Mathematics - Unit Test
Moder Paper
Weightage Tables
Table : 1
Weightage to Academic Standards
S. No.
Academic Standards
Weightage %
Marks
1.
Problem Solving
40
10
2.
Reasoning & Proof
20
5
3.
Communication
12
3
4.
Connnections
16
4
5.
Representation & Visualisation
12
3
100%
25
Total
Table : 2
Weightage to Content
S. No.
Chapter
Weightage %
Marks
1.
Real numbers
48%
12
2.
Sets
20%
5
3.
Polynomials
32%
8
100%
25
Table : 3
Weightage to difficulty level
S. No.
Difficulty level
Weightage %
Marks
1.
Easy
24%
06
2.
Average
52%
13
3.
Difficulty
24%
06
100%
25
Table : 4
Weightage to type of questions
S. No.
Type of Questions
1.
Objective
2.
3.
Weightage %
No. of Questions
Marks
28%
07
07
Short Answer
40%
05
10
Essay
32%
02
08
100%
14
25
1
2
Real Numbers
Sets
Polynominals
2.
3.
Content
1.
S. No.
-
(1)1
02
(2)1 (2)2 (1)4 10
(1)4 05
-
(1)2
-
03
(1)1
-
(1)1
-
-
-
-
01
- (1)4 05
-
-
- (1)4 04
-
-
-
(1)2 -
-
(1)1 (1)2 -
-
-
(1)1
03
-
02
01
-
-
(2)1 (1)2
(1)1
-
(1)1 (1)2
Representation
-
-
-
-
04
01
-
03
-
-
(1)2 -
-
-
(1)1 (1)2 -
-
-
(1)1
03
02
-
01
25
08
05
12
E Total Obj SA E Total Total
Connection
E Total Obj SA E Total Obj SA
Reasoning & Proof Communication
E Total Obj SA
-
SA
(1)1 (1)2
Obj
Problem Solving
Academic Standards
Blue Print
Unit: Containing Chapters Real Numbers, Sets & Polynominals
Mathematics - Unit Test
(Real numbers, sets, Pohynomials)
Class: X
Max Marks: 25
Time: 45 min
Instructions:
· The question paper consists of three sections.
· All questions are compulsory.
Section - I
7 ´ 1 = 7 marks
Note:
1. Answer all the questions. Each question carries 1 mark.
2. Choose the correct anwer from the four alternatives given for each question and write capital letters A, B, C or D in the brackets.
1.
2.
The prime factorisation form of 156
A) 2 ´ 3´ 13
B) 22 ´ 32 ´ 13
The
A)
4.
7
23
7
16
C)
B) 1 and 2
3
8
D)
B) A Ç B ¹ q
C) A - B = A
B)
3
2
C)
-2
3
B)
C) x +
2x + 5
D)
3
1
x
)
(
)
(
)
(
)
(
)
D) A- B = f
-3
2
one of the following algebraic expression is not a polynomial
A) - 2x 2
(
D) -1 and 1
The zero of the polynomial 2x-3
2
3
)
7
22
3
lies between
4
C) 3 and 4
(
D) log2 x = 8
A = {x / x is a boy} B = {x / x is a girl} them
A)
7.
B)
Which of the following integers does
A) A È B = f
6.
C) logx 2 = 8
p
form of the decimal 0.875
q
A) 0 and 1
5.
B) log8 2 = x
)
D) 2 ´ 32 ´ 13
The logarithemic form of 8x = 2
A) logx 8 = 2
3.
C) 22 ´ 3 ´ 13
(
D) 5 - 2x
Section - II
5 ´ 2 = 10 marks
Note:
1. Answer all the questions.
2. Each question carries 2 marks.
8.
Write the following rationals as decimals without actual division
i)
9.
13
25
Expand log
ii)
143
110
x3
y2
10.
If A = {1, 2, 3}, B = {2, 3, 4, 5} find A È B and A Ç B
11.
Write the following sets in roster form
(i) A = The set of natural numbers less than 7
(ii) B = {x : x is a letter in the word ‘School’}
12.
Draw the graph of P(x) = x-2 and find where it interesects X-axis.
Section - III
2 ´ 4 = 8 marks
Note:
1. Answer all the questions, choosing one from each question.
2. Each question carries 4 marks.
13.
Prove that 2 is irrational by the method of contradiction
(or)
Prove that 3 - 2 5 is irrational.
14.
Find the zeros of the quadratic polynomial x2+5x+6 and verify the relationship
between the zeroes and coefficients.
Divide 3x3 + x2 + 2x+5 by 3x-1 and verify the result with division algorithm.
4
X class Mathematics
(2014-15)
Unit wise Division of Syllabus
Unit - I:
1.
2.
3.
Real numbers
Sets
Polynomial
1.
2.
Similar Triangles
Linear Equations in 2 variables
1.
2.
Progressions
Tangents and secants to a circle
1.
2.
Application of Trigonometry
Probatrility
Unit - II:
Unit - III:
Unit - IV:
5
X class
Mathematics (2014-15)
Chapter wise Division of Syllabus
Under Paper I and Paper II
Paper - I
Paper - II
1. Real numbers
1. Similar Triangles
(ydŸeï dŸ+K«\T)
(dŸsÖÁ |Ÿ çÜuó„TC²\T)
2. Sets
(dŸ$TÔáT\T)
2. Tangents and secants to a circle
3. Polynomials
(‹VŸQ|Ÿ<TŠ \T)
3. Mensuration
4. Pair of Linear equations in two variables
(Âs+&ƒT #ássÁ Xø—\ýË s¹ ¿¡jTá dŸMT¿£sDÁ ²\ ÈÔá)
4. Trigonometry
5. Quadratic Equations
(esÁZ dŸMT¿£sÁD²\T)
5. Applications of Trigonometry
6. Progressions
(çXâ&Tóƒ \T)
6. Probability
7. Co-ordinate Geometry
(“sÁÖ|Ÿ¿£ ¹sU² >·DìÔ+á )
7. Statastics
(eÔï“¿ì dŸÎsÁôs¹ ¿£\T eT]jáTT #ó<û qŠ s¹ K\T)
(¹¿çŒ Ôá$TÜ)
(çÜ¿ÃD$TÜ)
(çÜ¿ÃD$TÜ nqTesÁHï \T)
(dŸ+uó²e«Ôá)
(kÍ+K«¿£ XæçdŸï+)
6
SSC Public Examinations - March - 2015
Model Paper - Mathematics
Weightage Tables
Paper - 1
Table - 1:
S. No.
Weightage to Academic Standards
Academic Standards
Weightage (%)
Marks
1.
Problem Solving
40%
32
2.
3.
Reasoning and Proof
Communication
20%
10%
16
08
4.
Connection
15%
12
5.
Representation
15%
11
100%
79
Total
Paper-I
Part A- 64 marks
Part B- 15 marks
Including choice
questions
Table : 2
Weightage to Content
S. No.
Cotent Area
Weightage %
Marks
1.
Number System
24%
19
2.
Algebra
60%
47
3.
Co-ordinate Gemetry
16%
13
100%
79
Weightage %
Marks
Total
Table : 3
Weightage to difficulty level
S. No.
Difficulty level
1.
Easy
25%
20
2.
Average
50%
39
3.
Difficulty
25%
20
100%
79
Total
7
Table - 4:
S. No.
Weightage to type of Questions
Type of Questions
Weightage (%)
No. of Questions
Marks
1.
Objective type
(½)
19%
30
15
2.
3.
4.
5.
Very short answer type (1)
Short answer type
(2)
Essay type
(4)
Graph
(5)
08%
20%
41%
12%
06
08
08
02
06
16
32
10
100%
54
79
Total
Table - 5: Area wise, Standard wise Division of Question paper
Q.No.
Marks
Area
Ae. Std
Q.No.
Marks
Area
Ae. Std
1
2
Num.Sys.
PS
28(4)
½
Algebra
COM
2
2
Num.Sys.
R/P
29(5)
½
Algebra
CON
3
2
Algebra
PS
30(6)
½
Algebra
REP
4.
2
Algebra
PS
31(7)
½
Co-Geo
PS
5.
2
Algebra
COM
32(8)
½
Co-Geo
PS
6.
2
Algebra
CON
33(9)
½
Co-Geo
R/P
7.
8
9.
2
2
1
Co-Geo
Co-Geo
Num.Sys.
PS
CON
PS
34(10)
35(11)
36(12)
½
½
½
Co-Geo
Num.Sys.
Num.Sys.
CON
R/P
REP
10.
11.
1
1
Num.Sys.
Num.Sys.
PS
CON
37(13)
38(14)
½
½
Algebra
Algebra
PS
R/P
12.
1
Algebra
PS
39(15)
½
Algebra
COM
13.
1
Algebra
CON
40(16)
½
Algebra
CON
14.
1
Co-Geo
COM
41(17)
½
Co-Geo
PS
15.
4
Num. Sys
42(18)
½
Co-Geo
PS
16.
4
Num. Sys
PS
43(19)
½
Co-Geo
COM
17.
18.
4
4
Algebra
Algebra
R/P
PS
44(20)
45(21)
½
½
Co-Geo
Num.Sys.
CON
COM
19.
4
Algebra
PS
46(22)
½
Num.Sys.
CON
20.
4
Algebra
RP
47(23)
½
Num.Sys.
COM
21.
4
Algebra
CON.
48(24)
½
Num.Sys.
COM
22.
4
Co-Geo
PS
49(25)
½
Num.Sys.
COM
23.
5
Algebra
REP
50(26)
½
Algebra
PS
24.
5
Algebra
REP
51(27)
½
Algebra
PS
25(1)
½
Num.Sys.
PS
52(28)
½
Algebra
PS
26(2)
½
Algebra
PS
53(29)
½
Algebra
PS
27(3)
½
Algebra
R/P
51(30)
½
Algebra
PS
PART-A
PART-B
8
9
Total
(1)2 (1)4
(12)½ (2)1 (4)2 (4)4
-
Co-ordinate
Geometry
3
(4)½
Algebra
(7)½ (1)1 (2)2 (2)4
- Polynomials
- Linear Equation
intro variables
- Quadratic Eqn.
