AP Class 10 Model Paper 2026 Maths
Download the AP Class 10 Model Paper 2026 Maths PDF for free at AglaSem. Designed as per the latest AP Class 10 exam pattern and marking scheme, this sample paper lets you practise likely questions, manage time and self-assess before the exam.
More Detail
Latest News
Finished viewing? Save it for later —
Download AP Class 10 Model Paper 2026 Maths (PDF · 14 pages)Downloaded 203 times
About AP Class 10 Model Paper 2026 Maths
AP Class 10 Model Paper 2026 Maths is available here for free download. Published by Andhra Pradesh Board for Class 10, this sample paper can be viewed online or downloaded as a PDF (14 pages). Candidates preparing for Class 10 can use AP Class 10 Model Paper 2026 Maths to understand the exam pattern, the type of questions asked, and the overall difficulty level.
Frequently Asked Questions
How can I download AP Class 10 Model Paper 2026 Maths?
Open this page and click the Download button to save AP Class 10 Model Paper 2026 Maths as a PDF. It is completely free on AglaSem Docs.
Is AP Class 10 Model Paper 2026 Maths free to download?
Yes. AP Class 10 Model Paper 2026 Maths can be viewed online and downloaded as a PDF free of cost on AglaSem Docs.
How many pages does AP Class 10 Model Paper 2026 Maths have?
AP Class 10 Model Paper 2026 Maths contains 14 pages, which you can read online or download together as a single PDF.
Where can I find more Class 10 study material?
You can find more Class 10 question papers, sample papers, syllabus, and answer keys on AglaSem Docs.
AP Class 10 Model Paper 2026 Maths – Text
Read the full text of this sample paper below — useful to quickly search, copy and reference the content online without downloading the PDF.
📄 View text version (12 pages)
Page 1
BLUE PRINT & MODEL PAPERS OF SSC PUBLIC EXAMINATIONS FOR THE ACADEMIC YEAR 2025-26
BY THE DIRECTOR OF GOVERNMENT EXAMINATIONS (SSC BOARD), A.P.
BY THE DIRECTOR OF GOVERNMENT EXAMINATIONS (SSC BOARD), A.P.
Page 3
BLUE PRINT & MODEL PAPERS OF SSC PUBLIC EXAMINATIONS FOR THE ACADEMIC YEAR 2025-26
BY THE DIRECTOR OF GOVERNMENT EXAMINATIONS (SSC BOARD), A.P.
SSC PUBLIC EXAMATIN
EXAMATINATIONS 2025 - 26
TINA
MATHEMA
MATHEMATICS
THEMATICS (MODEL PAPER - 1)
(ENGLISH VERSION)
Time : 3 Hours 15 Minutes Max. Marks : 100
Instructions :
1. In the duration of 3hours 15 minutes, 15 minutes of time is allotted to read the question
paper.
2. All answers shall be written in the answer booklet only.
3. Question paper consists of 4 Sections and 33 questions.
4. Internal choice is available in section - IV only.
5. Answers shall be written neatly and legibly.
SECTION - I 12 ´ 1 = 12 M
Note : i) Answer all the questions in one word or phrase.
ii) Each question carries 1 mark.
1. Two positive integers A and B are written as A = p3q2 and B = pq3 where p,q are prime numbers
then HCF (A,B) is
A) p3q2 B) pq2 C) p3q D) pq
2. The coefficient of x in p(x) = 7x 6x + 5x + 8 is
3 2
A) 7 B) 6 C) 5 D) 5
3. Write a polynmial of degree 4, having constant term 6.
4. Create a linear equation which is parallel to the given line 2x + 3y + 8 = 0.
5. Assertion (A) : 4 is the common diffrence of A.P. 5, 9, 13 ..... 185.
Reason (R) : The common diffrence of an A.P. d = an an1
Now, choose the correct answer.
A) Both A and R are True and R is correct explanation of A.
B) Both A and R are True and R is not correct explanation of A.
C) A is true, R is false.
D) A is false, R is true.
6. In the adjacent figure if AD = 2cm, BD = 4cm A
2cm 5cm
D > E
and AE = 5cm then EC = .... cm.
4cm
B > C
A) 7 B) 10 C) 14 D) 20
BY THE DIRECTOR OF GOVERNMENT EXAMINATIONS (SSC BOARD), A.P.
SSC PUBLIC EXAMATIN
EXAMATINATIONS 2025 - 26
TINA
MATHEMA
MATHEMATICS
THEMATICS (MODEL PAPER - 1)
(ENGLISH VERSION)
Time : 3 Hours 15 Minutes Max. Marks : 100
Instructions :
1. In the duration of 3hours 15 minutes, 15 minutes of time is allotted to read the question
paper.
2. All answers shall be written in the answer booklet only.
3. Question paper consists of 4 Sections and 33 questions.
4. Internal choice is available in section - IV only.
5. Answers shall be written neatly and legibly.
SECTION - I 12 ´ 1 = 12 M
Note : i) Answer all the questions in one word or phrase.
ii) Each question carries 1 mark.
1. Two positive integers A and B are written as A = p3q2 and B = pq3 where p,q are prime numbers
then HCF (A,B) is
A) p3q2 B) pq2 C) p3q D) pq
2. The coefficient of x in p(x) = 7x 6x + 5x + 8 is
3 2
A) 7 B) 6 C) 5 D) 5
3. Write a polynmial of degree 4, having constant term 6.
4. Create a linear equation which is parallel to the given line 2x + 3y + 8 = 0.
5. Assertion (A) : 4 is the common diffrence of A.P. 5, 9, 13 ..... 185.
Reason (R) : The common diffrence of an A.P. d = an an1
Now, choose the correct answer.
A) Both A and R are True and R is correct explanation of A.
B) Both A and R are True and R is not correct explanation of A.
C) A is true, R is false.
D) A is false, R is true.
6. In the adjacent figure if AD = 2cm, BD = 4cm A
2cm 5cm
D > E
and AE = 5cm then EC = .... cm.
4cm
B > C
A) 7 B) 10 C) 14 D) 20
Page 4
7. Which Trigonometric ratio is equal to Adjacent side of θ/hypotenuse
A) sin θ B) cos θ C) tan θ D) cot θ
8. In Heights and Distance problems, angles are always taken with respect to horizontal
line. (True / False)
9. Surface area Hemisphere having radius r is
A) πr2 B) 2 πr2 C) 3 πr2 D) 4 πr2
()
10. P(E) + P E = ________
A) 0 B) 1 C) 1 D) More than 1
11. Create a geometrical design involving two tangents drawn from an external point to
the circle.
