. 24 17. In the adj. fig XY l l BC, AX = p – 3 , BX = 2p – 2 and

AY 1 = , then ‘ p’ = --CY 4

A. 3 B.2 C.5 D. 4 18. The height of a rectangle is 4 units and its length is 4 times its height then the curved surface area of the cylinder is ------------- sq units A. 5h

2

B. 4 h2

C. 2h2

D.

1 2h 2

19. When a solid cone is melted and recast into a cylinder, which of the following does not changes? A. Total surface area B. Volume C. Curved surface area D. height 20. Which is the correct matrix of the given graph ? 0 3 0 A. 3 0 2 B. 0 2 0

0 0 3 0 3 2 C. 0 2 0

0 3 0 0 3 0 3 0 2 D. 0 3 2 2 0 0 0 2 0

Fill in the blanks 10*1=10 21. The set of numbers arranged according to some rule is called ---22. If a, H , b are in H.P, then H = --------------23. If the order of a given matrix is m x n, then the order of its transpose matrix is – 24. The formula A + ∑

fd x i is used to calculate N

25. The process of multiplying a surd with another surd is called ------26. A straight line which cuts the circle at two distinct points is called -------27. The converse of B.P.T is ---------28. The area of a square drawn on the hypotenuse of a right angle triangle is 144 sq.cm, then the length of the hypotenuse is ----- cm 29. A solid described by the rotation of a semicircle about a fixed diameter is ------2

30. A graph having only even nodes is called -----------Answer the following questions 18*2=36 31. If A = { Set of even numbers less than 11 } and B = { Set of perfect square number less than 11 }, then Show that A ∩ B = B ∩ A 32. There are seven passengers in a compartment of a train. 5 can speak Hindi, 4 can speak English and 2 can speak both the languages. How many passengers can speak (i) only Hindi ( ii) Only English. 5 x 1 1 3 11 4 + = . 5 5 6 7 11 12

33. Find ‘x’ If

34. Simplify by rationalizing the denomination

5+ 3 5− 3

35. Solve 6 y 2 y – 15 =0 using formula 36. Subtract 5 a +3 b from 8 a +5 b 37. If B =

3 2 a solve for ‘a’ and find the value of ‘a’ if B = 16 4

3

38. Construct a Cayley’s table for Z5 under multiplication modulo 5 39. Draw a circle of radius 4 cm, draw two radii such that the angle between them is 800.Draw two tangents at the ends of the radii. 40. Calculate the total surface area of a cone of radius 7 cm and slant height 10 cm. 41. Find the number of faces, vertices and edges of Dodaco hedron and also verify Euler’s formula 42. Draw a plan by using the data and scale given below ( Scale 20 m = 1 cm)

80 to D 60 to E

To C ( in metres) 200 180 120 80 40 From A

40 to B

43. In how many ways six different books (Kannada, English Hindi , Maths, Science and Social studies ) be arranged in a shelf such that maths and Science books are always together? 44. If Tn+6 = 35 and Tn+1 = 15 , then find c.d 45. The sum to n terms of arithmetic series is Sn = 2n2 +6n. Find the first term and the c.d. 3

46. Form a quadratic equation whose roots are 3 + 5 and 3 - 5 . 47. For what value of ‘m’ the roots of the equation x 2 + mx + 4 = 0 are distinct. 48. For the given graph identify the even and odd nodes. Verify the traversability of the graph

49. How many three digit numbers can be formed using 2,3,4,5 and 6 without repeat ion? How many of them are even? 6*3=18 50. Calculate the S.D for the following scores 10 ,20,30,40,50 51. Find the H.C.F of 2 a 3 – 3 a 2 – 9a + 5 and 2 a 4 – a 3 – 10 a 2 – 11 a+8 52. If ( a – b )3 = ( b – a ) 3 , then prove that ( a + b ) 3 = 8a 3 53. The base of a triangle is 4 cm longer than its altitude. If the area of the triangle is 48 sq. cm. Find its base and altitude. 54. Prove that “tangents drawn from the external point are equal”. 55. Find the ratio between the sums of first four terms to the sum of first eight terms of G.P. 4*4=16 56. Draw the graph for y = x 2 and y = 2 –x and hence solve the equation x 2 + x – 2 = 0 57. Construct two transverse common tangents to two circles of radii 3 cm and 2 cm, such that the centres are 8 cm apart. 58. Prove that “if two triangles are equiangular, then their corresponding sides are proportional”.