- Progression
2
(1)1 (1)2 (1)4
Numbers System (1)½
- Real numbers
- Sets
E
1
O VSA SA
-
-
-
-
(1)½
32 (4)½
8
16½ (2)½
7½ (1)½
-
-
-
-
-
-
(2)4 -
-
(1)2 (3)4 -
-
-
(1)2 (1)4
E G
(2)½ -
E
-
-
(1)2 -
-
16 (8)½ (2)1 (1)2
½ (1)½ (1)1
9
6½ (5)½ (1)1
Tot O VSA SA
-
-
Connection
-
-
G
(1)2 -
-
-
- 08 (4)½ (2)1 (2)2 (1)4 -
-
3 (2)½ (1)1 (1)2 (1)4 -
- (1)1
- 1½ (2)½
-
- 3½
G Tot O VSA SA E
Standards
Communication
Academic Standards
Academic Reasoning
and Proof
G Tot O VSA SA
Problem Solving
Blue Print - Maths Paper - I
Sl. Content Area
No.
Table - 6:
12
3
8
1
(2)½
-
(1)½
(1)½
-
-
-
-
-
-
-
-
Tot O VSA SA
-
-
-
-
E
½
Tot
19
(GT)
Tot
al
(2)5
-
11
-
79
13
(2)5 10½ 47
-
G
Representation
Mathematics - Paper - I
(English Version)
Part A and B
Time: 2½ hours
Max Marks: 50
Instructions:
1. Answer the questions under Part-A on a seperate answer book.
2. Write the answerws to the questions under Part-B on the question paper
itself and attach it to the answerbook of Part - A
Part-A
Section - I
Time: 2 hours
Marks: 35
Note:
1. Answer any five questions choosing at least two from each of the following two group, i.e., A and B.
2. Each question carries 2 marks.
Group - A
(Real numbers, sets, polynomials, Quadratic Equations)
1.
Find H.C.F. and L.C.M. of 220 and 284 by Prime factorisation method.
2.
Check whether A {x: x2 = 25 and 6x = 15} is an empty set or not? Justify your answer.
3.
The sum of zeroes of a quadratic polynomial Kx2 –3x +1is 1, find the value of K.
4.
Find two numbers where sum is 27 and product is 182.
Group - B
(Lineor Equations in two variables, Progressions, Co-ordinate Geometry)
5.
Formulate a pair of linear equations in two variables “3 pens and 4 books together cost
Rs.50 where as 5 pens and 3 books together cost Rs. 54”.
6.
In a nursary, there are 17 rose plants in the first row, 14 in the second row, 11 in the
third row and so on. It there are 2 rose plants in the last two, find how many rows of
rose plants are there in the nursary.
7.
Find the point on the X-axis which is equidistant from (2 – 5) and (– 2, 9).
8.
Verify that the points (1, 5), (2, 3) and (– 2, – 1) are colinear are not?
10
Section - II
Marks: 4 ´ 1 = 4
Note:
1. Answer any four of the following six questions.
2. Each question carries 1 mark.
9.
Determine the value of log3 243
10.
Let A = {1, 3, 5, 7}, B = {1, 2, 3, 4, 6} find A – B and B – A.
11.
Give any two examples of disjoint sets from your daily life.
12.
Find the zeroes of the polynomial P(y) = y2–1.
13.
Do the irrational numbers
common difference.
14.
What do you mean by “slope” of a straight line?
2,
8,
18 ,
32 ............. from an A.P.? If so, find
Section - III
Marks: 4 ´ 4 = 16
Note:
1. Answer any four questions, choosing two from each of the following
groups, i.e., A and B.
2. Each question carries 4 mark.
Group - A
(Real numbers, Sets, Polynomials, Quadratic Equations)
15.
Prove that 3 is irrational by the method of contradiction.
16.
Let
17.
A = {x : x is an even number}
B = {x : x is an odd number}
C = {x : x is a prime number}
D = {x : x is a multiple of 3}
Find (i) A È B
(ii) A Ç B
(iii) C – D
set builder form.
(iv) A Ç C and describe the sets in
Find a quadratic polynominal whose sum of zeroes is
-3
and product is –1. How
2
many such polynomials you can find in this process?
18.
Find the roots of the equation 5x2 – 6x– 2 = 0 by the method of completing the square.
11
Group - B
(Linear Equations in two variables, Progressions and co-ordinate Geometry)
2
3
4
9
+
= 2 and
= -1.
x
y
x
y
19.
Solve the euqations
20.
Check whether the given pair of linear equations represent intersecting, parallel or
co-incident lines. Find the solution if the equations are consistent.
(i) 3x + 2y = 5
2x – 3y = 7
(ii) 2x – 3y = 5
4x – 6y = 15
21.
The number of bacteria in a certain culture triples every hour. If there were 50
bacteria present in the culture originally, what would be the number of bacteria in
3rd hour? 5th hour? 10th hour? 11th hour?
22.
Find the area of triangle formed by the points (8, –5) (–2, –7) and (5, 1) by using
Heron’s formula.
Section - IV
(Polynomials, Linear Equations in two variables)
Marks: 5 ´ 2 = 10
Note:
1. Answer any one question from the following.
2. This question carries 5 marks.
23.
Draw the graph of P(x) = x2 – 6x + 9 and find zeroes. Verify the zeroes of the
polynomial.
24.
Solve the pair of linear equations graphically
2x – y
=5
3x + 2y = 11
12
Mathematics - Paper - I
(English Version)
Part A and B
Time: 2½ hours
Max Marks: 50
Part - B
Time: 30 minutes
Marks: 15
Note:
1.
2.
3.
4.
All questions are to be answered.
Each question carries ½ mark
Answer are to be written in the question paper only.
Marks will not be given for over - writing, re-writing or erased answers.
I. Write the Capital letters of the correct answer in the brackets provided against
each question.
10´ ½ = 5 marks
1.
One of the following is an irrational number.
A)
2.
2
3
B)
16
25
C) 8
B) 4
C) –7
)
(
)
D) 0.04
The product of zeroes of the cubic polynomial 2 x3–5 x2–14 x+8 is
A) – 4
(
D)
5
2
3.
A pair of Linear equations which satisfies dependent system
A) 2x + y – 5 = 0 ; 3x – 2y – 4 = 0
B) 3x + 4y = 2
; 6x + 8y = 4
C) x + 2y = 3
; 2x + 4y = 5
D) x + 2y – 30 = 0 ; 3x + 6y + 60 = 0
(
)
4.
The n term of G.P. is an = arn-1 where ‘r’ represents
A) Firs terms
B) Common difference
C) Common ratio
D) Radius
(
)
5.
The number of two digit numbers which are divisible by 3
A) 30
B) 20
C) 29
D) 31
(
)
6.
The euqation of the line which intersects X-axis at (3, 0) is
A) x + 3 = 0
B) y + 3 = 0
C) x – 3 = 0
D) y – 3 = 0
(
)
7.
The coordinates of the centre of the circle if the ends of the diameter are
(
)
(2, – 5) and (–2, 9)
A) (0, 0)
B) (2, –2)
C) (–5, 9)
13
D) (0, 2)
8.
The point of intersection of the lines x = 2014 and y = 2015 is
A) (2015, 2014)
B) (2014, 2015)
C) (0, 0) D) (1, 1)
(
)
9.
Which of the following vertices form a triangle
(
)
(
)
10.
A) (1, 2), (1, 3), (1, 4)
B) (5, 1), (6, 1), (7, 1)
C) (0, 0), ( –1, 0), (2, 0)
D) (1, 2), (2, 3), (3, 4)
The slope of a ladder making an angle 300 with the floor
A) 1
B)
1
C) 3
3
D)
1
2
900
300
10´ ½ = 5 marks
II. Fill in the blanks with suitable answers
23
11.
The decimal form of 2 3 ´ 5 2 is ______________
12.
The shaded region in the diagram represents ______________
A
B
1
is one zero of 3x2 + 5x– 2 then the other zero is ______________
3
13.
If
14.
The value of ‘K’ for which a pair of linear equations 3x + 4y+ 2 = 0 and 9x +12y+K = 0
represent coincident lines is ______________
15.
The quadratic equation having roots a and b is ______________
16.
The sum of first 20 odd numbers is ______________
17.
The distance between the origin to the point ( – 4, – 5) is ______________ units.
18.
The centroid of the triangle whose vertices are (3, –5), (–7, 4) and (10, –2) is
______________
19.
The distance between two points (x1, y1) and (x2, y2) on the line parallel to X-axis is
______________
20.
(
)
o
o
The mid point of the line joining the points log82 , log16
4 and (sin 90 , cos 0 ) is
______________
14
For the following questions under Group-A choose the correct answer from the
master list Group-B and write the letter of the correct answer in the brackets
provided against each item.
10´ ½ = 5 marks
(i)
Group - A
Group - B
21.
The logirithmic form of 210 = 1024
(
)
A) 4 (log5 + log2)
22.
The Exponential form of log100.01
(
)
B) 0
23.
The Expansion of log 10000
(
)
C) log4
24.
The short form of log16 – 2 log2
(
)
D) log 1024
=10
2
25.
The value of log11000
(
)
E) log8
F) log1000
G) – 2
H) log125 + log800
(ii)
Group - A
Group - B
3
2
26.
Product of zeroes of x2 – 3
(
)
I)
27.
Sum of zeroes of 2x3 – 3x2 – 14x+18
(
)
J) 3
28.
The common root of 2x2 + x –6 = 0
and x2 – 3x – 10 = 0 is
(
)
K) 0
29.
The value of the polynomial
p(x) = 3x2 – 5x – 2 at x = 2
(
)
L) 36
30.