12. Form a quadratic equation which has 1 as one of its roots
SECTION - II 8 ´ 2 = 16 M
Note : i) Answer all the questions.
ii) Each question carries 2 marks.
13. Create a quadratic polynomial whose sum and product of zeroes are 3 and 2
respectively.
14. Find the value of k, if both the roots of 2x2 + kx + 3 = 0 are equal.
15. State SAS criterian in similarities of triangles.
1
16. If tan (A +B) = 3 and tan (AB)= ; 0 < A + B ≤ 90 ° and A > B Find A.
3
17. Define angle of elevation with a simple rough diagram.
18. A Quadrilatera ABCD is drawn to circumscribe a circle then write the relation between
its sides.
19. Find the volume of largest circular cone that can be cut out of a cube of edge 7cm.
20. Write the formulae to find the distance between
i) the two points (x1y1) and (x2y2)
ii) Origin and a point (x,y)
A) sin θ B) cos θ C) tan θ D) cot θ
8. In Heights and Distance problems, angles are always taken with respect to horizontal
line. (True / False)
9. Surface area Hemisphere having radius r is
A) πr2 B) 2 πr2 C) 3 πr2 D) 4 πr2
()
10. P(E) + P E = ________
A) 0 B) 1 C) 1 D) More than 1
11. Create a geometrical design involving two tangents drawn from an external point to
the circle.
12. Form a quadratic equation which has 1 as one of its roots
SECTION - II 8 ´ 2 = 16 M
Note : i) Answer all the questions.
ii) Each question carries 2 marks.
13. Create a quadratic polynomial whose sum and product of zeroes are 3 and 2
respectively.
14. Find the value of k, if both the roots of 2x2 + kx + 3 = 0 are equal.
15. State SAS criterian in similarities of triangles.
1
16. If tan (A +B) = 3 and tan (AB)= ; 0 < A + B ≤ 90 ° and A > B Find A.
3
17. Define angle of elevation with a simple rough diagram.
18. A Quadrilatera ABCD is drawn to circumscribe a circle then write the relation between
its sides.
19. Find the volume of largest circular cone that can be cut out of a cube of edge 7cm.
20. Write the formulae to find the distance between
i) the two points (x1y1) and (x2y2)
ii) Origin and a point (x,y)
Page 5
SECTION - III 8 ´ 4 = 32 M
Note : i) Answer all the questions.
ii) Each question carries 4 marks.
21. One card is drawn from a well-shuffled deck of 52 cards. "Calculate the probability
that the drawn card will be an ace" ?
Now create 4 such type of questions.
22. Write the formula to find mode of a grouped data and explain the terms in it.
23. A solid is in the shape of a cone standing on a hemisphere with both their radii being
equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the
solid in terms of π.
1
24. Find the discriminant of the equation 3x2 2x + = 0 and hence find the nature of its
3
roots. Find them if they are real.
25. State three identies that used in Trignometry.
26. Write the following formulae of A.P. a1,a2,a3 ...... and name the terms in each
A) nth term (an)
B) Sum of first n terms (Sn)
C) Common difference (d)
27. Prove that the parallelogram circumscribing circle is a rhombus.
28. By observing the graph Answer the following Questions.
Y
X' 3 4 X
1) What is the shape of the graph.
2) How many zeros it has ?
3) What are the zeroes
Y'
4) Find the sum of Zeroes.
Note : i) Answer all the questions.
ii) Each question carries 4 marks.
21. One card is drawn from a well-shuffled deck of 52 cards. "Calculate the probability
that the drawn card will be an ace" ?
Now create 4 such type of questions.
22. Write the formula to find mode of a grouped data and explain the terms in it.
23. A solid is in the shape of a cone standing on a hemisphere with both their radii being
equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the
solid in terms of π.
1
24. Find the discriminant of the equation 3x2 2x + = 0 and hence find the nature of its
3
roots. Find them if they are real.
25. State three identies that used in Trignometry.
26. Write the following formulae of A.P. a1,a2,a3 ...... and name the terms in each
A) nth term (an)
B) Sum of first n terms (Sn)
C) Common difference (d)
27. Prove that the parallelogram circumscribing circle is a rhombus.
28. By observing the graph Answer the following Questions.
Y
X' 3 4 X
1) What is the shape of the graph.
2) How many zeros it has ?
3) What are the zeroes
Y'
4) Find the sum of Zeroes.
Page 6
SECTION - IV 5 ´ 8 = 40 M
Note : i) Answer all the questions.
ii) Each question carries 8 marks.
iii) There is an internal choice for each question.
29. a) Is 3 + 2 5 irrational ? justify your answer.
OR
b) Sides AB and AC and Median AD of a triangle ABC are respectively proportional to
the sides PQ and PR and Median PM of another triangle PQR.
Show that ∆ABC ~ ∆PQR.
30. a) Two students Claim to have found the points of trisection of the line segment joining
A (4,1) and B(2,3) as follows.
⎛ 5⎞ ⎛ 7⎞
Students A : ⎜ 0 , ⎟ and ⎜ 0 , ⎟
⎝ 3⎠ ⎝ 3⎠
⎛ −5 ⎞ ⎛ −7 ⎞
Students B : ⎜ 2, ⎟ and ⎜0, ⎟
⎝ 3⎠ ⎝ 3⎠
Who is correct ? Justify.
OR
b) A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by
means of a 5 m long rope. Find
i) the area of that part of the field in which the horse can graze.
ii) the increase in the gazing area if the rope was 10 m long instead of 5 m.
(use π = 3.14)
31. a) A game of chance consists of spinning an arrow which comes to rest pointing at one
of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely out comes. Caliculate
the probabilities that it will point at 8 1
7 2
i) 8 ii) an odd number
→
6 3
iii) a number greater than 3 iv) a number less thant or equal to 8 5 4
OR
b) From a point on a bridge across a river, the angles of depression of the banks on
opposite sides of the rivers are 30° and 45° , respectively. If the bridge is at a height
of 3m from the banks, find the width of the river.
Note : i) Answer all the questions.
ii) Each question carries 8 marks.
iii) There is an internal choice for each question.
29. a) Is 3 + 2 5 irrational ? justify your answer.
OR
b) Sides AB and AC and Median AD of a triangle ABC are respectively proportional to
the sides PQ and PR and Median PM of another triangle PQR.
Show that ∆ABC ~ ∆PQR.
30. a) Two students Claim to have found the points of trisection of the line segment joining
A (4,1) and B(2,3) as follows.