4

C.K.S GIRLS’ HIGH SCHOOL K.R. PURAM HASSAN X: Standard M Α ┼∏ ∋ M Α ┼ ⊥ CS Marks: 100 Model paper – 3 Time : 3 hours Choose the most appropriate answer for the following questions 20*1=20 1. If A, B & C are any three non empty sets, then (A ∩ B)U (A ∩ C) = A. AU(BUC) B. A ∩ (BUC) C. AU(B ∩ C) D. A ∩ (B ∩ C) 2. In an Geometric series if there are infinite terms , then S ∞ = A.

a (1 − r n ) a B. 1− r 1− r

C.

1− r a

D.

a (r n − 1) r −1

3. If A and B are any two matrix, then ( A B)1 =----D. AB A. B A B. B 1 A 1 C. A1 B1 4. Number diagonals drawn in a regular pentagon is ---A. 6 B. 5 C. 9 D. 21 5. The L.C.M of ( x + y ) and ( x – y ) is -----------A. ( x + y ) B. ( x – y)0 C. (x 2 + y 2 ) D.( x +y) ( x – y ) 6. The H.C.F and L.C.M of two expressions are 5 x 2 y 2 and 10 x 3 y 3 respectively, if one expression is 5 x 2 y 3, then the other expression is – A. 10 x 3 y 2 B.

1 10 x 3 y 2

C. 5 x 2 y2

D. 10 x 3 y3

7. The expression a 2 + b 2 + c 2 – ab – bc – ac can be expressed using ∑ notation as A. ∑ a(a − b) 2 B. ∑ a(a − b) C. ∑ a(a + b) D. ∑ a 2 + ab 8. If a+b+c= 2s, then a 2 – b 2 – c 2 + 2bc =---------A. 4 ( s-b)(s-c)B. 4s(s-b)(s – c) C. 4 ( s – b ) D. 4s ( s – c ) 9. If x − y is multiplied with its Rationalizing factor then the product so obtained is A. x +y B. x − y x + y C. ( x – y )2 D. ( x – y ) 10. An equation having 2 roots is called ------------A. linear equation B. pure quadratic equation C. straight line D. adefected quadratic equation 11. The roots of the equation m 2 – m = 6 are A. – 3 and – 2 B. – 3 and + 2 C. 3 and 1 D. 3 and -2 12. The roots of the given graph are --A. 0 & - 2 B. – 2 & 0 C. – 1 & 2 D. 2 & - 2

13. The quadratic equation having the roots 2 and 3 is – 1

A. x 2 – 5 x + 6 = 0 B. x 2+5x +6 = 0 C. x 2 – 6x + 5= 0 D. x 2 + 6x – 5 = 0 14. In the adj. fig secant is --------A. AC B. CDC. ABD. AD 15. If two circles touch each other externally, then distance between their centres is equal to ------. A. sum of their radii B, difference of their radii C. product of their radii D. division of their radii 16. The each face of Icosahedrons is A. equilateral triangle B. Square C. regular pentagon D. Right angle triangle 17. In the adj. fig LM 1 1 OP, MO = 8 m , ON = 2 m and OP = 1.5 m, then LM = ---- m A. 8 B. 1.5 C. 10 D. 7.5

18. The length of a tangent drawn to a circle of radius 8 cm from an external point which is at a distance of 10 cm is ------- cm C. 6 D. 10 A. 18 B. 164 19. The volume of a solid ----------- is

2 3 πr 3

A. sphere B. cylinder C. cone D. hemisphere 20. Area of base of a cone is 154 sq cm and height is 12 cm, then volume of the cone is -----A. 616 sq.cm B.616 c.c C. 1848 c.c D. 1848 sq.cm II. Fill in the blanks 10*1=10 21. In a G.P S 2 n ÷ S n =----------22. The eight term of an A.P is 23. The transpose of a matrix

11 , 12 1 3

then the eight term of H.P is --2 , then the matrix is -------4

24. The A.M of the marks scored by some students is 49.8 and sum of their scores is 498, then number of students =------25. The H.C.F of two expressions is 1, then the expressions are --26. The value of ∑ a(b − c) is --------a ,b,c