The discriment of quadratic equation
x2 – 4x + 5 = 0
(
)
M) – 2
(
)
N) – 3
(
)
O) – 7
(
)
P) – 4
15
Mathematics - Paper - II
Moder Paper
Weightage Tables
Table : 1
Weightage to Academic Standards
S. No.
1.
2.
3.
4.
5.
Table : 2
Academic Standards
Problem Solving
Reasoning & Proof
Communication
Connnections
Representation & Visualisation
Total
Weightage %
40
20
10
15
15
100%
Marks
32
16
8
12
11
79
Weightage %
27
Marks
22
Weightage to Areas
S. No.
1.
Area
Geometry
(i) Similar Triangles
(ii) Targents and Secauts to a circle
2.
Mensuration
19
15
3.
Trigonametry
(i) Trigonametry
(ii) Apps of Trigonametry
Statistics
(i) Statistics
(ii) Probability
29
23
25
19
4
100%
Table : 3
79
Weightage to difficulty level
S. No.
1
2
3
Table : 4
Type
Weightage %
25%
50%
25%
100%
Easy
Average
Difficult
Marks
20
39
20
79
Weightage to type of questions
S. No.
1.
2.
3.
4
Type of Questions
Long Answer
Short Answer
Very Short Answer
Objective
Total
1
Weightage %
Marks
53%
20%
8%
19%
100%
42
16
06
15
79
2
-
-
-
(3)½
(1)1 (2)½
Trigonometry (1)5 (1)2
(Trigonametry& (1)4
Application or
Trigonometry
Statistics
(Statistics &
Probability)
(1) 2
(1)5 (4)2
(4)3
-
(1)½
(2)½
-
-
16
-
-
-
(2)1 (10)½ 32 (2)4 (2)2 (1)1 (6)½
-
(1) 2
-
(1)½
-
(1) 4
-
-
-
(1)1 (1)½
-
-
(1)1 (1)½
(1)4 (1)2
(1)4 (1)2
Mensuration
Geometry
(Similar
Triangles &
Circles
SA VSA Obj Tot
Reasoning & Proof
(1) 4 (1)2
SA VSA Obj Tot E
-
E
(1)½
Content
Areas
Problem Solving
(1)2
-
-
-
-
(1)1
-
-
(1)½
-
-
(1)½
-
-
-
-
-
(1)4
-
-
SA VSA Obj Tot E
-
-
(1)2
-
(4)½
(1)½
(1)1 (2)½
-
-
(1) 1 (1)½
-
-
-
-
(1)4
-
-
(1) 5
SA VSA Obj Tot E
Connection
(1)4 (1)2 (1)1 (2)½ 08 (1)4 (1)2 (2)1 (8)½ 12 (1)5
(1)4
-
-
(1)4
-
E
Communication
Blue Print (Paper - II)
79
-
(4)½ 11
-
19
23
-
- (2)½ -
15
22
-
-
-
(1)½
-
(1)½
-
-
-
-
-
-
SA VSA Obj Tot Tot
Representation
SSC Model Question Paper
Mathematics - Paper - II
(English Version)
Part A and B
Time: 2½ hours
Max Marks: 50
Instructions:
1. Answer the questions under Part-A on a seperate answer book.
2. Write the answerws to the questions under Part-B on the question paper
itself and attach it to the answerbook of Part - A
Part-A
Section - I
Time: 2 hours
Marks: 35
Note:
1. Answer any five questions choosing atleast two from each of the
following two groups i.e., A and B.
2. Each question carries 2 marks.
Group - A
(Similar triangles, Tangents and secants to a circle, mensuration)
1.
Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the
squares of its diagonals.
2.
A Tangent is drawn from a point which is 34 cms away from centre of a circle. If the
diameter of the circle is 34 cms, then find the length of the tangent.
3.
Find the volume and the total surface area of a hemisphere of radius 3.5 cms.
4.
An oil drum is in the shape of a cylinder having the following dimensions: diameter is
2m. and height is 7m. If the painter charges 3 per m2. To paint the drum find the
charges to be paid to the painter.
Group - B
3
5
5.
If sin q = , find the value of sec 2 q + tan 2 q .
6.
Ravi is on the top of a 20m high building. Rahim is 20m. away from the bottom of the
building, Can Rahim able to see Ravi at 450 angle? Justify your answer.
7.
A bag contains 5 Red and 8 white balls. If a ball is drawn at Random from the bag what
is the probability that it will be (i) white ball (ii) not a white ball.
8.
Write the formula of median for a grouped data? Explain the symbols in words.
3
Section - II
Marks: 4 ´ 1 = 4
Note:
1. Answer any four of the following six questions.
2. Each question carries 1 mark.
9.
Write the properties of similar triangles.
10.
Find the area of required cloth to cover the heep of grain in conical shape, of whose
diameter is 8m and slant height of 3m.
11.
A die is thrown at once. Find the probability of getting an even prime number.
12.
Find the mode of the data 5, 6, 9, 6, 12, 3 , 6. 11, 6 and 7.
13.
Express tan q in terms of sin q .
14.
A doctor observed that the pulse rate of 4 students is 72, 3 students is 78 and 2
students is 80. Find the mean of the pulse rate of the above students.
Section - III
Marks: 4 ´ 4 = 16
Note:
1. Answer any four questions, choosing two from each of the following
groups, i.e., A and B.
2. Each question carries 4 mark.
Group - A
15.
A chord makes a right angle at the centre of a circle having a radius 10 cms. find
(i) Area of minor segment (ii) Area of major segment
16.
State and prove pythogorus theroem.
17.
Metallic spheres of radius 6 cm, 8cm and 10 cm. respectively are melted to form a
single solid sphere. Find the radius of the resulting sphere.
18.
Find the ratio of surface areas of sphere and cylinder having same radius and height.
Comment on the result.
Group - B
19.
If sec q + tan q = P then find the value of Sinq in terms of ‘P’.
20.
A boat has to cross a river. It crosses the river by making an angle of 600 with the bank
of the river, due to the stream of the river and travels distance of 600 mts., to reach the
another side of the river. What is the width of the river?
4
21.
Two dice are rolled simultaneouly and counts are added (i) complete the table given
below.
Event
2
(sum of 2 dice)
Probability
(ii)
3
4
5
6
7
1
36
8
9 10 11
12
5
36
A student argues that there are 11 posible out comes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.
Therefore each of them as a probability
1
. Do you agree with this argument . Justify
11
your answer.
22.
Draw “OGIVE CURVE” of the following frequency distribution table.
Classes
0-20
20-40
40-60
60-80
80-100
100-120
Frequency
9
16
24
15
4
2
Section - IV
Marks: 5 ´ 2 = 10
Note:
1. Answer one question from the following.
2. Each question carries five marks.
23.
Construct a triangle of sides 4 cm. 5 cm. and 6cm. Then construct a triangle similar to
it. Whose slides are
24.
2
of the corresponding sides of the first triangle.
3
The angle of elevation of a jet plane from a point A on the ground is 600 after a flight
of 15 seconds, the angle of elevation changes to 300. If the jet plane is flying at a
constant height of 1500 3 meter, find the speed of a jet plane.
5
Mathematics - Paper-II
Part - B
(English Version)
Time: 30 min
Max Marks: 15
Instructions:
1. The question paper carries
1
mark.
2
2. Answer are to be written is the question paper only.
3. All questions are to be answered.
4. Marks will not be awarded is case of any over writing or re-writing or
erased answers.
Part-B
10 ´
1
= 5 marks
2
I. Write the capital letters showing the answer in the brackets provided against each
question.
B
M
1.
from the diagram LM || CB and LN CD the which ( )
A
C of the following is true.
L
N
D
A)
2.
AM
AN
=
MB
ND
4.
C)
AN
AM
=
NL
ML
D)
AM
AN
=
MB
AD
(
)
The A.M. of 30 students is 42. Among them two got zero marks then A.M.
of remaining students
A) 40
B) 42
C) 45
D) 28
(
)
The probability of getting kind or green card from the play cards (1 deek)
(
)
(
)
A)
5.
AN
AM
=
ND
AB
The distance between the points ( cosq , 0 ) , (0, sin q )
A) 1
3.
B)
1
52
B) -1
B)
C) 0
1
13
C) 45
æ
f - f
ö
0
The h indicates in Mode Z = l + çç 2 f - f - f ÷÷ ´ h
0
1 ø
è
A) Frequency
B) Length of the CI
6
D)
-1
D) 28
C) Lower boundary of mode class
6.
7.
Which of the following is incorrect
A) The ratio of surface areas of cylinder and core is 1:1
B) The ratio SA (Surface Area) of sphere and hemisphere is 2:1
C) The ratio TSA (Total Surface Area) of sphere and hemisphere is 2:1
D) The ratio of volumes of cylinder and core is 3:1
(
)
(
)
Among the numbers 1, 2, 3, ............. 15 the probability of choosing a number
which is a multiple of 4
(
)
cos 23o - sin 67 o
=
tan 26 o . tan 64 o
A) sin 90°
8.
A)
9.
D) Mode
B) tan 30°
4
15
B)
C) tan 0°
2
15
C)
D) cot 30°
1
5
D)
3
5
21
Which of the following representations sin q =
29 A
Q
(
)
(
)
q
29
A)
B)
21
P
21
29
q
B
R
X
D
29
C)
10.
29
D)
Y
C
q
21
Z
E
q
21
F
Gita said that the probability of impossible events is 1. Pravillika said that
probability of sure events is 0 and Atiya said that the probability of any
event lies in between 0 and 1. In the above with whom you will agree.
A) Gita
B) Pravillaka
C) Atiya
7
D) All the three
II. Fill in the blanks with suitable words.
11.
The angle between a tangent to a circle and the radius drawn at the plant of contact
is ______________
12.
The ratio between Leteral surface area and total surface area of cube is ____________
13.
A man goes to East and then to South. The trigonamentric ratio involved to find the
distance travelled from the starting point is ______________
14.
