sslc mathematics question bank 2012
DESCRIPTION
SSLC Mathematics Question Bank 2012 from Hassan District Mathematics Teachers' Club, HassanTRANSCRIPT
S S L C
MATHEM ATICS - 2012MODEL QUESTION PAPERS
HASSAN DISTRICT MATHEMATICS TEACHERS’ CUBURL: http://hassanmathsclub.blogspot.com
http://freeganita.com/ & www.eshale.org/qkosha/
DEPARTMENT OF PUBLIC INSTRUCTIONHASSAN
1
C.K.S GIRLS’ HIGH SCHOOL K.R. PURAM HASSAN
X: Standard MΑ┼∏ ∋MΑ┼ ⊥ 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 -------
A. ( AUB) 1 = A
1 U B
1 B. ( A ∩ B)
1 = A
1 ∩ 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 r
nP and r
nC is
A. r
nP = r
nC B. r
nP =
!r
Cr
n
C. r
nP =
!r
Pr
n
D. !rC
p
r
n
r
n
=
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 . . . . . . . . . . . . . . . . . . .
8. If A =
−
+
112
31
x
x is a symmetric matrix , then ‘x’ = ---
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 nm 32 − is -------
A. nm 32 − B. nm 32 + C. nm 32 − D. nm 32 +
Ans . . . . . . . . . . . . . . . . . . .
2
11. If 0,,
=∑zyx
x , then x 2 + y
2 – z
2 + 2 xy = -----
A. 2yz B. 0 C. x 2 + y
2 + 2xy – z
2 D. ( x + y )
2 + z
2
Ans . . . . . . . . . . . . . . . . . . . 12. If ∑ =
cba
a,,
2 16 and ∑ =
cba
ab,,
92 , then a+b+c = ----
A. 0 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 c
2 , 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. 2
2
h
l B. 22
hl + C. 22hl −± D. 22
lh −
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 --------
A. x 2 + 4 x + 1 = 0 B. x
2 – 4 x + 1 = 0
C. x 2 + 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 ---------
A.
010
110
010
B.
010
121
010
C.
011
102
120
D.
010
102
020
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 . . . . . . . . . . . . . . . . . . .
3
II. Fill in the blanks 10*1=10
21. The nth term of the sequence 2
1,
3
2,
4
3. . . . . . . . . . is ----------
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 3 108⊕ 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 ∑ −
zyx
zyx,,
)( is ----------
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?
4
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
5
36. If A =
−
53
21, Find A x A
1
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
38. If a+b+c=0, then prove that 333
++
++
+
c
ba
b
ac
a
cb= - 3
6
39. Simplify by rationalizing the denominator 23
2
23
5
−
−
+
40. If K = 2
1mv
2, then solve for ‘v’ and find the value of ‘v’
when K = 100 and m = 2
41. Factories 2 ( a 2 – 1 ) = a ( 1 – a )
7
42. Find the sum and product of the roots of the equation
2 x 2 + 5 x – 8 = 0
43. Construct Cayley’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
8
45. Verify Euler’s formula for square based pyramid
46. Draw the network for the matrix
210
141
012
47. Draw a plan by using the data and scale given below
( Scale 20 m =1 cm)
To D
(in meteres)
80 to D
50 to E
180
120
60
20
70 to B
From A
9
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
10
50. Divide Rs 20 into two parts such that sum of their reciprocal is 15
4
51. Find the L.C.M of x 3 – 2 x
2 – 13 x – 10 and x
3 – x
2 – 10 x - 8.
11
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
12
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 4*4=16
C-1 F
5-9 2
10-14 4
15-19 8
20-24 5
25-29 1
N= 20
13
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”.
14
58. Construct Transverse common tangents to two circles of radii 4 cm
and 2.5 cm, whose centres are 10 cm apart.
1
D.D.P.I HASSAN X: Standard MΑ┼∏ ∋MΑ┼ ⊥ 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. If A =
41
23 and I =
10
01, then I A = ---------
A.
41
32 B.
41
23C.
14
32 D.
42
13
4. The value of 3Pn 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 )
5. 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
6. The L.C.M and H.C.F of 2 a b and 6 a c2 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
7. If ∑cba
a,,
= 0 , then
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. ∑ +
zyx
xx,,
2 B. ∑ −
zyx
xx,,
2 C. ∑ + xx2 D. ∑ +
zyx
yx,,
2
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
2
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 4
1=
CY
AY, then ‘ p’ = ---
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 h
2 C. 2h
2 D.
22
1
h
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 ?
A.
020
203
030
B.
020
230
300
C.
002
203
030
D.
020
230
030
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 xN
fdA
+∑
i is used to calculate
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 -------
3
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.