⎛ 5⎞ ⎛ 7⎞
Students A : ⎜ 0 , ⎟ and ⎜ 0 , ⎟
⎝ 3⎠ ⎝ 3⎠
⎛ −5 ⎞ ⎛ −7 ⎞
Students B : ⎜ 2, ⎟ and ⎜0, ⎟
⎝ 3⎠ ⎝ 3⎠
Who is correct ? Justify.
OR
b) A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by
means of a 5 m long rope. Find
i) the area of that part of the field in which the horse can graze.
ii) the increase in the gazing area if the rope was 10 m long instead of 5 m.
(use π = 3.14)
31. a) A game of chance consists of spinning an arrow which comes to rest pointing at one
of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely out comes. Caliculate
the probabilities that it will point at 8 1
7 2
i) 8 ii) an odd number
→
6 3
iii) a number greater than 3 iv) a number less thant or equal to 8 5 4
OR
b) From a point on a bridge across a river, the angles of depression of the banks on
opposite sides of the rivers are 30° and 45° , respectively. If the bridge is at a height
of 3m from the banks, find the width of the river.
Page 7
32. a) A life insurance agent found the following data for distribution of ages of 100 policy
holders. Calculate the median age, if policies are given only to persons having age
18 years onwords but less than 60 years.
Age in Below Below Below Below Below Below Below Below Below
years 20 25 30 35 40 45 50 55 60
Number of 2 6 24 45 78 89 92 98 100
Policy holders
OR
b) In a school, stundts thought of planning trees in and around the school to reduce air
pollution. It was decided that the number of trees, that each section of each class will
plant, will be the same as the class, in which they are studying. e.g. a section of class I
will plant 1 trees, a section of class II will plant 2 trees and so on till class XII. There are
three sections of each class. How many trees will be planted by the students ?
33. a) Draw the graph of the following pair of linear equations and find the solution from
the graph.
x y + 1 = 0 and 3x + 2y 12 = 0
OR
b) 5 pencils and 7 pens together cost Rs.50 where as 7 pencils 5 pens together cost
Rs.46. Find the cost of one pencil and that of one pen.
Form the pair of linear equations for the above problem and find their solution
graphically.
holders. Calculate the median age, if policies are given only to persons having age
18 years onwords but less than 60 years.
Age in Below Below Below Below Below Below Below Below Below
years 20 25 30 35 40 45 50 55 60
Number of 2 6 24 45 78 89 92 98 100
Policy holders
OR
b) In a school, stundts thought of planning trees in and around the school to reduce air
pollution. It was decided that the number of trees, that each section of each class will
plant, will be the same as the class, in which they are studying. e.g. a section of class I
will plant 1 trees, a section of class II will plant 2 trees and so on till class XII. There are
three sections of each class. How many trees will be planted by the students ?
33. a) Draw the graph of the following pair of linear equations and find the solution from
the graph.
x y + 1 = 0 and 3x + 2y 12 = 0
OR
b) 5 pencils and 7 pens together cost Rs.50 where as 7 pencils 5 pens together cost
Rs.46. Find the cost of one pencil and that of one pen.
Form the pair of linear equations for the above problem and find their solution
graphically.
Page 8
BLUE PRINT & MODEL P
BLUE APERS OF SSC PUBLIC EXAMIN
PAPERS ATIONS FOR THE ACADEMIC YEAR 2025-26
EXAMINA
BY THE DIRECTOR OF GOVERNMENT EXAMIN
DIRECTOR GOVERNMENT EXAMINA ATIONS (SSC BOARD), A.P
BOARD), A.P..
BLUE APERS OF SSC PUBLIC EXAMIN
PAPERS ATIONS FOR THE ACADEMIC YEAR 2025-26
EXAMINA
BY THE DIRECTOR OF GOVERNMENT EXAMIN
DIRECTOR GOVERNMENT EXAMINA ATIONS (SSC BOARD), A.P
BOARD), A.P..
Page 10
BLUE PRINT & MODEL P
BLUE APERS OF SSC PUBLIC EXAMIN
PAPERS ATIONS FOR THE ACADEMIC YEAR 2025-26
EXAMINA
BY THE DIRECTOR OF GOVERNMENT EXAMIN
DIRECTOR GOVERNMENT EXAMINA ATIONS (SSC BOARD), A.P
BOARD), A.P..
SSC PUBLIC EXAMATIN
EXAMATINATIONS 2025 - 26
TINA
MATHEMA
MATHEMATICS
THEMATICS (MODEL PAPER - 1)
(TELUGU VERSION)
Time : 3 Hours 15 Minutes Max. Marks : 100
dÖ#áq\T :
1. 3 >·+öö15 öö\ýË 15 $TcÍ\T ç|Xø |çÔáeTTqT #á<T eÚ³Â¿Õ ¿¹ {²sTT+#á&q~.
2. n ç|Xø \Å£ deÖ<óqeTT\T MT¿ìeÇ&q deÖ<óq |çÔáeTTýËHû sjáTeýÉqT.
3. ç|Xø |çÔá+ýË yîTTÔá+ï 4 $uó²>±\T eT]jáTT 33 ç|Xø \T HsTT.
4. H\T>·e $uó²>·+ýË ç|Xø \Å£ eÖçÔáyTû n+ÔásÔ ZÁ á m+|¾¿Å£ £ ne¿±Xø+ ¿£\<T.
5. n deÖ<óqeTT\T dÎw+¼ >±qT, >·T+ç&eTT>± sjáT+&.
$uó²>·+ ` I 12 ´ 1 = 12 M
dÖ#áq\T : i) n ç|Xø\Å£ ÿ¿£ |<+ ýñ< ÿ¿£ eÖ³ýË deÖ<óq+ sjáT+&.
ii) ç|Ü ç|XøÅ£ 1 eÖsÁTØ.
1. A = p3q2 eT]jáTT B = pq3 \T ¿£Ø& A,B \T <óq
|PsÁ d+K«\T eT]jáTT p,q \T ç|<ó H+¿±\T nsTTq
>·qkÍuó²(A,B) =
A) p3q2 B) pq2 C) p3q D) pq
2. p(x) = 7x3 6x2 + 5x + 8 q+<T x ` >·TD¿£eTT
A) 7 B) 6 C) 5 D) 5
3. |]eÖDeTT 4, eT]jáTT d¾s
|
Á <
e
TT `6 >± >·\ VQ|~ sjáT+&.
4. 2x + 3y + 8 = 0 Å£ deÖ+Ôás+
Á >± >·\ eTs=¿£ s¹ FjáT dMT¿£sD
Á eTT sÁÖbõ+~+#á+&.