20
15
10
From the figure the possible measures of central tendency
can be found is ______________
5
15.
5
10
R
Y
15
R Y R
R
20
From the figure the probability to get yellow colour ball
is ______________
R = Red
Y = Yellow
16.
The Medians of two similar Triangles are 3cm. and 5cm. Then the ratio of areas of
above two triangles is ______________
17.
The area of the base of a cylander is 616 sq. cm. then its radius is ______________
18.
The length of the chard making an angle 600 at the centre of the circle having radius
6 cm is ______________
19.
Marks
No. of students
10
20
30
5
9
3
From the above data the value of median is ______________
20.
A game of chance consists of spinning an arrow which
7
comes to rest at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8
and these are equally likely outcomes. The possibility that the
arrow will point at a number greater than 2 is ______________ 6
8
8
1
2
3
5
4
5´ ½ = 2½ marks
Match the following
Group - A
21.
Group - B
In triangle ABC, D and E are the
points on AB and AC and
(
)
A) 20
AD AE
=
then
DC EC
22.
In triangle BED, ÐE = 90° and
ED 2 = BD. CD then
(
)
B) 4
23.
Volume of a hemicphere is
(
)
C)
(
)
D) 15
(
(
)
)
E) DE || BC
F) DE ^ BC
(
)
G) 8
(
)
H)
24.
25.
2250 cm3 than its radius
The horizontel distance from the foot
of the leader having height 25m touches
the window at a height of 15m is
Two concentric circles of radii 5cm.
and 3cm. are drawn. The length of the
chord of larger circle touches to
small circle
If sec q + tan q =
22
7
5´ ½ = 2½ marks
Match the following
Group - A
26.
77
3
Group - B
1
then
2
(
)
I) 0
sec q - tan q value
27.
cos 0 o ´ cos1o ´ cos 2 o ´ ........´ cos180 o
(
)
J) 1
28.
if cos A =
4
then sin A value
5
(
)
K) 50°
29.
The length of the shadow of a tower of
(
)
L)
If tangents PA and PB from a point
(
)
M) –
P to a circle with centre O are inclined
(
)
2
3
N) 60°
to each other at an angle of 80° than
(
)
O) 2
ÐPOA
(
)
P)
3
5
height 15m. at 7A.M. is 15 3 than the
angle made by sum with the earth
30.
9
3
|Ÿ<eŠ Ôás>Á Ü· qeTÖH ç|ŸX•ø |ŸçÔá+
jáT֓{Ù fÉd¼t
>·DÔì +á
Ôás>Á Ü· : 10
yîTTÔáï+ eÖsÁTØ\T 25
dŸeTjáT+ : 45 “;
dŸÖ#áq\T:
·
ç|ŸXæ•|ŸçÔá+ eTÖ&ƒT ™d¿£ŒqT¢ ¿£*Ð –+³T+~.
™d¿£HŒ Ž ` 1
n“• ç|ŸX•ø \Å£” Èy‹T\T sjáT+&. ç¿ì+<Š“eNj&q H\T>·T dŸeÖ<ó‘qeTT\ qT+& dŸ]jîT® q
Èy‹TqT dŸÖº+#áT n¿£sŒ ÁeTT (A / B /C / D)qT ‚eNj&q çu²Â¿³¢ýË sjáT+&.
7 ´ 1 = 7 eÖsÁTØ\T
1.
156 jîTT¿£Ø ç|Ÿ<‘ó q ¿±sÁD²+¿£ \‹Ý sÁÖ|Ÿ+.
A) 2 ´ 3´ 13
2.
8x = 2 jîTT¿£Ø
B) 2 ´ 3 ´ 13
2
0.875 jîTT¿£Ø
A)
4.
5.
p
q
C) logx 2 = 8
B)
7
16
C)
3
8
A) 0 eT]jáTT 1
C) 3 eT]jáTT 4
A = {x / x ÿ¿£
2x-3 ‹VŸQ|Ÿ~
2
3
B) 1 eT]jáTT 2
u²\T&ƒT}
B = {x / x ÿ¿£
B) A Ç B ¹ q
3
2
-2
3
B)
C) x +
2x + 5
D)
1
1
x
)
(
)
(
)
(
)
(
)
D) A- B = f
-3
2
ç¿ì+~ y“ýË @ ;JjáT dŸeÖdŸeTT ‹VŸQ|Ÿ~¿±<ŠT.
A) - 2x 2
(
D) -1 eT]jáTT 1
u²*¿£} nsTTq
C)
)
7
22
XøSq« $\Te.
B)
(
D) log2 x = 8
–+³T+~.
C) A - B = A
)
D) 2 ´ 3 ´ 13
D)
3
4
(
2
sÁÖ|ŸeTT.
¿ì+~ y“ýË dŸ+U²«¹sK™|Õ @ |ŸPsÁd’ +Ÿ K«\ eT<ó«Š
A)
7.
B) log8 2 = x
7
23
A) A È B = f
6.
2
dŸ+esÁZeÖq sÁÖ|ŸeTT.
A) logx 8 = 2
3.
C) 2 ´ 3 ´ 13
2
D) 5-2x
™d¿£HŒ Ž ` II
5 ´ 2 = 10 eÖsÁTØ\T
n“• ç|ŸX•ø \Å£” Èy‹T\T sjáT+&.
ç|ŸÜ ç|ŸX•ø Å£” Âs+&ƒT eÖsÁTØ\T.
8.
¿ì+~ n¿£sD
Á j
¡ Tá dŸ+K«\qT uó²>·VäŸ sÁ+ #ûjTá Å£”+&†Hû <ŠXæ+XøsÖÁ |Ÿ+ýË sjáT+&.
i)
9.
13
25
ii)
x3
y2
log
143
110
qT $dŸ]ï +#áTeTT.
10.
A = {1, 2, 5}, B = {2, 3, 4, 5} nsTTq A È B
11.
¿ì+~ y““ C²_Ԑ sÁÖ|Ÿ+ýË sjáT+&.
eT]jáTT A Ç B \qT ¿£qT>=q+&.
(i) A = {x / x ÎN, x<7}
(ii) B = {x / x nHû~ ‘School’ nHû |Ÿ<+Š ýË n¿£ŒsÁeTT}
12.
P(x) = x-2 jîTT¿£Ø
ç>±|˜t ^jáT+&. n~ X- n¿Œ±“• b#á³ K+&dTŸ ï+<à Ôî\|Ÿ+&.
™d¿£HŒ Ž ` III
1.
2.
13.
n“• ç|ŸX•ø \Å£” Èy‹T\T sjáT+&.
ç|ŸÜ ç|ŸXø• qT+& ÿ¿£ <‘““ b+#áT¿Ã+&. ç|ŸÜ ç|ŸX•ø Å£” 4 eÖsÁTØ\T
$sÁT<ŠÆÔá <‘Çs
3-2 5
14.
2 ´ 4 = 8 marks
qT ¿£sDÁ ¡jáT dŸ+K« n“ #áÖ|Ÿ+&.
(ýñ<‘)
qT ¿£sDÁ ì n“ #áÖ|Ÿ+&.
2
x2+5x+6
nHû ‹VŸQ|Ÿ~ XøSq« $\Te\T ¿£qT>=q+&. eT]jáTT XøSq« $\Te\T, >·TD¿±\ eT<ó«Š
dŸ+‹+<󑓕 Ôî\Î+&.
(ýñ<‘)
3x3 + x2 + 2x+5 qT (3x-1) #û
uó²Ð+#á+&. eT]jáTT uó²>·VŸäsÁ “jáTe֓• dŸ]#áÖ&ƒ+&.
2
Mathematics - Paper - I
(Telugu Version)
Part A and B
Time: 2½ hours
Max Marks: 50
Instructions:
1. Answer the questions under Part-A on a seperate answer book.
2. Write the answerws to the questions under Part-B on the question paper
itself and attach it to the answerbook of Part - A
Part-A
Section - I
Time: 2 hours
Marks: 35
dŸÖ#áq\T:
1. ‡ ç¿ì+<ŠqTq• A eT]jáTT B ç>·Ö|ŸÚ\ýË ÿ¿=Ø¿£Ø <‘“ qT+& ¿£údŸ+ s +&ƒT ç|ŸX•ø \ #=|ŸÚÎq
yîTTÔáï+ ×<ŠT ç|ŸXø•\Å£” dŸeÖ<ó‘qeTT\T çyjáT+&.
2. ç|ŸÜ ç|ŸX•ø Å£” Âs+&ƒT eÖsÁTØ\T.
Group - A
(ydŸïe dŸ+K«\T, dŸ$TÔáT\T, ‹VŸQ|Ÿ<ŠT\T, esÁZdŸMT¿£sDÁ ²\T)
1.
220 eT]jáTT 284 \ >·.kÍ.¿±. eT]jáTT ¿£.kÍ.>·T.\qT ç|Ÿ<‘ó q ¿±sÁD²+¿±\ \‹Ý |Ÿ<ÜƊ ýË ¿£qT>=q+&.
2.
A {x: x2 = 25 eT]jáTT 6x = 15} nHû~ XøSq«dŸ$TÜ neÚHà ¿±<à #áÖ&ƒ+&. MT Èy‹TqT dŸeT]œ+#á+&.
3.
Kx2 –3x +1nHû
4.
yîTTÔá+ï 27 eT]jáTT \‹Ý+ 182 njûT«³T¢ s +&ƒT dŸ+K«\qT ¿£qT>=q+&.
esÁZ ‹VŸQ|Ÿ~ XøSq«eTT\ yîTTÔáï+ 1 nsTTq K $\Te b+Ôá?
Group - B
(Âs+&ƒT
#ásÁsXø—\ýË s¹ FjáT dŸMT¿£sDÁ eTT, çXâ&Tóƒ \T, “sÁÖ|Ÿ¿£ C²«$TÜ)
5.