27. If the corresponding sides of two triangles are proportional, then the triangles are -------28. The triangle whose sides satisfies Pythagorean triplets is called -------- triangle 29. If two triangles intersect each other, then -----2

30. ------------- is a solid obtained by the rotation of a semicircle about a fixed diameter. III. Answer the following questions 18*2=36 31. If U = { 0,1,2,3,4,5,6,7,8,9} A = { 1,4,9} and B = { 3,6,9}, then show that (AUB)1 = A 1 ∩ B 1 32. There are seven passengers in a compartment of a train. 5 can speak Hindi , 4 can speak English and 2 can speak both the languages. How many passengers can speak (i) only Hindi ( ii) Only English. Draw Venn diagram. 33. In a G.P of six terms, the first and last terms are 5 and 160 respectively, Find the remaining terms. 34. The Harmonic mean of two numbers is 4, if one number is 6. Find the other number. 35. If 11 Pr = 990 Find ‘r’. x 2

3 x 1 0 1 − 2 = Find ‘x’ − 1 0 6 5 4 5 37. Find the product of 3 5 and 4 2

36. If

38. Simplify by rationalizing the denominator

2

−

2+ 3

2 2− 3

2

39. If the roots of the equation x – ( p + 2 ) x + 4 = 0 are equal. Find the value of ‘p’ 40. Construct Cayle’s table for S = { 1,5,7,11} under multiplication modulo 12 41. Construct two tangents to the circle of radius 4 cm from a point 5 cm away from the centre. 42. Find the total surface area of the cylinder, given that the diameter is 10 cm and height is 12.5 cm. 43. If B =

3 2 a solve for ‘a’ and find the value of ‘a’ if B = 16 4

44. Solve 2 p 2 – p = 15 using formula.

45. Sum of a number and its reciprocal is 5

1 . Find the number. 5

46. Draw a plan by using the data and scale given below ( Scale 20 m = 1 cm) To C ( in meteres) 220 120 to D 210 120 200 to B 180 to E 80 From A

3

3

2 1 0 47. Draw the graph for the matrix 1 4 1 0 1 2

48. Verify whether the network is traversable or not? If not give reason

IV. 6*3=18 49. From 8 gentlemen and 5 ladies, a committee of 6 is to be formed. In how many ways can this be done so that each committee contains at least 3ladies ? 50. The marks scored by 60 students in a mathematics test are given below Marks 10 20 30 40 50 60 (X) No. of 8 12 20 10 7 3 students Find the Variance and Standard Deviation of the marks 51. Find the L.C.M of m 4 + 3m 3 – m – 3 and m 3 + m 2 – 5 m + 3 52. If a+ b+ c = 2s , the prove that ( 2 b c +a2 – b 2 – c 2 ) ( 2 b c – a 2 + b 2 + c 2 ) = 16s ( s – a) ( s – b ) ( s – c )

53. A tree 32 m tall broke due to a gale and its top fell at a distance of 16 m from its foot. At what height above the ground did the tree break? 54. In two concentric circles of radii 6 cm and 10 cm with centre ‘O’ . Op is the radius of the smaller circle, OP ⊥ AB which cuts the outer circle at A and B. Find the length of AB. V. 4*4 =16 55. Find the sum of all natural numbers between 91 and 170 which are divisible by 5 56. Solve x 2 – x – 2 = 0 graphically 57. Construct two transverse common tangents to two circles of radii 4 cm and 3 cm, such that the centres are 9 cm apart. 58. Prove that “ Areas of similar triangles are proportional to squares of their corresponding sides”.

4

D.D.P.I HASSAN X: Standard

M Α ┼∏ ∋ M Α ┼ ⊥ CS

Marks: 100 Model paper – 4 Time : 3 hours I. Choose the most appropriate answer for the following questions; 1. If A = [ 2,3,4,5} and B = { 4,5}, then which one the following is a null set? D. B – A 20*1=20 A. A – B B. AUB C. A ∩ B 2. If the value of n is nearest to infinity, then S ∞ = a 1− r A. B. D. ar0 C. arn – 1 1− r a 0 4 x + 6 3. If A = is a scalar matrix then value of ‘x’ = --------2 x + 10 0 A. 2 B. 4 C. 3 D. 6 4. If 6 Pr =360, and 6 C r = 15, then the value of ‘r’ is ---A. 4 B. 15 C. 24 D. 36 5. The H.C.F of a 2 – 4 and a 2 – 5a + 6 is --A. a – 4 B. a – 2 C. a+ 4 D. a+ 2 6. The H.C.F and L.C.M of two algebraic expressions A and B are 5 x 2 y 2 and 10 x 2 y 2 respectively. If expression A = 5 x2 y 3, then the expression B =--A. 10 x y B. 10 x y 2 C. 10x 2 y D. 10 x 2 y 2 7. ∑ a 2 + ∑ 2ab =---------a ,b , c