5. ç|¿£³q (A) : A.P. 5, 9, 13 ..... 185 q+<T kÍeÖq« uó<
ñ e
TT (|<+Ôáse
Á TT) 4.
¿±sÁD+ (R) : ÿ¿£ n+¿£çXâ&ý
ó Ë |<+Ôáse
Á TT d = an an1
ds q
Õ deÖ<óqeTTqT mqT¿=q+&.
A) A eT]jáTT R \T dÔ«á eTT. eT]jáTT R, A deT]+#áTqT.
B) A eT]jáTT R \T dÔ«á eTT. eT]jáTT R, A deT]+#á<T .
C) A dÔá«eTT, R ndÔ«á eTT.
D) A ndÔá«eTT, R dÔá«eTT.
6. ç|¿Ø£ |³eTTýË AD = 2d+.MT., BD = 4 d+.MT.
A
2cm
eT]jáTT AE = 5d+.MT. nsTTq EC = .... d+.MT. D
5cm
> E
4cm
A) 7 B) 10 C) 14 D) 20 B > C
BLUE APERS OF SSC PUBLIC EXAMIN
PAPERS ATIONS FOR THE ACADEMIC YEAR 2025-26
EXAMINA
BY THE DIRECTOR OF GOVERNMENT EXAMIN
DIRECTOR GOVERNMENT EXAMINA ATIONS (SSC BOARD), A.P
BOARD), A.P..
SSC PUBLIC EXAMATIN
EXAMATINATIONS 2025 - 26
TINA
MATHEMA
MATHEMATICS
THEMATICS (MODEL PAPER - 1)
(TELUGU VERSION)
Time : 3 Hours 15 Minutes Max. Marks : 100
dÖ#áq\T :
1. 3 >·+öö15 öö\ýË 15 $TcÍ\T ç|Xø |çÔáeTTqT #á<T eÚ³Â¿Õ ¿¹ {²sTT+#á&q~.
2. n ç|Xø \Å£ deÖ<óqeTT\T MT¿ìeÇ&q deÖ<óq |çÔáeTTýËHû sjáTeýÉqT.
3. ç|Xø |çÔá+ýË yîTTÔá+ï 4 $uó²>±\T eT]jáTT 33 ç|Xø \T HsTT.
4. H\T>·e $uó²>·+ýË ç|Xø \Å£ eÖçÔáyTû n+ÔásÔ ZÁ á m+|¾¿Å£ £ ne¿±Xø+ ¿£\<T.
5. n deÖ<óqeTT\T dÎw+¼ >±qT, >·T+ç&eTT>± sjáT+&.
$uó²>·+ ` I 12 ´ 1 = 12 M
dÖ#áq\T : i) n ç|Xø\Å£ ÿ¿£ |<+ ýñ< ÿ¿£ eÖ³ýË deÖ<óq+ sjáT+&.
ii) ç|Ü ç|XøÅ£ 1 eÖsÁTØ.
1. A = p3q2 eT]jáTT B = pq3 \T ¿£Ø& A,B \T <óq
|PsÁ d+K«\T eT]jáTT p,q \T ç|<ó H+¿±\T nsTTq
>·qkÍuó²(A,B) =
A) p3q2 B) pq2 C) p3q D) pq
2. p(x) = 7x3 6x2 + 5x + 8 q+<T x ` >·TD¿£eTT
A) 7 B) 6 C) 5 D) 5
3. |]eÖDeTT 4, eT]jáTT d¾s
|
Á <
e
TT `6 >± >·\ VQ|~ sjáT+&.
4. 2x + 3y + 8 = 0 Å£ deÖ+Ôás+
Á >± >·\ eTs=¿£ s¹ FjáT dMT¿£sD
Á eTT sÁÖbõ+~+#á+&.
5. ç|¿£³q (A) : A.P. 5, 9, 13 ..... 185 q+<T kÍeÖq« uó<
ñ e
TT (|<+Ôáse
Á TT) 4.
¿±sÁD+ (R) : ÿ¿£ n+¿£çXâ&ý
ó Ë |<+Ôáse
Á TT d = an an1
ds q
Õ deÖ<óqeTTqT mqT¿=q+&.
A) A eT]jáTT R \T dÔ«á eTT. eT]jáTT R, A deT]+#áTqT.
B) A eT]jáTT R \T dÔ«á eTT. eT]jáTT R, A deT]+#á<T .
C) A dÔá«eTT, R ndÔ«á eTT.
D) A ndÔá«eTT, R dÔá«eTT.
6. ç|¿Ø£ |³eTTýË AD = 2d+.MT., BD = 4 d+.MT.
A
2cm
eT]jáTT AE = 5d+.MT. nsTTq EC = .... d+.MT. D
5cm
> E
4cm
A) 7 B) 10 C) 14 D) 20 B > C
Page 11
7. θ Å£ dq uóT ÈeTT/¿£se
Á TT qT dÖº+#áT çÜ¿ÃD$TrjáT wÎÜï
A) sin θ B) cos θ C) tan θ D) cot θ
8. mÔáT\
ï T eT]jáTT <Ös\T deTd«\ýË ¿ÃDeTT\qT <w¾s¹¼ K <ósÁ+>± |]>·Dk
ì ÍïeTT. (dÔ«á eTT / ndÔ«á eTT)
9. 'r' y«kÍsÁe
Æ TT >·\ nsÁ>
Æ ÃÞøeTT |]Ôá\ yîX
Õ æ\«+
A) πr2 B) 2 πr2 C) 3 πr2 D) 4 πr2
()
10. P(E) + P E = ________
A) 0 B) 1 C) 1 D) 1 ¿£+fñ mÅ£Øe.
11. eÔï¿ì u²V²« _+<TeÚ qT+& s
 +&T dÎsÁôs¹ K\T +&Tq³T¢ C²«$TrjáT ¿±sÁeTT sÁÖbõ+~+#áTeTT.
12. 1 ÿ¿£ eTÖ\eTT>± >·\ ÿ¿£ esÁd
Z M
T¿£sD
Á eTT sÁÖbõ+~+#áTeTT.
$uó²>·+ ` II 8 ´ 2 = 16 M
dÖ#áq\T : i) n ç|Xø \Å£ deÖ<óq+ sjáT+&.
ii) ç|Ü ç|XøÅ£ 2 eÖsÁTØ\T.
13. eTÖý²\ yîTTÔáïeTT 3 eT]jáTT eTÖý²\ \ÝeTT 2 >± >·\ ÿ¿£ esÁZ VQ|~ sÁÖbõ+~+#á+&.