3 ¿£\eTT\T, 4 |ŸÚd￟ e£ TT\ yîTTÔáï+ yî\ sÁÖ. 50 \T. 5 ¿£\eTT\T, 3 |ŸÚdŸ¿ï £eTT\ yîTTÔá+ï yî\ sÁÖ.54\T.
nqT <ŠÔï+X擿ì s +&ƒT #ásÁsXø—\ýË ÿ¿£ ÈÔá s¹ FjáT dŸMT¿£sÁDeTT\T sjáT+&.
6.
ÿ¿£ qsÁà¯ýË 17 >·Tý²; yîTT¿£Ø\T yîTT<Š{ì esÁTdŸýË, 14 yîTT¿£Ø\T s +&ƒe esÁTdŸýË, 11 yîTT¿£Ø\T eTÖ&ƒe
esÁTdŸýË –q•$. n<û $<ó+Š >± ºe] esÁTdŸýË 2 yîTT¿£Ø\T –q•$. nsTTq € qsÁà¯ýË b“• esÁTdŸ\
>·Tý²; yîTT¿£Ø\T –q•$.
7.
X-
8.
(1, 5), (2, 3), (– 2, – 1) _+<ŠTeÚ\T
n¿£+Œ ™|Õ –+³Ö _+<ŠTeÚ\T (2 – 5) eT]jáTT (– 2, 9) \Å£” dŸeÖq <ŠÖsÁ+ýËqTq• _+<ŠTeÚqT
¿£qT>=q+&.
dŸs¹ FjáÖ\T neÚԐjáÖ? ¿±<‘? dŸ]#áÖ&ƒ+&.
3
Section - II
Marks: 4 ´ 1 = 4
dŸÖ#áq:
1. ¿ì+~ y“ýË @yû“ H\T>·T ç|ŸX•ø \Å£” dŸeÖ<ó‘qeTT\T sjáT+&.
2. ç|ŸÜ ç|ŸX•ø Å£” ÿ¿£ eÖsÁTØ.
9.
log3 243
jîTT¿£Ø $\TeqT “sÝ]+#á+&.
10.
A = {1, 3, 5, 7}, B = {1, 2, 3, 4, 6} nsTTq A – B ¿£qT>=q+&.
11.
MT <îÕq+~q J$Ôá+ qT+& $jáTT¿£ï dŸ$TÔáT\Å£” @yû“ Âs+&ƒT –<‘VŸ²sÁD*eÇ+&.
12.
P(y) = y2–1 ‹VŸQ|Ÿ~
jîTT¿£Ø XøSq«$\Te\T ¿£qT>=q+&..
13.
....... nHû ¿£sÁD¡jáT dŸ+K«\T ÿ¿£ n+¿£çXâ&ó“ @sÁÎsÁ#Tá #áTq•y? nsTTq#Ã
kÍeÖq« uñ<eóŠ TT ¿£qT>=q+&.
14.
ÿ¿£ dŸsÁÞ¹øsK y\T n+fñ @$T{ì?
2,
8,
18 ,
32
Section - III
Marks: 4 ´ 4 = 16
dŸÖ#áq:
1. ‡ ç¿ì+<ŠqTq• A eT]jáTT B ç>·Ö|ŸÚ\ýË ÿ¿=Ø¿£Ø <‘“qT+& ¿£údŸ+ s +&ƒT ç|ŸXø•\ #=|ŸÚÎq
yîTTÔá+ï H\T>·T ç|ŸX•ø \Å£” dŸeÖ<ó‘HeTT\T çyjáTTeTT.
2. ç|ŸÜ ç|ŸX•ø Å£” 4 eÖsÁTØ\T.
Group - A
(ydŸe
ï
15.
16.
3
qT ¿£sDÁ ¡jáT dŸ+K« n“ »$sÃ<ó‘uó²dŸ+µ <‘Çs “sÁÖ|¾+#á+&..
A = {x : x
ÿ¿£ dŸ]dŸ+K«}
B = {x : x ÿ¿£ uñd¾ dŸ+K«}
C = {x : x ÿ¿£ ç|Ÿ<‘ó q dŸ+K«}
D = {x : x ÿ¿£ 3 jîTT¿£Ø >·TD¿£eTT} nsTTq
(i) A È B
17.
dŸ+K«\T, dŸ$TÔáT\T, ‹VŸQ|Ÿ<TŠ \T, esÁZdŸMT¿£sDÁ ²\T)
(ii) A Ç B
(iii) C – D
(iv) A Ç C
\qT ¿£qT>=q+&.
ÿ¿£ esÁZ ‹VŸQ|Ÿ~ jîTT¿£Ø XøSH«\ yîTTÔáeï TT eT]jáTT \‹ÝeTT esÁTdŸ>±
-3
2
eT]jáTT –1 nsTTq €
esÁ‹Z VŸQ|Ÿ~“ ¿£qT>=qTeTT. ‡ ç¿£eT+ýË n³Te+{ì esÁZ ‹VŸQ|Ÿ<TŠ \qT b“•+{ì“ ¿£qT>=q>·\eÚ?
18.
5x2 – 6x– 2 = 0
esÁdZ MŸ T¿£sDÁ eTÖ\eTT\qT, esÁeZ TTqT |ŸP]ï#j
û Tá T |Ÿ<ÜƊ <‘Çs ¿£qT>=qTeTT.
4
Group - B
(Âs+&ƒT
19.
20.
#ássÁ Xø—\ýË s¹ FjáT dŸMT¿£sDÁ eTT, çXâ&Tóƒ \T, eT]jáTT “sÁÖ|Ÿ¿£ C²«$TÜ)
2
3
+
= 2
x
y
eT]jáTT
4
9
= -1.dŸMT¿£sD
Á ²\qT
x
y
kÍ~ó+#á+&.
¿ì+~ dŸMT¿£sD
Á ²\ ÈÔá K+&ƒqs¹ Ký², dŸeÖ+ÔásÁ s¹ Ký² ýñ<‘ @¿¡u$„ó +#áT s¹ Ký² dŸ]#áÖ&ƒ+&. €
dŸMT¿£sD
Á eTT\T dŸ+>·Ôeá TT nsTT“ y{ì kÍ<óqŠ ¿£qT>=qTeTT.
(i) 3x + 2y = 5
2x – 3y = 7
(ii) 2x – 3y = 5
4x – 6y = 15
21.
ç|ŸÜ >·+³Å£” 3 Âs³T¢ njûT« ÿ¿£ u²¿¡¼]jáÖ ¿£\ÌsYýË yîTT<Š{ì >·+³ýË 50 u²«¿¡¼]jáÖ\T –q•
3e >·+³ýË eÚ+&û u²«¿¡]¼ jáÖ\ dŸ+K« b+Ôá? 5e >·+³ýË eÚ+&û u²«¿¡]¼ jáÖ\ dŸ+K« b+Ôá?
10 e >·+³ýË eÚ+&û u²«¿¡]¼ jáÖ\ dŸ+K« b+Ôá?
22.
™V²sHŽ dŸÖçÔá+qT|ŸjÖî Ð+º (8, –5) (–2, –7) eT]jáTT (5, 1) _+<ŠTeÚ\q” osü\T>± >·*qZ çÜuóT„ È
yîXÕ æ\«+ ¿£qT>=q+&.
Section - IV
(‹VŸQ|Ÿ<TŠ \T,
s +&ƒT #ássÁ Xø—\ýË, s¹ FjáT dŸMT¿£sDÁ ²\T)
Marks: 5 ´ 2 = 10
dŸÖ#áq:
1. ç¿ì+~ y“ýË @<à ÿ¿£ ç|ŸX•ø Å£” dŸeÖ<ó‘qeTT çyjáTTeTT.
2. € ç|ŸXø•Å£” 5 eÖsÁTØ\T.
23.
P(x) = x2 – 6x + 9 ‹VŸQ|Ÿ~¿ì ÔáÐq s
¹ U² ºçÔáeTT ^º, XøSH«\T ¿£qT>=q+&. |˜*Ÿ Ԑ“• dŸeT]œ+#á+&..
24.
¿ì+~ ÈÔá s¹ FjáT dŸMT¿£sDÁ ²\qT ç>±|˜t |Ÿ<ÜŠÆ ýË kÍ~ó+#á+&.
2x – y
=5
3x + 2y = 11
5
Mathematics - Paper - I
(Telugu Version)
Parts A and B
Time: 2½ hours
Max Marks: 50
>·eT“¿£:
‡ ç¿ì+~ ç|ŸXø•\Å£” dŸeÖ<ó‘H\qT b<ŠTsÁT>± >·\ U²°\ýË çyd¾
Part- A Èy‹T |ŸçԐ“¿ì ÈÔá#j
û áTTeTT.
Part-B
ç|ŸXæ•|ŸçԐ“•
Part - B
dŸeTjáT+: 30 “.
eÖsÁTØ\T: 15
dŸÖ#áq\T:
1. n“• ç|ŸX•ø \Å£” dŸeÖ<ó‘qeTT\T çyjáTTeTT.
2. ç|ŸÜ ç|ŸXø•Å£” ½ eÖsÁTØ.
3. dŸeÖ<ó‘HeTT\qT ç|ŸX•ø |ŸçÔáeTTýËHû çyjáTTeTT.
4. ¿=fñd¼ ¾ çyjáT‹&q, ~<Š‹Ý &q ýñ<‘ #î]|¾ydû ¾ çyjáT‹&q dŸeÖ<ó‘qeTT\Å£” eÖsÁTØ\T ‚eNj&ƒeÚ.
5. ‹VŸQÞèºÕ ÌÛ¿£ ç|ŸXø•\ dŸeÖ<ó‘qeTT\T çyjáTT³Å£” ™|<ŠÝ n¿£sŒ ÁeTT\ (€+>·¢ esÁ’eÖ\)qT
–|ŸjÖî Ð+#áTeTT.
I.