a ,b , c

A. ( a – b ) 2 B. ( a + b ) 3 C. ( a 2 + b 2 + c 2 ) D. ( a+ b+ c) 2 8. If a+ b+ c = 2 s, the value of b + c – a = ----A. 2 s – a B. 2 ( s – a ) C. 2 ( s + a ) D. 2s + c 9. The product of 3 54 and 3 8 is ----b. 6 3 2 C2 3 2 D. 4 3 2 A. 3 3 2 10. Which one of the following is a pure quadratic equation? B. 3 x 2 + 1 = 28 C. x 2 – x – 7 = 0 D. x – x 2 = 0 A. 2 x 2 + x = 5 11. The roots of x 2 – 3 x = 0 are A. 0 , 3 B. 0 , - 3 C. 1, - 3 D. 1, 2 12. The value of discriminent of 2 x 2 = 5 x is ----A. 27 B. 25 C. 23 D. 10 13. Which one of the graph is named as parabola? A. Linear equation B. simultaneous equation C. quadratic equation D. polynomial equation 14. If the distance between the centres of two circles of radii 5 cm and 3 cm is 6 cm, then the circles, A. touch each other externally B. intersect each other C. touch each other internally D. concentric circles

1

15. ∆ ABC 111 ∆ PQR, area of ∆ ABC is 144 sq. cm and area of ∆ PQR is 196 sq.cm, if the altitude of ∆ ABC is 6 cm, then its corresponding altitude of ∆ PQR is --- cm A. 7 B. 3.5 C.. 12 D. 14 16. In the adj. fig. ∠PAO = 40 0 , Which measure of ∠POA makes AP as a tangent? A. 90 B. 60 C. 50 D. 40

17. AE, CE and CH are the tangents to the circle at B, D and F respectively. If CE = 10 cm and DE = 3.5 cm then the measure of BE = ---- cm A. 10 B. 6.5 C. 5 D. 3.5

18. The solid obtained by a semicircle on its diameter is ----A. Cone B. cylinder C. hemisphere D. Sphere 19. The volume of a cone is 90 cc.The volume of a cylinder whose radius and height are as same as the cone is ----- c c A. 30 B. 45 C. 90 D. 270

2 1 0 20. The given matrix is a network of ----- 1 4 1 0 1 2 A.

B.

C.

D.

Fill in the blanks 10*1=10 21. The c.d. of A.P is ---22. If a, H , b are in H.P, then H = --3a 0 23. If A = is a skew symmetric matrix then ‘a’ =-a − 8 0 24. If ∑ fd 2 =210 and σ 2 = 21, then N = ----25. The L.C.M of a 2 – b 2 and a 3 – b 3 is -----26. If ∑ a = 0 , then ∑ a 3 = --a ,b , c

a ,b ,c

27. If the perimeter of a square is 20 cm , then the length of the diagonal is --- cm 28. Polygons which are always similar ----29. In a right angled triangle, the longest side is ---Solve the following 18*2=36 30. The formula used to calculate the curved surface area of a cone is ---31. Out of 7 members of a compartment of a train, 5 can speak Kannada, 2 can speak both English and Kannada, and then how many can speak only English. Draw venn diagram. 32. If U = { 0 , 1, 2, 3,4 } A = { 2,3,4} and B = { 0 , 2, 3 }Find ( A ∩ B)1 2

33. The Harmonic mean of two numbers is 4, if one number is 6 find the other 34. Verify n C r + n C r − 1 = n +1 C r for n = 6 and r = 4 1 2 2 3 35. If A = and B = Find AB 3 4 4 − 5 36. 5 Girls are participating in a competition having 3 different prizes. In how many ways can they win the prizes? 37. Subtract ( 5 a − 3 b ) from (8 a + 5 b ) 38. Simplify by rationalizing the denominator