14. 2x2 + kx + 3 = 0 esÁZ dMT¿£sD
Á eTT s +&T deÖq yde
ï eTÖý²\T ¿£*Ð +fñ k $\TeqT ¿£qT>=qTeTT.
15. uóT .¿Ã.uóT dsÖ
Á |¿Ô
£ á jáTeTeTTqT çyjáT+&.
1
16. tan (A +B) = 3 eT]jáTT tan (AB)= ; 0 < A + B ≤ 90 ° eT]jáTT A > B nsTTq A $\Te
3
¿£qT>=qTeTT.
17. ÿ¿£ ºÔáTï |³eTT |jÖ
î Ð+º }sÁÇ ¿ÃDeTTqT sÁǺ+#áTeTT.
18. ABCD #áÔTá sÁTÒÛÈeTTýË ÿ¿£ eÔáe
ï TT n+Ôá]Ï
¢ +#á&+~. nsTTq < uóT C²\ eT<ó« >·\ d++<óe
TTqT Ôî\T|ÚeTT.
19. 7 d+.MT. uóTÈeTT>± >·\ deT|TqeTT qT+& >·]w÷ |Tq|]eÖDeTT >·\ ç¿£eTeÔ￱sÁ Xø+KTeÚqT
ÔájÖ
á sÁT#ûjTá >·*Ðq < |T q|]eÖDeTT ¿£qT>=qTeTT.
20. i) (x1y1) eT]jáTT (x2y2) _+<TeÚ\ eT<ó« <ÖsÁeTT
ii) eTÖ\ _+<TeÚ qT+& _+<TeÚ (x,y)Å£ >·\ <ÖsÁeTT\T ¿£qT>=qT³Å£ >·\ dÖçÔáeTT\T çyjáT+&.
Á TT qT dÖº+#áT çÜ¿ÃD$TrjáT wÎÜï
A) sin θ B) cos θ C) tan θ D) cot θ
8. mÔáT\
ï T eT]jáTT <Ös\T deTd«\ýË ¿ÃDeTT\qT <w¾s¹¼ K <ósÁ+>± |]>·Dk
ì ÍïeTT. (dÔ«á eTT / ndÔ«á eTT)
9. 'r' y«kÍsÁe
Æ TT >·\ nsÁ>
Æ ÃÞøeTT |]Ôá\ yîX
Õ æ\«+
A) πr2 B) 2 πr2 C) 3 πr2 D) 4 πr2
()
10. P(E) + P E = ________
A) 0 B) 1 C) 1 D) 1 ¿£+fñ mÅ£Øe.
11. eÔï¿ì u²V²« _+<TeÚ qT+& s
 +&T dÎsÁôs¹ K\T +&Tq³T¢ C²«$TrjáT ¿±sÁeTT sÁÖbõ+~+#áTeTT.
12. 1 ÿ¿£ eTÖ\eTT>± >·\ ÿ¿£ esÁd
Z M
T¿£sD
Á eTT sÁÖbõ+~+#áTeTT.
$uó²>·+ ` II 8 ´ 2 = 16 M
dÖ#áq\T : i) n ç|Xø \Å£ deÖ<óq+ sjáT+&.
ii) ç|Ü ç|XøÅ£ 2 eÖsÁTØ\T.
13. eTÖý²\ yîTTÔáïeTT 3 eT]jáTT eTÖý²\ \ÝeTT 2 >± >·\ ÿ¿£ esÁZ VQ|~ sÁÖbõ+~+#á+&.
14. 2x2 + kx + 3 = 0 esÁZ dMT¿£sD
Á eTT s +&T deÖq yde
ï eTÖý²\T ¿£*Ð +fñ k $\TeqT ¿£qT>=qTeTT.
15. uóT .¿Ã.uóT dsÖ
Á |¿Ô
£ á jáTeTeTTqT çyjáT+&.
1
16. tan (A +B) = 3 eT]jáTT tan (AB)= ; 0 < A + B ≤ 90 ° eT]jáTT A > B nsTTq A $\Te
3
¿£qT>=qTeTT.
17. ÿ¿£ ºÔáTï |³eTT |jÖ
î Ð+º }sÁÇ ¿ÃDeTTqT sÁǺ+#áTeTT.
18. ABCD #áÔTá sÁTÒÛÈeTTýË ÿ¿£ eÔáe
ï TT n+Ôá]Ï
¢ +#á&+~. nsTTq < uóT C²\ eT<ó« >·\ d++<óe
TTqT Ôî\T|ÚeTT.
19. 7 d+.MT. uóTÈeTT>± >·\ deT|TqeTT qT+& >·]w÷ |Tq|]eÖDeTT >·\ ç¿£eTeÔ￱sÁ Xø+KTeÚqT
ÔájÖ
á sÁT#ûjTá >·*Ðq < |T q|]eÖDeTT ¿£qT>=qTeTT.
20. i) (x1y1) eT]jáTT (x2y2) _+<TeÚ\ eT<ó« <ÖsÁeTT
ii) eTÖ\ _+<TeÚ qT+& _+<TeÚ (x,y)Å£ >·\ <ÖsÁeTT\T ¿£qT>=qT³Å£ >·\ dÖçÔáeTT\T çyjáT+&.
Page 12
$uó²>·+ ` III 8 ´ 4 = 32 M
dÖ#áq\T : i) ç¿ì+~ n ç|Xø\Å£ deÖ<óqeTT\T çyjáTTeTT.
ii) ç|Ü ç|XøÅ£ 4 eÖsÁTØ\T.
21. u²>·T>± ¿£\T|&q |¿£¿±sÁT\
¦ ¿£³¼ qT+& ÿ¿£ ¿±sÁT¦ rjáTT³|Õ 4 ç|Xø \qT sÁÖbõ+~+#á+&.
<V²sÁD : |¿£eTT¿£Ø\ ¿£³q
¼ T+& @dt ¿±sÁT¦ rjáTT³Å£ >·\ d+uó²e«Ôá m+Ôá ?
22. e¯Z¿£ Ôá <Ôï+XøeTT qT+& u²VQÞø¿e
£ TT ¿£qT>=qT³Å£ dÖçÔáeTT çyd¾ n+<* |<\qT $e]+#áTeTT.
23. nsÁ>
ÃÞøeTT|Õ Xø+KT neTsÁÌ&q ¿±sÁeTTýË ÿ¿£ |T H¿£Ü +~. s +&+{ì y«kÍs\T ÿ¿£ d+.MT.¿ì deÖqeTT.
Xø+Å£eÚ jîTT¿£Ø mÔáTï < y«kÍs¿ì deÖqeTT. nsTTq |T H¿£Ü |]eÖD+ π \ýË ¿£qT>=q+&.