‡ ~>·Te ç|ŸÜ ç|ŸX•ø Å£” b<ŠTsÁT>± 4 Èy‹T©jáT‹&q$. y{ìýË dŸs qÕ Èy‹T dŸÖº+#áT €+>·¢ ™|<ŠÝ
n¿£sŒ “• € ç|ŸX•ø ¿Â <ŠTsÁT>± ‚eNj&ƒ¦ çu²Â¿³¢ýË çyjáTTeTT.
10´ ½ = 5 eÖsÁTØ\T
1.
¿ì+~ y“ýË ¿£sÁDj
¡ áT dŸ+K«
A)
2.
2
3
2 x3–5 x2–14 x+8 nHû
A) – 4
3.
C) 8
|˜TŸ q ‹VŸQ|Ÿ~ XøSH«\ \‹Ý+.
B) 4
C) –7
;
;
;
;
)
(
)
(
)
(
)
D) 0.04
D)
5
2
ç¿ì+~ y“ýË |ŸsÁdŸÎs<ó‘sÁ dŸMT¿£sDÁ ²\ e«edŸqœ T dŸÖº+#áTq$.
A) 2x + y – 5 = 0
B) 3x + 4y = 2
C) x + 2y = 3
D) x + 2y – 30 = 0
4.
16
25
B)
(
3x – 2y – 4 = 0
6x + 8y = 4
2x + 4y = 5
3x + 6y + 60 = 0
ÿ¿£ >·TDçXâ&ó n e |Ÿ<eŠ TT an = arn-1 nsTTq ‘r’ dŸÖº+#áTq~.
A) yîTT<Š{|
ì <Ÿ +Š B) kÍeÖq« uñ<+óŠ C) kÍeÖq« “wŸÎÜï
6
D) y«kÍsÁe
œ TT
5.
3#û “XâôwŸ+>± uó²Ð+|Ÿ‹&ƒT Âs+&ƒ+¿Â \ dŸ+K«.
A) 30
6.
X-n¿Œ±“• (3, 0) e<ŠÝ K+&+#áT
A) x + 3 = 0
7.
x = 2014 eT]jáTT y = 2015 ¹sK\
10.
C) (–5, 9)
K+&ƒq _+<ŠTeÚ.
B) (2014, 2015)
C) (0, 0)
A) (1, 2), (1, 3), (1, 4)
B) (5, 1), (6, 1), (7, 1)
C) (0, 0), ( –1, 0), (2, 0)
D) (1, 2), (2, 3), (3, 4)
A) 1
B)
300 ¿ÃDeTT
1
3
D)
11.
23
2 ´ 52
12.
¿ì+~ |Ÿ³+ýË w&Ž #ûjTá ‹&q çbÍ+Ôá+ dŸÖº+#áTq~. ______________
jîTT¿£Ø <ŠXæ+Xø sÁÖ|Ÿ+
(
)
(
)
300
B
1
3
13.
3x2 + 5x– 2 nHû
14.
3x + 4y+ 2 = 0 eT]jáTT 9x +12y+K = 0
______________
15.
a
16.
yîTT<Š{ì 20 uñd¾ dŸ+K«\ yîTTÔáï+ ______________
17.
eTÖ\_+<ŠTeÚ qT+& ( – 4,
b
)
______________
A
eT]jáTT
(
10´ ½ = 5 eÖsÁTØ\T
dŸ]jîT® q Èy‹T\Ôà U²°\T |ŸP]+#á+&.
3
)
1
2
900
II.
(
D) (1, 1)
#ûjTá T#áTq• n~ #ûjTá Ty\T
C) 3
)
D) (0, 2)
ç¿ì+~ y“ýË @ _+<ŠTeÚ\T çÜuóT„ C²“• @sÁÎsÁ#á>·\eÚ?
Hû\Ôà ÿ¿£ “#îÌq
(
D) y – 3 = 0
ÿ¿£ eÔáï y«dŸ|ŸÚ ºe] _+<ŠTeÚ\T (2, – 5), (–2, 9) nsTTq €eÔΌï +ç<Š “sÁÖ|Ÿ¿±\T
A) (2015, 2014)
9.
C) x – 3 = 0
B) (2, –2)
)
D) 31
s¹ U² dŸMT¿£sDÁ +.
B) y + 3 = 0
A) (0, 0)
8.
C) -29
B) 20
(
‹VŸQ|Ÿ~ ÿ¿£ XøSq«+
nsTTq s +&à XøSq«+
______________
¹sK\T ÿ¿£ ÈÔá @¿¡u$„ó +#áT s¹ K\sTTq
\T eTÖý²\T >·\ esÁZ dŸMT¿£sDÁ + ______________
– 5)
_+<ŠTeÚÅ£” >·\ <ŠÖsÁ+ ______________
7
‘K’
$\Te
18.
(3, –5), (–7, 4), (10, –2) osü\T>·\
19.
X-n¿£e
Œ TTqÅ£”
çÜuóT„ È >·TsÁTÔáÇ ¿¹ +ç<Š+ ______________
dŸeÖ+ÔásÁ+>± –+&û s¹ K™|Õ eÚq•
(x1, y1)
eT]jáTT (x2,
y2 )
_+<ŠTeÚ\ eT<óŠ«
<ŠÖsÁ+____________
20.
III)
(log82 , log164) eT]jáTT (sin 90o , cos 0o ) _+<ŠTeÚ\qT ¿£\T|ŸÚ s¹ K eT<ó«Š _+<ŠTeÚ _____________
ç¿ì+<Š Group-A ýË ‚eNj&q ç|ŸX•ø \Å£”, Group-B ý˓ dŸ]jî®Tq dŸeÖ<ó‘qeTTqT dŸÖº+#áT n¿£sŒ eÁ TTqT
ç|ŸX•ø \¿<ŠTsÁT>± ‡jáT‹&q çu²Â¿³¢jTá +<ŠT >·T]ï+#áTeTT.
10´ ½ = 5 eÖsÁTØ\T
(i)
Group - A
21.
210 = 1024
22.
0.01
jîTT¿£Ø
log10
23.
log 10000
24.
log16 – 2 log2 jîTT¿£Ø
25.
log11000
Group - B
jîTT¿£Ø dŸ+esÁeZ ÖqsÁÖ|Ÿ+
|˜ŸÖԐ+¿£sÁÖ|Ÿ+
jîTT¿£Ø $dŸsï ÁD sÁÖ|Ÿ+
dŸ+¿ìŒ|ïsŸ ÁÖ|Ÿ+
$\Te
(
)
A) 4 (log5 + log2)
(
)
B) 0
(
)
C) log4
(
)
D) log 1024
=10
2
(
)
E) log8
F) log1000
G) – 2
H) log125 + log800
(ii)
Group - A
Group - B
26.
x2 – 3 ‹VŸQ|Ÿ~ XøSH«\
27.
2x3 – 3x2 – 14x+ 8 XøSH«\
28.
2x2 + x –6 = 0 eT]jáTT x2 – 3x – 10 = 0
\‹Ý+
yîTTÔá+ï
3
2
(
)
I)
(
)
J) 3
(
)
K) 0
(
)
L) 36
(
)
M) – 2
(
)
N) – 3
(
)
O) – 7
(
)
P) – 4
dŸMT¿£sD
Á ²\ –eTˆ& eTÖ\+
29.
x = 2 e<ŠÝ p(x) = 3x2 – 5x – 2 jîTT¿£Ø
30.
x2 – 4x + 5 = 0 esÁZdŸMT¿£sD
Á
$\Te
$#ῌD£ ì
8
Mathematics - Paper - II
(Telugu Version)
Part A and B
Time: 2½ hours
Max Marks: 50
Instructions:
1. Answer the questions under Part-A on a seperate answer book.
2. Write the answerws to the questions under Part-B on the question paper
itself and attach it to the answerbook of Part - A
Part-A
Section - I
Time: 2 hours
Marks: 35
Note:
1. Answer any five questions choosing atleast two from each of the
following two group, i.e., A and B.
2. Each question carries 2 marks.
Group - A
(dŸsÖ
Á |Ÿ
çÜuóT„ C²\T, eÔï\ dŸÎsÁôs¹ K\T eT]jáTT #û<qóŠ s¹ K\T, ¿¹ ŒçÔá$TÜ)
1.
ÿ¿£ s+‹dtýË uóT„ C²\ esZ\ yîTTÔá+ï , <‘“ ¿£s’\ esZ\ yîTTÔáïeTTqÅ£” dŸeÖqeT“ #áÖ|ŸÚeTT.
2.
32 ™d+.MT. y«dŸ+>·\ eÔï“¿ì, eÔá¹ï¿+ç<Š+ qT+& 34 ™d+.MT. <ŠÖsÁ+ýË >·\ _+<ŠTeÚ qT+&
^jáT‹&q dŸÎsÁô¹sK bõ&ƒeÚ ¿£qT>=qTeTT.
3.
y«kÍsÁeœ TT 3.5 ™d+.MT. ¿£*Ðq nsÁ>œ ÃÞøeTT jîTT¿£Ø dŸ+|ŸPsÁԒ \á yîXÕ æ\«eTTqT eT]jáTT |˜TŸ q|Ÿ]eÖDeTTqT
¿£qT¿ÃØ+&.
4.
dŸÖbœ Í¿±sÁ+ýË eÚq• qÖHî |ÓbÍ 2 MT³sÁ¢ uóք y«kÍsÁœ+, 7 MT³sÁ¢ bÔáTï ¿£*ÐeÚq•~. #á<sŠ |Á ڟ MT³sÁTÅ£”
sÁÖ. 3 e+ÔáTq sÁ+>·T yûjáTT³Å£” njûT« KsÁTÌ b+Ôá?
Group - B
(çÜ¿ÃD$TÜ, çÜ¿ÃD$TÜ nqTesÁHï \T, dŸ+uó²e«Ôá, kÍ+K«¿£XæçdŸï+)
5.
6.
7.
8.