5+ 3

5− 3 39. The sum of the two numbers is 18 and sum of their square is 290. Find the numbers x 2 9 40. Solve for ‘x’ − = 2 x 5 41. If ( a + 8)2 – 5 = 31. Find ‘a’ 42. Form a quadratic equation whose roots are 3 ± 5 43. Construct a cay ley’s table for Z4, under multiplication modulo 4 44. Construct two tangents to a circle of radius 4 cm from an external point 13 cm away from the centre. 45. The circumference of the base of the cylinder is 44 cm and height 10 cm, then find its curved surface area. 46. Draw a plan for the following data using the scale given below ( 25 m = 1 cm )

50 to C 25 to B

To D ( in meteres) 200 150 100 50 From A

75 to E

47. Construct the matrix for the given graph 48. Verify Euler’s formula for square based pyramid n

49. If P4 = n C 5 , then find ‘n’ 6*3=18 50. Calculate the Standard deviation for the following scores C–I 1-5 6-10 11-15 16-20 F 2 3 4 1 51. The product of two algebraic expressions are a 4 – 9 a 2 + 4 a + 4a +12, if the H.C.F is a – 2, then Find L.C.M 52. If a + b + c = 12, and a 2 + b 2 + c 2 = 50. Find ab + b c + ca 53. The areas of two similar triangles are 392 sq.cm and 20 sq.cm. Find the ratio of their corresponding sides. 54. The sides of a quadrilateral are tangents to the circle, if AB = 8 cm and CD = 5 cm, then Find AD +BC 55. Find the three numbers of A.P whose sum and product are 24 and 440.4*4=16

3

56. Draw the graph of y = x 2 and y = 2 x + 3 and hence solve the equation x 2 – 2 x–3=0 57. Construct two Direct common tangents to two circles of radii 5 cm and 3 cm whose centres are 10 cm apart. Measure the length of the tangents. 58. Prove that “ In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of other two sides”.

4

D.D.P.I HASSAN M Α ┼∏ ∋ M Α ┼ ⊥ CS

X: Standard

Marks: 100 Model paper – 5 Time : 3 hours I. Choose the most appropriate answer for the following questions;

1. The law (AUB)UC = AU(BUC) represents 20*1=20 A. union of sets is commutative B. Union of sets is associative C. union of sets is distributive over Intersection D. Intersection of sets is distributive over Union 2. The formula used to calculate the sum to n terms of Geometric series is a (1 − r n ) rn −1 n(n + 1) n B. (n 2 + 1) C. D. (1 − r ) a (r − 1) 2 2 1 3 3. If A = then A 1 = --- 2 4

A.

1 2

4. 5.

6. 7.

1 3

1 2

1 3

A. C. D. B. 2 4 4 3 3 4 4 2 If n P3 = 120 , then ‘n’ = ---A. 12 B. 10 C. 8 D. 6 The H.C.F of two algebraic expressions is a x and their L.C.M 12 a x 2b 3 y. if one expression is 4 a xy, then the other expression is C. 3x 2 a b 3 D. 3xab2 A. 3xa2b2 B. 3x2a The H.C.F of ( a + b ) and ( a – b ) is --A. ( a + b ) B. ( a 2 – b 2) C. 1 D. 0 The value of ∑ ( x + y ) is x, y, z

A. x + y + z B. 2 x + 2y + 2 z C. 3 x + 3y + 3 z D. 3xyz 8. The expression a 2 + b 2 + c 2 – a b – bc – ca can be expressed using ∑ notation as A.

∑a a ,b , c

2

−

∑a a ,b , c

B.

∑a a ,b , c

2

+

∑a a ,b , c

C.

∑a a ,b , c

2

+

∑ ab a ,b , c

D.