1
24. 3x2 2x + = 0 jîTT¿£Ø $#á¿D
£
ì ¿£qT>=qTeTT. Ôá<Çs eTÖý²\ dÇuó²y Ôî\T|ÚeTT. ÿ¿£yÞû ø yde
ï
3
eTÖý²\T ¿£*Ð +fñ y{ì ¿£qT>=qTeTT.
25. çÜ¿ÃD$TÜýË |jÖ
î Ð+#û eTÖ&T dsÇÁ dMT¿£sD
Á ²\T çyjáT+&.
26. n+¿£çXâ&¿
ó ì a1,a2,a3 ...... #î+~q ç¿ì+~ dÖçÔ\qT çyjáT+& eT]jáTT y{ìýË q |<\qT >·T]ï+#á+&.
A) ne |<+
(an)
B) yîTT<{ì n |<\ yîTTÔá+
ï (Sn)
C) |<+Ôás+
Á (d)
27. ÿ¿£ deÖ+ÔásÁ #áÔTá sÁTÒÛÈ+ýË eÔáe
ï TT n+Ôá]Ï
¢ +#á&q n~ deT#áÔTá sÁTÒÛÈeT>·Tq #áÖ|+&.
28. Y
X' 3 4 X
Y'
|Õ ç>±|
t |]o*+º ç¿ì+~ ç|Xø \Å£ deÖ<óH\T çyjáT+&.
1) ç>±|t ¿±sÁ+ |¹s$T?
2) B¿ì >·\ XøSH«\T m ?
3) XøSH«\qT çyjáTTeTT.
4) XøSH«\ yîTTÔá+
ï ¿£qT>=qTeTT.
dÖ#áq\T : i) ç¿ì+~ n ç|Xø\Å£ deÖ<óqeTT\T çyjáTTeTT.
ii) ç|Ü ç|XøÅ£ 4 eÖsÁTØ\T.
21. u²>·T>± ¿£\T|&q |¿£¿±sÁT\
¦ ¿£³¼ qT+& ÿ¿£ ¿±sÁT¦ rjáTT³|Õ 4 ç|Xø \qT sÁÖbõ+~+#á+&.
<V²sÁD : |¿£eTT¿£Ø\ ¿£³q
¼ T+& @dt ¿±sÁT¦ rjáTT³Å£ >·\ d+uó²e«Ôá m+Ôá ?
22. e¯Z¿£ Ôá <Ôï+XøeTT qT+& u²VQÞø¿e
£ TT ¿£qT>=qT³Å£ dÖçÔáeTT çyd¾ n+<* |<\qT $e]+#áTeTT.
23. nsÁ>
ÃÞøeTT|Õ Xø+KT neTsÁÌ&q ¿±sÁeTTýË ÿ¿£ |T H¿£Ü +~. s +&+{ì y«kÍs\T ÿ¿£ d+.MT.¿ì deÖqeTT.
Xø+Å£eÚ jîTT¿£Ø mÔáTï < y«kÍs¿ì deÖqeTT. nsTTq |T H¿£Ü |]eÖD+ π \ýË ¿£qT>=q+&.
1
24. 3x2 2x + = 0 jîTT¿£Ø $#á¿D
£
ì ¿£qT>=qTeTT. Ôá<Çs eTÖý²\ dÇuó²y Ôî\T|ÚeTT. ÿ¿£yÞû ø yde
ï
3
eTÖý²\T ¿£*Ð +fñ y{ì ¿£qT>=qTeTT.
25. çÜ¿ÃD$TÜýË |jÖ
î Ð+#û eTÖ&T dsÇÁ dMT¿£sD
Á ²\T çyjáT+&.
26. n+¿£çXâ&¿
ó ì a1,a2,a3 ...... #î+~q ç¿ì+~ dÖçÔ\qT çyjáT+& eT]jáTT y{ìýË q |<\qT >·T]ï+#á+&.
A) ne |<+
(an)
B) yîTT<{ì n |<\ yîTTÔá+
ï (Sn)
C) |<+Ôás+
Á (d)
27. ÿ¿£ deÖ+ÔásÁ #áÔTá sÁTÒÛÈ+ýË eÔáe
ï TT n+Ôá]Ï
¢ +#á&q n~ deT#áÔTá sÁTÒÛÈeT>·Tq #áÖ|+&.
28. Y
X' 3 4 X
Y'
|Õ ç>±|
t |]o*+º ç¿ì+~ ç|Xø \Å£ deÖ<óH\T çyjáT+&.
1) ç>±|t ¿±sÁ+ |¹s$T?
2) B¿ì >·\ XøSH«\T m ?
3) XøSH«\qT çyjáTTeTT.
4) XøSH«\ yîTTÔá+
ï ¿£qT>=qTeTT.
Page 13
$uó²>·+ ` IV 5 ´ 8 = 40 M
dÖ#áq\T : i) n ç|Xø\Å£ deÖ<óqeTT\T sjáT+&.
ii) ç|Ü ç|XøÅ£ 8 eÖsÁTØ\T.
iii) ç|Ü ç|XøÅ£ n+ÔásÁZÔá m+|¾¿£ ¿£\<T.
29. a) 3 + 2 5 ÿ¿£ ¿£sD
Á j
¡ Tá d+K« n>·TH ? ú deÖ<óH deT]+#áTeTT.
(ýñ<)
b) çÜuóTÈeTT ABC ýË uóT C²\T AB, AC eT]jáTT eT<ó«>·Ôá ¹sK AD esÁTd>±, ∆PQR ýË uóTC²\T
PQ, PR eT]jáTT eT<ó« >·Ôá s
¹ K PM \T nqTbÍÔá+ýË q ∆ABC ~ ∆PQR n #áÖ|ÚeTT.
30. a) A (4,1) eT]jáTT B(2,3) nHû _+<TeÚ\qT ¿£*| s
¹ U²K+&|Ú çÜ<¸¿£sD
Á _+<TeÚ\T <sÝ TÁ $<«sÁT\
T
ç¿ì+~ $<ó+ >± ¿£qT>=HsÁT.
⎛ 5⎞ ⎛ 7⎞
$<«] A : ⎜ 0 , ⎟ eT]jáTT ⎜ 0 , ⎟
⎝ 3 ⎠ ⎝3 ⎠
⎛ −5 ⎞ ⎛ −7 ⎞
$<«] B : ⎜ 2, ⎟ eT]jáTT ⎜0, ⎟
⎝ 3 ⎠ 3 ⎝ ⎠
M]ýË @ $<«] deÖ<óq+ d]jîT® q~. MT deÖ<óH deT]+#áTeTT.