3
sin q = ,
5
nsTTq
sec 2 q + tan 2 q .$\Te
b+Ôá?
sÁ$ 20 MT. bÔáT>ï \· uóe„ q+™|Õ “\‹& eÚH•&ƒT. € uóe„ q+ n&ƒT>·T uó²>·+ qT+& 20 MT. <ŠÖsÁ+ýË >·\
_+<ŠTeÚ e<Š>Ý \· sE 450 ¿ÃD+Ôà sÁ$“ #áÖ&ƒ>\· &†? ú dŸeÖ<ó‘H“• dŸeT]œ+#áTeTT.
ÿ¿£ dŸ+ºýË 5 bsÁT|ŸÚ, 8 Ôî\T|ŸÚ ‹+ÔáT\T>·\eÚ. € dŸ+º qT+& jáÖ<ŠºÌ¿£+>± ÿ¿£ ‹+ܓ rdï n~
(1) Ôî\T|ŸÚ ‹+Ü njûT« (2) Ôî\T|ŸÚ ‹+Ü ¿±Å£”+&† eÚ+&û dŸ+uó²e«Ôá b+Ôá?
ÿ¿£ e¯Z¿£ Ôá <ŠÔï+XøeTTqÅ£” eT<ó«Š >·Ô+á ¿£qT>=qT³Å£” dŸÖçÔá+ çyd¾, n+<ŠTý˓ |Ÿ<‘\qT $e]+#á+&.
1
Section - II
Marks: 4 ´ 1 = 4
Note:
1. Answer any four of the following six questions.
2. Each question carries 1 mark.
9.
Âs+&ƒT çÜuóT„ C²\T dŸsÖÁ bÍ\T ¿±e&†“¿ì “jáTeÖ\qT MT kõ+Ôá eÖ³\ýË çyjáT+&.
10.
8 MT³sÁ¢ y«dŸ+ 3 MT³sÁ¢ y\TfÉÔTá ï >·\ <ó‘q«|ŸÚ Å£”|ŸÎqT |ŸP]ï>± ¿£|Ο &†“¿ì nedŸsÁeTjûT« >·T&ƒ¦
yîXÕ æ\«+ b+Ôá?
11.
ÿ¿£ bͺ¿£qT ÿ¿£kÍ] <=]¢+ºq|ŸÚ&Tƒ @sÁÎ&û |ŸsÁ«ekÍqeTT\ýË dŸ] ç|Ÿ<ó‘q dŸ+K« njûT« dŸ+uó²e«ÔáqT
¿£qT>=qTeTT.
12.
5, 6, 9, 6, 12, 3 , 6. 11, 6, 7 \
13.
tan q
14.
10 eT+~ $<‘«sÁT\œ |ŸýÙà s¹ ³TqT ÿ¿£ &†¿£s¼ Y >·eT“dï 72, 78, 80 |ŸýÙà ¿£*qZ $<‘«sÁT\œ dŸ+K« esÁTdŸ>±
4, 3, 2 >± >·eT“+#á&+ƒ È]Ðq~. nsTTq#à y] dŸ>·³T |ŸýÙàqT ¿£qT>=qeTT.
u²VŸQÞø¿e£ TTqT ¿£qT>=qTeTT.
qT sin q |Ÿ<‘\ýË e«¿¡¿ï ]£ +#áTeTT.
Section - III
Marks: 4 ´ 4 = 16
Note:
1. Answer any four questions, choosing two from each of the following
groups, i.e., A and B.
2. Each question carries 4 mark.
Group - A
(dŸsÖÁ |Ÿ çÜuóT„ C²\T, eÔï“¿ì dŸÎsÁôs¹ K\T eT]jáTT #û<qŠó s¹ K\T, ¿¹ çŒ Ôá$TÜ )
15.
10 ™d+.MT. y«kÍsÁ+œ >± >·\ eÔá+ï ýË ÿ¿£ C²« ¿¹ +ç<Š+ e<ŠÝ #ûjTá T ¿ÃD+ \+‹¿ÃD+ nsTTq
(1) n\ÎeÔáKï +&ƒ+ (2) n~ó¿e£ Ôáï K+&ƒ+\ yîXÕ æ\«+ ¿£qT>=qTeTT.
16.
™|<Õ ‘¸ >·sdÁ t d¾<‘Ý+ÔáeTTqT ç|Ÿeº+º, “sÁÖ|¾+#áTeTT.
17.
6 ™d+.MT., 8 ™d+.MT., 10 ™d+.MT. y«kÍsœ\T>± >·\ |˜TŸ q >ÃÞøeTT\T ¿£]Ð+º, ÿ¿£ ™|<ŠÝ |˜ŸTq >ÃÞø+>±
eÖ]Ìq <‘“ y«kÍsÁeœ TT b+Ôá?
18.
ÿ¹¿ y«kÍsÁeœ TT, ÿ¹¿ bÔáTï ¿£*Ðq >ÃÞøeTT, dŸÖœ|ŸeTT jîTT¿£Ø –|Ÿ]Ôá\ yîÕXæý²«\ “wŸÎÜï“ ¿£qT>=qTeTT?
|˜*Ÿ ÔáeTTqT ú kõ+Ôá eÖ³\ýË $e]+#áTeTT.
2
Group - B
19.
If sec q + tan q = P
20.
ÿ¿£ He ÿ¿£ q~“ <‘{²*à eÚ+~. qBç|ŸyVŸ²+ ¿±sÁD+>± € qB rsÁ+ýË 600 ¿ÃD+ #ûdTŸ qï •
eÖsÁ+Z ýË € He 600 MT³sÁT¢ ç|ŸjÖá Dì+º neÔá* rs“• #û]+~. €q~ yî&ýƒ ÎÉ +Ôá?
21.
ÿ¹¿kÍ] s +&ƒT bͺ¿£\qT <=]Z+º y{ì™|Õ dŸ+K«\qT Å£L&q#à e#áTÌ (i) yîTTԐï\ dŸ+uó²e«ÔáqT Ôî\T|ŸÚ
‡ ¿ì+~ |Ÿ{¿ì¼ q£ T |ŸP]+#áTeTT.
Âs+&ƒT bͺ¿£\™|Õ
yîTTÔá+ï (|˜ŸT³q)
dŸ+uó²eÔá
(ii)
2
nsTTq
3
Sinq
4
$\TeqT ‘P’ \ýË ¿£qT>=qTeTT.
5
6
7
1
36
8
9 10 11
12
5
36
ÿ¿£ $<‘«]œ ç|ŸjÖî >·+ýË 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 nHû 11 |Ÿs«Á ekÍH\Tq•$. ¿±eÚq
1
ÿ¿=Ø¿£Ø |Ÿs«Á ekÍq+ dŸ+uó²e«Ôá 11 nH•sÁT. ‡ dŸeÖ<ó‘q+Ôà @¿¡u„$ó dŸTHï •y? $e]+#á+&.
22.
‡ ç¿ì+~ båq'|ŸÚq« $uó²ÈH“¿ì z›yŽ eç¿£+^jáT+&.
Ôás>Á ·ÔTá \T
0-20
20-40
40-60
60-80
80-100
100-120
båq'|ŸÚq«+
9
16
24
15
4
2
Section - IV
Marks: 5 ´ 2 = 10
Note:
1. Answer any one of the following questions.
2. Each question carries five marks.
23.
4 ™d+.MT., 5 ™d+.MT., 6 ™d+.MT. uóT„ C²\T>± >·\ ÿ¿£ çÜuóT„ È+ “]ˆ+º, <‘“¿ì dŸsÖÁ |Ÿ+>±
2
3
Âs³T¢
>·\ çÜuóT„ C²“• “]ˆ+#áTeTT.
24.
uóք $T™|Õ qTq• A _+<ŠTeÚ qT+& ÿ¿£ CÉ{Ù $eÖH“• |Ÿ]o*dï 600 }sÁÇÆ ¿ÃD+ #ûdŸT+ï ~. 15 ™d¿£q¢
ÔásÇÔá <‘“ }sÁǜ ¿ÃD+ 300 eÖsÁTÔáT+~. € CÉ{Ù $eÖq+ 1500 3 MT³sÁ¢ d¾sœ Á bÔáTïýË b>·TsÁTÔáÖ
eÚ+fñ <‘“ yû>±“• ¿£qT¿ÃØ+&.
3
Mathematics - Paper - II
Part - B
(Telugu Version)
Time: 30 min
Max Marks: 15
Instructions:
1.
n“• ç|ŸX•ø \Å£” dŸeÖ<ó‘q+ ¿£qT>=qTeTT.
2.
ç|ŸÜ ç|ŸXø•Å£”
3.
dŸeÖ<ó‘H\qT ç|ŸX•ø |ŸçÔáeTTýËHû çyjáT+&.
¿=fñd¼ ¾ çyjáT‹&q, ~<Š‹Ý &q, #î]|¾ydû ¾ çyjáT‹&q dŸeÖ<ó‘H\Å£” eÖsÁTØ\T ‚eNj&ƒeÚ.
‹VŸQÞèպ̿£ ç|ŸXø•\ dŸeÖ<ó‘qeTT\T çyjáTT³Å£” ™ |<ŠÝ n¿£ŒsÁeTT\ (€+>·¢esÁ’eÖ\)qT
–|ŸjÖî Ð+#áTeTT.
4.
5.
1
2
eÖsÁTØ.
Part-B
10 ´
I.
1
= 5 marks
2
‡ ~>·Te ç|ŸÜç|ŸX•ø Å£” b<ŠTsÁT>± 4 Èy‹T©jáT‹&q$. y{ìýË dŸs qÕ Èy‹T dŸÖº+#áT €+>·¢ ™|<ŠÝ
n¿£sŒ “• € ç|ŸX•ø ¿Â <ŠTsÁT>± ‚eNj&ƒ¦ çu²Â¿³¢ýË çyjáTTeTT.
B
M
1. A
Ð
ç|Ÿ¿Ø£ |Ÿ³+ýË LM || CB eT]jáTT LN || CD nsTTq
¿ì+~ y“ýË dŸ]jî®Tq~.