∑a a ,b , c

2

−

∑ ab a ,b , c

9. The factors of which expression are (a +b) and ( a 2 + b 2 – a b) A. a 3 + b 3 B. a 3 – b 3 C. ( a + b ) 3 D. ( a – b ) 3 10. If 2 − 3 is subtracted from 3 − 2 then A. 2 ( 2 − 3 ) B. 2( 3 − 2 ) C. 0 D. 1 11. The quadratic equation whose roots are 5 and – 6 A. x 2 – 30x – 1 = 0 B. x 2 – x – 30 = 0 2 C. x + x – 30 = 0 D. x 2 – x + 30 = 0

1

1 2 gt , then ‘t’ = -----2 2s 2s 2g B. C. A. ± g g s

12. If S =

D. ±

2g s

13. The discriminent of the equation ax 2 + b x + c = 0 is A. b 2 – 4 a c B. b 2 + 4 a cC. b – 4 a c D. b + 4 a c 14. If the roots of the equation x 2 + mx + 4 = 0 are equal , then ‘m’ =A. ± 4 B. ± 2 C. 0 D. ± 1 15. The angle between the radius and the tangent to the circle is ----A. 30 B. 180 C. 90 D. 60 16. In the adj. fig XY 11 AB,AX = 9 c.m, XC = 7 cm and BC= 20 cm, then BY = --- cm A. 11.25 B. 10.25 C. 10 D. 15 17. In the adj. fig the length of OP = ---- cm A. 5 B. 4 C. 3 D. 25 18. The circumference of the base of the cylinder is 14 cm and height is 20 cm, then Curved surface area of the cylinder is ---- sq.cm A. 280 B. 1760 C. 880 D. 140 19. The formula used to calculate Total surface area of a cone is A. 2 π r(r+h)

B. π r9r+h) C. π r(r+l)

D.

1 2 πr h 3

20. The matrix for the given graph is 0 3

3 0

3 3

2 3

A. B. 0 3 C. 3 3 D. 3 2 3 0 Fill in the blanks 10*1=10 21. The formula used to calculate the nth term of G.P is ----22. If the S.D of some scores is 0.9, then its variance is 23. If a, H b are in H. P, then H = ---24. If A = A1, then the matrix A is called ----25. The H.C.F of 3 a – 15 and 3 a 2 – 75 is ----26. The value of ∑ x 2 is ---------x, y, z

27. The mathematician who proposed B.P.T is ---28. The formula used to calculate the volume of a hemisphere is 29. Number of faces in a regular hexagon=---------30. The rationalizing factor of p q − q p is ---Solve the following 18*2=36 31. If A={ 1,2} B = { 2,3,5} and C = { 2,3,6,8}, then show that A ∩ ( B ∩ C) = ( AUB) ∩ ( AUC) 32. In a class of 60 students, 22 students play volley ball , 12 students play both Volley ball and Kho-Kho. If 17 students do not play any

2

of these, then how many of these play only Kho- Kho. Draw Venn diagram. 33. In a G.P If T6 = 32 and r = 2, then find the first term 34. In a H.P, if T4 =

1 1 and T10= Find ‘a’ and ‘d’ 12 42

2 3

1 35. If A = Find A A 5 1 36. How many three digit numbers can be formed using the digits 2,3,4,5 and 6 without repeatition? How many of them are even? 37. Simplify 28 + 5 2 + 200

38. Simplify by rationalizing the denominator

3 3− 2

2

39. If one root of the equation x + px + q = 0, is three times the other, then prove that 3 p 2 = 16 q 40. Solve (x + 4 ) ( x – 4 ) = 6x 41. Construct Cayley’s table for Z4 under multiplication modulo 4 42. If m and n are the roots of the equation x 2 – 2 x + 4 = 0, form a quadratic equation whose roots are m 2 and n 2 . 43. Solve x 2 – 2x + 4 = 0 using formula. 44. In a circle of radius 3.5 cm. draw two radii such that the angle between them is 1100. Construct two tangents at the ends of the radii. 45. Verify Eulers’ formula for the given polyhedral solid

46. Draw a plan for the following data using the scale given below To D ( in meteres) 150 100 70 to C 80 to E 80 30 40 to B From A 47. The surface area of the sphere is 616 sq. cm. Find the diameter of the sphere. 0 3 0 48. Draw the graph for the given matrix 3 0 2 0 2 0