(ýñ<)
b) 15 MT³sÁ¢ uóT ÈeTT>± >·\ #áÔTá sÁçkÍ¿±sÁ >·&¦ yîT<
® q+ ÿ¿£ eTÖ\ýË 5 MT³sÁT¢ bõ&yq
Õî Ô&TÔÃ ÿ¿£ >·TçsÁeTT
ÿ¿£ >·T+ÈÅ£ ¿£³
¼ & q~. nsTTq
i) >·TçsÁeTT >·&y
¦ Tû jáTT³Å£ ne¿±XøeTT>·\ çbÍ+Ôá yîX
Õ æ\«eTT ¿£qT>=q+&.
ii) 5MT³sÁ¢ <T\T 10MT³sÁ¢ bõ&yq
Õî Ô&TÔÃ >·Tçs ¿£{y
¼ì d
û q
¾ n~ >·&y
¦ Tû jáT>·\ çbÍ+Ôá yîX
Õ æ\«+ýË e#ûÌ
|sÁT>·T<\qT ¿£qT>=q+&. (π = 3.14)
31. a) ÿ¿£ ³q+<T yû>+
· >± Ü|Î&q u²D|Ú >·TsÁTï 1, 2, 3, 4, 5, 6, 7, 8 d+K«\ýË ÿ¿£ < #áÖ|¾dÖ
ï
>·TÔáT+~. n |s«Á ekÍqeTT\T deTd+uóy
ýÉÔ Õ û u²D² ÿ¿£kÍ] Ü|Î&+ e\q n~ ç¿ì+~y dÖº+#û
d+uó²e«Ôá\T m+Ôî+Ôá ? 8 1
i) 8 ii) uñd¾ d+K« 7 2
→
6 3
iii) 3 ¿£+fñ |<Ý d+K« iv) 8 ¿£+fñ ÔáÅ£ Øe ýñ< deÖqeTjûT« d+K«
5 4
(ýñ<)
b) ÿ¿£ q~¿ì >·\ e+Ôîq|Õ ÿ¿£ kÍq+ qT+& #áÖdï q~¿ì sÁTyî|
Õ Ú ý² >·\ s +&T rs\T esÁTd>± 30° eT]jáTT
45° eT¿ÃD²\ýË ¿£q|&¦sTT. rs\ qT+& e+Ôîq 3 MT³sÁ¢ mÔáTý
ï Ë +fñ q~ yî&\
TÎ ¿£qT>=q+&.
dÖ#áq\T : i) n ç|Xø\Å£ deÖ<óqeTT\T sjáT+&.
ii) ç|Ü ç|XøÅ£ 8 eÖsÁTØ\T.
iii) ç|Ü ç|XøÅ£ n+ÔásÁZÔá m+|¾¿£ ¿£\<T.
29. a) 3 + 2 5 ÿ¿£ ¿£sD
Á j
¡ Tá d+K« n>·TH ? ú deÖ<óH deT]+#áTeTT.
(ýñ<)
b) çÜuóTÈeTT ABC ýË uóT C²\T AB, AC eT]jáTT eT<ó«>·Ôá ¹sK AD esÁTd>±, ∆PQR ýË uóTC²\T
PQ, PR eT]jáTT eT<ó« >·Ôá s
¹ K PM \T nqTbÍÔá+ýË q ∆ABC ~ ∆PQR n #áÖ|ÚeTT.
30. a) A (4,1) eT]jáTT B(2,3) nHû _+<TeÚ\qT ¿£*| s
¹ U²K+&|Ú çÜ<¸¿£sD
Á _+<TeÚ\T <sÝ TÁ $<«sÁT\
T
ç¿ì+~ $<ó+ >± ¿£qT>=HsÁT.
⎛ 5⎞ ⎛ 7⎞
$<«] A : ⎜ 0 , ⎟ eT]jáTT ⎜ 0 , ⎟
⎝ 3 ⎠ ⎝3 ⎠
⎛ −5 ⎞ ⎛ −7 ⎞
$<«] B : ⎜ 2, ⎟ eT]jáTT ⎜0, ⎟
⎝ 3 ⎠ 3 ⎝ ⎠
M]ýË @ $<«] deÖ<óq+ d]jîT® q~. MT deÖ<óH deT]+#áTeTT.
(ýñ<)
b) 15 MT³sÁ¢ uóT ÈeTT>± >·\ #áÔTá sÁçkÍ¿±sÁ >·&¦ yîT<
® q+ ÿ¿£ eTÖ\ýË 5 MT³sÁT¢ bõ&yq
Õî Ô&TÔÃ ÿ¿£ >·TçsÁeTT
ÿ¿£ >·T+ÈÅ£ ¿£³
¼ & q~. nsTTq
i) >·TçsÁeTT >·&y
¦ Tû jáTT³Å£ ne¿±XøeTT>·\ çbÍ+Ôá yîX
Õ æ\«eTT ¿£qT>=q+&.
ii) 5MT³sÁ¢ <T\T 10MT³sÁ¢ bõ&yq
Õî Ô&TÔÃ >·Tçs ¿£{y
¼ì d
û q
¾ n~ >·&y
¦ Tû jáT>·\ çbÍ+Ôá yîX
Õ æ\«+ýË e#ûÌ
|sÁT>·T<\qT ¿£qT>=q+&. (π = 3.14)
31. a) ÿ¿£ ³q+<T yû>+
· >± Ü|Î&q u²D|Ú >·TsÁTï 1, 2, 3, 4, 5, 6, 7, 8 d+K«\ýË ÿ¿£ < #áÖ|¾dÖ
ï
>·TÔáT+~. n |s«Á ekÍqeTT\T deTd+uóy
ýÉÔ Õ û u²D² ÿ¿£kÍ] Ü|Î&+ e\q n~ ç¿ì+~y dÖº+#û
d+uó²e«Ôá\T m+Ôî+Ôá ? 8 1
i) 8 ii) uñd¾ d+K« 7 2
→
6 3
iii) 3 ¿£+fñ |<Ý d+K« iv) 8 ¿£+fñ ÔáÅ£ Øe ýñ< deÖqeTjûT« d+K«
5 4
(ýñ<)
b) ÿ¿£ q~¿ì >·\ e+Ôîq|Õ ÿ¿£ kÍq+ qT+& #áÖdï q~¿ì sÁTyî|
Õ Ú ý² >·\ s +&T rs\T esÁTd>± 30° eT]jáTT
45° eT¿ÃD²\ýË ¿£q|&¦sTT. rs\ qT+& e+Ôîq 3 MT³sÁ¢ mÔáTý
ï Ë +fñ q~ yî&\
TÎ ¿£qT>=q+&.