C
N
(
)
D
A)
2.
AM
AN
=
MB
ND
C)
AN
AM
=
NL
ML
D)
AM
AN
=
MB
AD
(
)
30 eT+~ $<‘«sÁT\œ dŸ>³· T 42. y]ýË ‚<Š]Ý ¿ì µ0» eÖsÁTØ\T eºÌq $TÐ*q
$<‘«sÁT\œ dŸ>·³T
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ÿ¿£ |¿£ýË qT+& rd¾q eTT¿£Ø sE (ýñ<‘) sDì ¿±e&†“¿ì dŸ+uó²e«Ôá
(
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A) 40
4.
AN
AM
=
ND
AB
( cosq , 0 ) , (0, sin q ) _+<ŠTeÚ\ eT<ó«Š <ŠÖsÁ+
A) 1
3.
B)
A)
1
52
B) -1
C) 0
B) 42
B)
C) 45
1
13
C) 45
4
D)
-1
D) 28
D) 28
5.
6.
7.
u²VŸQÞø¿£+ dŸÖçÔá+
æ f - f0 ö
÷÷ ´ h
Z = l + çç
è 2 f - f 0 - f1 ø
A) båq'|ŸÚq«eTT
B) ÔásÁ>·Ü bõ&ƒeÚ
C) ~>·Te
D) u²VŸQÞø¿+£
VŸ²<ŠTÝ
‡ ç¿ì+~ y“ýË dŸ]¿±“~
A) dŸÖ|
œ eŸ TT, >ÃÞ²\ eç¿£Ôýá ²\ yîXÕ æ\«eTT\ “wŸÎÜï 1:1
B) >ÃÞøeTT, nsÁ>
œ ÃÞ²\ eç¿£Ô\á yîXÕ æý²«\ “wŸÎÜï 2:1
C) >ÃÞøeTT, nsÁ>
œ ÃÞ²\ dŸ+|ŸPsÁԒ ýá ²\ yîXÕ æý²«\ “wŸÎÜï 2:1
D) dŸÖ|
œ eŸ TT, Xø+Å£”eÚ |˜TŸ q|Ÿ]eÖD²\ “wŸÎÜï 3:1
cos 23o - sin 67 o
tan 26o . tan 64 o
$\Te
A) sin 90°
8.
nsTTq h dŸÖº+#áTq~.
B) tan 30°
C) tan 0°
1, 2, 3, ............. 15 esÁŔ£ >·\ dŸ+K«\ýË ÿ¿£ dŸ+K«qT
9.
4
15
2
15
B)
ç¿ì+~ \+‹¿ÃD çÜuó„TC²\ýË
sin q =
C)
21
29
B)
q
1
5
D)
21
21
29
R
B
q
X
C)
29
29
q
21
C
D
D)
Y
Z
E
5
)
(
)
(
)
(
)
3
5
A
29
P
(
jáÖ<ŠºÌ¿£+>± bqT•¿=q•|ŸÚÎ&ƒT
qT dŸÖº+#áTq~.
Q
A)
)
D) cot 30°
n~ 4 jîTT¿£Ø >·TDìÈeTT njûT« dŸ+uó²e«Ôá
A)
(
q
21
F
10.
^Ôá ndŸ+uó„e |˜TŸ ³q\ dŸ+uó²e«Ôá 1 n“, ç|Ÿe*¢¿£ KºÌÔá |˜TŸ ³q\ dŸ+uó²e«Ôá 0 n“, nÜjáÖ @<û“
|˜TŸ ³q dŸ+uó²e«Ôá 0, 1 \ eT<ó«Š eÚ+³T+<Š“ #îbÍÎsÁT. úeÚ be]Ôà @¿¡u$„ó kÍïeÚ?
(
)
A) ^Ôá
II.
B) ç|Ÿe*¢¿£
C) nÜjáÖ
D) ™|Õ
eTT>·TsZ TÁ
ç¿ì+~ U²°\qT dŸs qÕ dŸeÖ<ó‘qeTT\Ôà |ŸP]+#áTeTT.
11.
ÿ¿£ eÔáï dŸÎsÁôs¹ KÅ£”, dŸÎsÁô_+<ŠTeÚ qT+& ^ºq y«kÍsÁeœ TTqÅ£” eT<óŠ« ¿ÃDeTT ______________
12.
dŸeT|˜TŸ qeTT jîTT¿£Ø ç|Ÿ¿Ø£ Ôá\, dŸ+|ŸPsÁԒ \á yîXÕ æý²«\ “wŸÎÜï
13.
ÿ¿£ eT“w¾ çbÍsÁ+uó„ k͜q+ qT+& ÔáÖsÁTÎqÅ£” yî[ß eTsÁý² <Š¿DŒì ²“¿ì ç|ŸjÖá D+ #ûd¾q|ŸÚ&Tƒ ‹jáT\T<û]q
k͜q+ qT+& € eT“w¾ eÚq• <ŠÖs“• ¿£qT>=qT³Å£” –|ŸjÖî Ð+#áT “wŸÎÜï ______________
____________
20
14.
ç|Ÿ¿Ø£ |Ÿ³+ qT+& ¿£qT>=q>·*qZ ¿¹ +çBjáT k͜q¿=\Ôá ____________
15
5
15.
5
10
15
R
Y
ç|Ÿ¿Ø£ |Ÿ³+ qT+& Y qT bõ+<Š>\· dŸ+uó²e«Ôá ______________
R = bsÁT|ŸÚ ‹+Ü
Y = |ŸdŸT|ŸÚ|#
Ÿ Ìá ‹+Ü
R Y R
16.
20
s +&ƒT dŸsÖÁ |Ÿ çÜuóT„ C²\ eT<ó«Š >·Ô\T esÁTdŸ>± 3 ™d+.MT., 5 ™d+.MT. nsTTq çÜuóT„ È yîXÕ æý²«\ “wŸÎÜï
______________
17.
ÿ¿£ dŸÖ|œ +Ÿ uóք yîÕXæ\«+ 616 #á. ™d+.MT. nsTTq <‘“ y«kÍsÁœeTT ______________
18.
6 ™d+.MT. y«kÍsÁ+œ >·\ eÔá+ï ýË ÿ¿£ C²« ¿¹ +ç<Š+ e<ŠÝ 600 ¿ÃD+ #ûdq¾ C²« bõ&ƒeÚ ______________
19.
eÖsÁTØ\T
båq'|ŸÚq«+
10
20
30
5
9
3
™|Õ <ŠÔï+XøeTTqÅ£” eT<ó«Š >·Ôá+ $\Te
20.
______________
8
ÿ¿£ €³jáT+<ŠT yû>+· >± çÜ|ŸÎ‹&q >·TsÁTï |Ÿ³+ýË #áÖ|Ÿ‹&q³T¢
1, 2, 3, 4, 5, 6, 7 ýñ¿£ 8 “ dŸÖºdŸÖï €>·TÔáT+~. n“•
|Ÿs«Á ekÍH\T dŸeTdŸ+uóe„ yîTÔ® û u²D+ >·TsÁTï 2 ¿£H• ™|<ŠÝ dŸ+K«qT
dŸÖº+#áT dŸ+uó²e«Ôá ______________
6
1
7
2
6
3
5
4
5´ ½ = 2½ marks
Match the following
Group - A
21.
Group - B
D ABC ýË D, E \T esÁTdŸ>±
(
)
A) 20
AB, AC \™|“
Õ _+<ŠTeÚ\T eT]jáTT
AD AE
=
DC EC
nsTTq
22.
D BED \+‹¿ÃD
çÜuóT„ È+ýË, ÐE = 90°,
ED2 = BD. CD nsTTq
(
)
B) 4
23.
nsÁ>Æ ÃÞø |˜TŸ q|Ÿ]eÖD+ 2250 cm3 nsTTq
(
)
C)
(
)
D) 15
(
)
E) DE || BC
(
)
F) DE ^ BC
(
)
G) 8
(
)
H)
24.
25.
<‘“ y«kÍsÁ+œ .
25 MT. bõ&ƒeÚ>\· “#îÌq >Ã&ƒ™|Õ 20 MT.
bÔáTqï eÚq• ¿ì{ì¿¡“ Ԑ¿ìq “#îÌq n&ƒT>·T
qT+& >Ã&ƒÅ”£ >·\ <ŠÖsÁ+.
5 ™d+.MT. eT]jáTT 3 ™d+.MT. y«kÍsœ\T
>·\ s +&ƒT @¿£¿¹ +ç<Š eÔï\ýË ºq• eÔï“•
dŸÎ]ô+#û ™|<ŠÝ eÔáeï TT C²« bõ&ƒeÚ
77
3
22
7
5´ ½ = 2½ marks
Match the following
Group - A
26.
sec q + tan q =
sec q - tan q
1
2
Group - B
(
)
I) 0
$\Te (
)
J) 1
nsTTq
$\Te
27.
cos 0 o ´ cos1o ´ cos 2 o ´ ........´ cos180 o
28.
cos A =
nsTTq sin A $\Te
(
)
K) 50°
29.
–<ŠjTá + 7 >·+³\Å£” 15MT. bÔáT>ï \· dŸ+ï uó+„
(
)
L)
3
5
»Oµ ¿¹ +ç<Š+>± >·\ eÔï“¿ì u²VŸ²«_+<ŠTeÚ P qT+&
(
)
M)
2
3
^jáT‹&q dŸÎsÁôs¹ K\T PA eT]jáTT PB. y{ìeT<ó«Š
¿ÃD+ 80° nsTTq ÐPOA $\Te
(
)
N) 60°
(
)
O) 2
(
)
P)
4
5
ú&ƒ bõ&ƒeÚ 15 3 MT. nsTTq dŸÖsÁ«¿ìsD
Á ²\T
uóք $TÔà #ûjTá T¿ÃDeTT.
30.
7
3