3

49. From 5 gentlemen and 3 ladies , a committee of 5 is to be formed. In how many ways can this be done so that each committee contains at least 2 ladies ? 6*3=18 50. Calculate Standard Deviation for the following scores 10 ,12 ,14, 16 ,18 , 20 51. The H.C.F and L.C.M of two algebraic expressions are ( x – 3 ) and ( x 3 – 5 x 2 – 2 x + 24 ) . If one expression is x 2 – 7x + 12 find the other expression. 52. If a +b +c = 2s prove that a 2 – b 2 – c 2 + 2 b c = 4 ( s – b) ( s – c ) 53. An insect is 8 m away from the foot of a lamp post which is 6 m tall, crawls towards it. After moving through a distance, its distance from the top of the lamp post is equal to the distance it has moved. How far is the insect away from the foot of the Lamp post? 54. Prove that “ If two circles touch each other, the point of contact and the centers of the circles are collinear”. 55. Find the three numbers of A.P whose sum and product are 12 and 48 respectively. 4*4=16 2 56. Draw the graph for y = x and y = 2x + 3 and hence solve the equation x 2 – 2 x- 3 =0 57. Prove that if two triangles are equiangular, then their corresponding sides are proportional. 58. Construct two Direct common tangents to two circles of radii 4 cm and 3 cm whose centers are 9 cm apart.

4

D.D.P.I HASSAN M Α ┼∏ ∋ M Α ┼ ⊥ CS

X: Standard

Marks: 100 Time : 3 hours

Model paper – 6

Choose the most appropriate answer for the following questions 1. Which of the following is Demorgan’s law? 20*1=20 A. A ∩ (BUC)= ( A ∩ B)U(A ∩ C) B. AU(B ∩ C)= (AUB) ∩ (A ∩ C) C. (AUB)1 = A1 ∩ B1 D(AUB)1 = A 1 U B 1 2. The c. r of the G.P, 3,6, 12, 24……………… A. 12 B. 6 C. 3 D. 2 2 4 1 1 3. If A = ,then (A ) = ---------6 8 2 4 2 6 2 8 2 6 A. B. C. D. 6 8 4 8 6 4 8 4 4. Which of the following relation is true? A. n P0 = n B. n Pn = n! C. n P1 = n! D. n Pr = n 5. The L.C.M of 2 a b and 6 a c 2 is ----A. 12ab B. 6 a b 2 c 2 C. 6 a 2 b 2 c 2 D. 6 a b c 2 6. The H.C.F and L.C.M of two algebraic expressions are 5 x 2 y 2 and 10 x 3 y 3 respectively. If one expression is 5 x 2 y 3, then the other expression is --A. 10 x 3 y 2 B. 10 x 2 y 3 C. 10 x 2 y 2 D. 10 x 3 y 3

7. The expression ( y – z ) 2 + ( z – x ) 2 + ( x – y ) 2 can be written using ∑ notation as A.

∑ ( z − y) x, y, z

2

B.

∑ ( y − x)

2

x, y, z

C.

∑ ( x − y) x, y, z

2

D.

∑ ( z + x)

2

x, y, z

8. The factors of ( a 3 – b 3 ) are A. ( a+ b ) 3 B. ( a – b ) 3 C. ( a – b ) ( a 2 + ab + b 2 )D. ( a + b ) ( a 2 - ab + b 2 ) 9. Which of the following is a pure quadratic equation? 2 2 A. x 2 + 2 = 2 x B. 5x = x ( x + 2 ) C. x + D. y = +1 x 3y 10. The factors of x ( 3x – 1 ) = 0 are 1 1 A. 0 , 3 B. 0 , C. 1, 3 D. 0 , 3 3 11. The nature of the roots of the equation x 2 – 6x + 9 = 0 is A. Real and rational B. Real and rational C. equal D. imaginary 12. The product of the roots of the equation a x 2 + b x + c = 0 is c −b b a A. B. C. D. a a a c

1

13. The angle in the minor segment is --B. Acute angle A. Right angle

C. Obtuse angle

D. Straight

14. In the adj. fig. ∆ AXY 1 1 1 ∆ ABC , the angle corresponding to ∠AXY is – B. ∠AYX C. ∠ACB D. ∠BXY A. ∠BAC

15. If two circles of radii 3.6 cm and 2.2 cm touch each other externally, then the distance between their centers is ---- cm A. 5.8 B. 1.4 C. 5 D. 1.5