Page 14
32. a) ÿ¿£ J$Ôá ;óeÖ d+d <ëР100eT+~ bÍ\dÓ\<sÁT\ ejáTdTà\qT {ì¼ ÔájÖ
á sÁT#ûdq
¾ $uóÈ
q |{¿¼ì £
ç¿ì+< eÇ&+~. 18 d+eÔáàsÁeTT\ qT+& 60 d+eÔáàsÁeTT\ ¿£H ÔáÅ£ Øe ejáTdTà >·\ y]¿ì eÖçÔáyTû
bÍ\dÓ\T ºÌq bÍ\dÓ<sÁT\ ejáTdTà\ eT<ó« >·Ô+á ¿£qT>=q+&.
ejáTdTà 20¿£+fñ 25 ¿£+fñ 30 ¿£+fñ 35 ¿£+fñ 40 ¿£+fñ 45 ¿£+fñ 50 ¿£+fñ 55 ¿£+fñ 60 ¿£+fñ
d+öö\ýË ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe
bÍ\dÓ<sÁT\ 2 6 24 45 78 89 92 98 100
d+K«
(ýñ<)
b) ÿ¿£ bÍsÄX
Á æ\ esÁDýË |s«esÁD |]sÁ¿D
£ Å£ $<«sÁT\
T yîTT¿£Ø\T H{²\ uó²$+#sÁT. ç|Ü d¿£H
$<«sÁT\
T
ysÁT #á<TeÚÔáTq ÔásÁ>·Ü d+K«Å£ deÖqyîT®q yîTT¿£Ø\qT nq>± 1e ÔásÁ>·Ü #á<TeÚÔáTq $<«sÁT\T
1 yîTT¿£ØqT, s +&e Ôás>
Á Ü
· #á<T eÚÔáTq $<«sÁT\
T 2 yîTT¿£Ø\qT H{²\, $<ó+ >± 12e Ôás>
Á Ü
· esÁÅ£
#ûjÖ
á \ sÁs TT+#áTÅ£HsÁT. nsTTÔû ç|Ü d¿£H
ý
Ë 3 Ôás>
Á Ô
· Tá \T q yîTTÔá+ï H{ìq yîTT¿£Ø\T m ?
33. a) ç¿ì+<eÇ&q s
¹ FjáT dMT¿£sD
Á ²\ ÈÔáÅ£ ç>±|t <Çs kÍ<óq
¿£qT>=q+&.
x y + 1 = 0 eT]jáTT 3x + 2y 12 = 0
(ýñ<)
b) 5 |àÞøß eT]jáTT 7 ¿£\eTT\T yîTTÔá+
ï $\Te sÁÖ. 50. ný²¹> 7 |àÞøß eT]jáTT 5 ¿£\eTT\ <ós Á yîTTÔáe
ï TT.
sÁÖ. 46. nsTTq ÿ¿£ |àýÙ eT]jáTT ÿ¿£ ¿£\eTT <ós q Á T ¿£qT>=qT³Å£ |jÖ
î >·|&
û s¹ FjáT dMT¿£sD
Á ²\
ÈÔáqT ÔájÖ
á sÁT#ûd¾ ç>±|t |<Ü
Æ ýË kÍ<óq
¿£qT>=q+&.
á sÁT#ûdq
¾ $uóÈ
q |{¿¼ì £
ç¿ì+< eÇ&+~. 18 d+eÔáàsÁeTT\ qT+& 60 d+eÔáàsÁeTT\ ¿£H ÔáÅ£ Øe ejáTdTà >·\ y]¿ì eÖçÔáyTû
bÍ\dÓ\T ºÌq bÍ\dÓ<sÁT\ ejáTdTà\ eT<ó« >·Ô+á ¿£qT>=q+&.
ejáTdTà 20¿£+fñ 25 ¿£+fñ 30 ¿£+fñ 35 ¿£+fñ 40 ¿£+fñ 45 ¿£+fñ 50 ¿£+fñ 55 ¿£+fñ 60 ¿£+fñ
d+öö\ýË ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe ÔáÅ£Øe
bÍ\dÓ<sÁT\ 2 6 24 45 78 89 92 98 100
d+K«
(ýñ<)
b) ÿ¿£ bÍsÄX
Á æ\ esÁDýË |s«esÁD |]sÁ¿D
£ Å£ $<«sÁT\
T yîTT¿£Ø\T H{²\ uó²$+#sÁT. ç|Ü d¿£H
$<«sÁT\
T
ysÁT #á<TeÚÔáTq ÔásÁ>·Ü d+K«Å£ deÖqyîT®q yîTT¿£Ø\qT nq>± 1e ÔásÁ>·Ü #á<TeÚÔáTq $<«sÁT\T
1 yîTT¿£ØqT, s +&e Ôás>
Á Ü
· #á<T eÚÔáTq $<«sÁT\
T 2 yîTT¿£Ø\qT H{²\, $<ó+ >± 12e Ôás>
Á Ü
· esÁÅ£
#ûjÖ
á \ sÁs TT+#áTÅ£HsÁT. nsTTÔû ç|Ü d¿£H
ý
Ë 3 Ôás>
Á Ô
· Tá \T q yîTTÔá+ï H{ìq yîTT¿£Ø\T m ?
33. a) ç¿ì+<eÇ&q s
¹ FjáT dMT¿£sD
Á ²\ ÈÔáÅ£ ç>±|t <Çs kÍ<óq
¿£qT>=q+&.
x y + 1 = 0 eT]jáTT 3x + 2y 12 = 0
(ýñ<)
b) 5 |àÞøß eT]jáTT 7 ¿£\eTT\T yîTTÔá+
ï $\Te sÁÖ. 50. ný²¹> 7 |àÞøß eT]jáTT 5 ¿£\eTT\ <ós Á yîTTÔáe
ï TT.
sÁÖ. 46. nsTTq ÿ¿£ |àýÙ eT]jáTT ÿ¿£ ¿£\eTT <ós q Á T ¿£qT>=qT³Å£ |jÖ
î >·|&
û s¹ FjáT dMT¿£sD
Á ²\
ÈÔáqT ÔájÖ
á sÁT#ûd¾ ç>±|t |<Ü
Æ ýË kÍ<óq
¿£qT>=q+&.
Document Details
| Board / Org | Andhra Pradesh Board |
| Exam | Class 10 |
| Type | Sample Paper |
| Pages | 14 |
| Updated | 24 Sep 2026 |