33. Find ‘x’ If
=
+
1211
411
76
31
55
15x.
34. Simplify by rationalizing the denomination 35
35
−
+
35. Solve 6 y 2 y – 15 =0 using formula
36. Subtract 5 a +3 b from 8 a +5 b
37. If B = 2
4
3a solve for ‘a’ and find the value of ‘a’ if B = 16 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)
To C
( in metres)
80 to D
60 to E
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.
4
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”.
1
C.K.S GIRLS’ HIGH SCHOOL K.R. PURAM HASSAN
X: Standard MΑ┼∏ ∋MΑ┼ ⊥ 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. r
ran
−
−
1
)1( B.
r
a
−1 C.
a
r−1 D.
1
)1(
−
−
r
ran
3. If A and B are any two matrix, then ( A B)1 =-----
A. B A B. B 1 A
1 C. A
1 B
1 D. AB
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.
2310
1
yx C. 5 x
2 y
2 D. 10 x
3 y
3
7. The expression a 2 + b
2 + c
2 – ab – bc – ac can be expressed using
∑ notation as
A. ∑ −2
)( baa B. ∑ − )( baa C. ∑ + )( baa D. ∑ + aba2
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 yx − is multiplied with its Rationalizing factor then the
product so obtained is
A. x +y B. yx − yx + 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 –
2
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. CD C. AB D. 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
A. 18 B. 164 C. 6 D. 10
19. The volume of a solid ----------- is 3
3
2rπ
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 nn SS ÷2 =-----------
22. The eight term of an A.P is 12
11, then the eight term of H.P is ---
23. The transpose of a matrix
43
21, then the matrix is --------
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 ∑ −
cba
cba,,
)( is ---------
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 ------
3
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 rP11 = 990 Find ‘r’.
36. If
=
−−
56
10
01
12
54
32 xx
Find ‘x’
37. Find the product of 3 5 and 4 2
38. Simplify by rationalizing the denominator 32
2
32
2
−
−
+
39. If the roots of the equation x 2 – ( 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 = 2
4
3a solve for ‘a’ and find the value of ‘a’ if B = 16 3
44. Solve 2 p 2 – p = 15 using formula.
45. Sum of a number and its reciprocal is 5 5
1. Find the number.
46. Draw a plan by using the data and scale given below
( Scale 20 m = 1 cm)
To C
( in meteres)
120 to D
180 to E
220
210
120
80
200 to B
From A
4
47. Draw the graph for the matrix
210
141
012
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
(X)
10 20 30 40 50 60
No. of
students
8 12 20 10 7 3
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 +a
2 – 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”.
1
D.D.P.I HASSAN X: Standard MΑ┼∏ ∋MΑ┼ ⊥ 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?
A. A – B B. AUB C. A ∩ B D. B – A 20*1=20
2. If the value of n is nearest to infinity, then ∞
S =
A. r
a
−1 B.
a
r−1 C. ar
n – 1 D. ar
0
3. If A =
+
+
1020
064
x
xis a scalar matrix then value of ‘x’ = ---------
A. 2 B. 4 C. 3 D. 6
4. If rP6 =360, and rC
6 = 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 x
2 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. ∑∑ +
cbacba
aba,,,,
2 2 =----------
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 -----
A. 3 3 2 b. 6 3 2 C 2 3 2 D. 4 3 2
10. Which one of the following is a pure quadratic equation?
A. 2 x 2
+ x = 5 B. 3 x 2 + 1 = 28 C. x
2 – x – 7 = 0 D. x – x
2 = 0
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
2
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. 040=∠PAO , 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
20. The given matrix is a network of -----
210
141
012
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 = ---
23. If A =
− 08
30
a
a is a skew symmetric matrix then ‘a’ =--
24. If ∑ 2fd =210 and 2
σ = 21, then N = -----
25. The L.C.M of a 2 – b
2 and a
3 – b
3 is ------
26. If 0,,
=∑cba
a , then ∑cba
a,,
3 = ---
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
3
33. The Harmonic mean of two numbers is 4, if one number is 6 find the other
34. Verify 1−+ r
n
r
nCC = r
nC
1+ for n = 6 and r = 4
35. If A =
43
21 and B =
− 54
32 Find AB
36. 5 Girls are participating in a competition having 3 different prizes. In
how many ways can they win the prizes?
37. Subtract ( 5 ba 3− ) from (8 ba 5+ )
38. Simplify by rationalizing the denominator 35
35
−
+
39. The sum of the two numbers is 18 and sum of their square is 290. Find the
numbers
40. Solve for ‘x’ 5
92
2=−
x
x
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 )
To D
( in meteres)
50 to C
25 to B
200
150
100
50
75 to E
From A
47. Construct the matrix for the given graph
48. Verify Euler’s formula for square based pyramid
49. If 54 CPn
n
= , 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
4
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”.