16. In the adj. fig, If AP = 3 cm, and PC = 8 cm, then the length of CD = --- cm A. 3 B. 5 C. 8 D. 11

17. The formula used to calculate the total surface area of a cone is A. π rl B. 2 π rh C. π r( r+ l) D. 2 π r( r + h) 18. The radius and height of a cone and cylinder are equal, if the volume of the cylinder is 81 c.c then volume of a cone is ----- c.c A. 3 B. 8 C. 27 D. 81 19. If the curved surface area of a hemisphere is 308 sq.cm, then its total surface area is ----sq.cm A. 154 B. 308 C. 316 D. 616 20. The Euler’s formula for network is A. R+N = A+ 2 B. A+ N = R + 2 C. R + N = N + 2 D. N + R = A +2 Fill in the blanks 10*1=10 21. The next term of the G.P 5, 10, 20 …………. is -----22. The nth term of the H.P is ----23. If A = - A 1, then the matrix A is ---24. The formula used to calculate C.V is -------25. The relationship between H.C.F ( H ) and L.C.M ( L ) of two expressions A and B is --------26. The value of ∑ a (b − c) is ------a ,b,c

27. The rationalizing factor of 5 − 3 is ---------28. Areas of two similar triangles are 60 sq.cm and 15 sq.cm, then ratio of their corresponding sides is --------2

29. In ∆ XYZ if X Z 2 = XY 2 + Y Z 2 then right angle vertex is ---30. PA & PB are the tangents drawn to the circle as shown in the fig. if ∠AOB = 140 0 , then ∠APB = -----------

Solve the following 18*2=36 31. If A = { 5,10,15, 20} B = { 5,15,20, 30 ,35} and C ={ 5,10, 25} Find A ∩ (BUC) 32. There are 60 students in a class. Every student learns at least one o fhte subjects Kannada or English. 45 students offer Kannada and 30 students offer English. How many students do not offer any of these subjects? Draw Venn diagram. 33. Find the sum the series 2+ 4+ 8 + --------- upto 10 terms 34. Find the Harmonic mean between 9 and 16 2 x 1 3 2 9 3 35. Find ‘x’ if + = 0 4 2 1 2 5 36. Simplify 4

3 − 3 12 + 2 75

10

37. Simplify by rationalizing the denominator

7+ 2 38. If K =

1 mv 2 , then solve for ‘v’ and find the value of ‘v’ when K = 100 and 2

m=2

39. Solve m 2 – 2m – 2 = 0 using formula. 40. The product of two consecutive number is 182. Find the numbers 41. Form a quadratic equation whose roots are (1 -

5 ) and (1 +

5)

42. Find the number of combination of the letters of the word “ CHEMISTRY”. 43. Construct Cayley’s table for Z5 under multiplication modulo 5 44. Draw a circle of radius 5.5 cm , construct two tangents to the circle from an external point 3.5 cm away from the circle

45. Circumference of the base of the cylinder is 44 cm and height is 10 cm .Calculate the curved surface area. 46. Plan the sketch for the following data To D ( in meteres)

3

80 to E

150 100 80 30 From A

70 to C 40 to B

2 1 0 47. Draw the graph for the given matrix 1 4 1 0 1 2

48. Identify the even and odd nodes for the given graph and verify whether it is a traversable or not?

49. In how many ways can 4 people be selected from a group of 6 among which Ashok is one ? How many of these include Ashok? 6*3=18 50. The marks scored by 60 students in a mathematics test are given below Scores(X) 10 20 30 40 50 60 No. of 8 12 20 10 7 3 sts(f) Calculate the Variance and Standard Deviation of the marks

51. Find the H.C.F of 4 a 3 – 11 a 2 + 25 a + 7 and 2 a 3 – 5 a 2 + 11 a + 7 52. If a+ b+ c = 2 s, then prove that a 2 – b 2 – c 2 + 2bc = 4 ( s – b ) ( s – c ) 53. A man walks 8 km due North, then 5 km due East and 4 km to North. How far is he from the starting point? 54. Three circles of radii 3 cm , 4 cm, and 5 cm, with centres A , B and C touch each other externally. Find the perimeter of the triangle ABC. 55. The fifth and tenth terms of an A.P are in the ratio 1 : 2 and T12 = 36. Find the A.P 4*4 =16 2 56. Draw the graph for y = x an y = 2x + 3 and hence solve the equation x 2 - 2x – 3 = 0 57. Construct two Direct common tangents to two circles of radius 4 cm and 2 cm, whose centres are 10 cm apart. 58. Prove that “ if two triangles are equiangular, then their corresponding sides are proportional”.

4

SSLC Mathematics Question Bank 2012

Published on Feb 4, 2012

SSLC Mathematics Question Bank 2012 from Hassan District Mathematics Teachers' Club, Hassan

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