1
D.D.P.I HASSAN X: Standard MΑ┼∏ ∋MΑ┼ ⊥ CS 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. 2
)1( +nn B. )1(
2
2+n
n C.
)1(
)1(
r
ran
−
− D.
)1(
1
−
−
ra
rn
3. If A =
42
31 then A
1 = ----
A.
34
21 B.
42
31 C.
43
21 D.
24
31
4. If 1203 =Pn , then ‘n’ = ----
A. 12 B. 10 C. 8 D. 6
5. 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 -
A. 3xa2b
2 B. 3x
2a C. 3x
2 a b
3 D. 3xab
2
6. The H.C.F of ( a + b ) and ( a – b ) is ---
A. ( a + b ) B. ( a 2 – b
2) C. 1 D. 0
7. The value of ∑ +
zyx
yx,,
)( is
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. ∑∑ −
cbacba
aa,,,,
2 B. ∑∑ +
cbacba
aa,,,,
2 C. ∑∑ +
cbacba
aba,,,,
2 D. ∑∑ −
cbacba
aba,,,,
2
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 32 − is subtracted from 23 − then
A. 2 ( 32 − ) B. 2( 23 − ) 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
C. x 2 + x – 30 = 0 D. x
2 – x + 30 = 0
2
12. If S = 2
2
1gt , then ‘t’ = ------
A. g
s2± B.
g
s2 C.
s
g2 D.
s
g2±
13. The discriminent of the equation ax 2 + b x + c = 0 is
A. b 2 – 4 a c B. b
2 + 4 a c C. 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. 2π r(r+h) B. π r9r+h) C. π r(r+l) D. hr2
3
1π
20. The matrix for the given graph is
A.
03
30B.
30
03C.
33
33 D.
23
32
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 ∑zyx
x,,
2 is ----------
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 pqq − 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
3
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 = 12
1 and T10=
42
1Find ‘a’ and ‘d’
35. If A =
15
32 Find A A
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 2002528 ++
38. Simplify by rationalizing the denominator 23
3
−
39. If one root of the equation x 2 + 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)
80 to E
150
100
80
30
70 to C
40 to B
From A
47. The surface area of the sphere is 616 sq. cm. Find the diameter of
the sphere.
48. Draw the graph for the given matrix
020
203
030
4
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
56. Draw the graph for y = x 2 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.
1
D.D.P.I HASSAN X: Standard MΑ┼∏ ∋MΑ┼ ⊥ CS Marks: 100
Model paper – 6 Time : 3 hours
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 = A
1∩ B
1
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
3. If A =
86
42,then (A
1)
1 = ----------
A.
86
42 B.
84
62 C.
46
82 D.
48
62
4. Which of the following relation is true?
A. nPn
=0 B. =n
nP n! C. =1P
n n! D. =r
nP 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. ∑ −
zyx
yz,,
2)( B. ∑ −
zyx
xy,,
2)( C. ∑ −
zyx
yx,,
2)( D. ∑ +
zyx
xz,,
2)(
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?
A. x 2 + 2 = 2 x B. 5x = x ( x + 2 ) C. x +
x
2 D. y = 1
3
2+
y
10. The factors of x ( 3x – 1 ) = 0 are
A. 0 , 3 B. 0 , 3
1 C. 1, 3 D. 0 , -
3
1
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
A. a
c B.
a
b− C.
a
b D.
c
a
2
13. The angle in the minor segment is ---
A. Right angle B. Acute angle C. Obtuse angle D. Straight
14. In the adj. fig. ∆ AXY 1 1 1 ∆ ABC , the angle corresponding to AXY∠ is –
A. BAC∠ B. AYX∠ C. ACB∠ D. BXY∠
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. 2π rh C. π r( r+ l) D. 2π 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 ∑ −
cba
cba,,
)( is -------
27. The rationalizing factor of 35 − is ----------
28. Areas of two similar triangles are 60 sq.cm and 15 sq.cm, then ratio of their
corresponding sides is ---------
3
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 0140=∠AOB , 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
35. Find ‘x’ if
=
+
52
39
12
23
40
12x
36. Simplify 4 7521233 +−
37. Simplify by rationalizing the denominator 27
10
+
38. If K = 2
2
1mv , then solve for ‘v’ and find the value of ‘v’ when K = 100 and
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)
4
80 to E
150
100
80
30
70 to C
40 to B
From A
47. Draw the graph for the given matrix
210
141
012
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
sts(f)
8 12 20 10 7 3
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
56. Draw the graph for y = x 2 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”.