TN 10th Question Paper 2023 Maths

Tamil Nadu
State Board

2023
QUESTION
PAPER

No. of Printed Pages : 12
2345
2345
2345
2345
2345
6822
2345

!6822Mathematics!
2345
2345
2345
2345
£vÄ Gs
2345
2345 Register Number
2345
2345
2345
2345
2345
2345
2345
2345

Part - III
Pou® / MATHEMATICS
( uªÌ ©ØÖ® B[Q» ÁÈ / Tamil & English Version)

Põ» AÍÄ : 3.00 ©o ÷|µ® ] [ ö©õzu ©v¨ö£sPÒ : 100
Time Allowed : 3.00 Hours ] [Maximum Marks : 100

AÔÄøµPÒ : (1) AøÚzx ÂÚõUPЮ \›¯õP Aa_¨ £vÁõQ EÒÍuõ GߣuøÚ
\›£õºzxU öPõÒÍÄ®. Aa_¨£vÂÀ SøÓ°¸¨¤ß AøÓU
PsPõo¨£õÍ›h® EhÚi¯õP öu›ÂUPÄ®.
(2) }»® AÀ»x P¸¨¦ ø©°øÚ ©mk÷© GÊxÁuØS®
AiU÷PõikÁuØS® £¯ß£kzu ÷Ásk®. £h[PÒ ÁøµÁuØS
ö£ß]À £¯ß£kzuÄ®.

Instructions : (1) Check the question paper for fairness of printing. If there is any lack of fairness,
inform the Hall Supervisor immediately.
(2) Use Blue or Black ink to write and underline and pencil to draw diagrams.

SÔ¨¦ : CÆÂÚõzuõÒ |õßS £SvPøÍ öPõshx.
Note : This question paper contains four parts.

£Sv & I / PART - I
SÔ¨¦ : (i) AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 14x1=14

(ii) öPõkUP¨£mkÒÍ ©õØÖ ÂøhPÎÀ ªPÄ® Hئøh¯ Âøh°øÚ
÷uº¢öukzxU SÔ±mkhß Âøh°øÚ²® ÷\ºzx GÊuÄ®.
Note : (i) Answer all the questions.
(ii) Choose the most appropriate answer from the given four alternatives and write

the option code and the corresponding answer.

[ v¸¨¦P / Turn over

6822 2

1. A={a, b, p}, B={2, 3}, C={p, q, r, s} GÛÀ, n[(A∪C)×B] BÚx :

(A) 8 (B) 20 (C) 12 (D) 16
A={a, b, p}, B={2, 3}, C={p, q, r, s} then n[(A∪C)×B] is :

(a) 8 (b) 20 (c) 12 (d) 16

2. n(A)=p, n(B)=q GÛÀ A &°¼¸¢x B &US QøhUS® ö©õzu EÓÄPÎß
GsoUøP¯õÚx __________.

(A) 0 (B) 1 (C) 2pq−1 (D) 2pq
If n(A)=p, n(B)=q, then the total number of relations that exist from A to B is
__________.

(a) 0 (b) 1 (c) 2pq−1 (d) 2pq

3. F1=1, F2=3 ©ØÖ® Fn=Fn−1+Fn−2 GÚU öPõkUP¨£iß, F5 BÚx :

(A) 3 (B) 5 (C) 8 (D) 11
Given F1=1, F2=3 and Fn=Fn−1+Fn−2 then, F5 is :

(a) 3 (b) 5 (c) 8 (d) 11

4. t1, t2, t3 ...... Gߣx J¸ Tmkz öuõhº Á›ø\ GÛÀ t6, t12, t18, ...... Gߣx :

(A) J¸ ö£¸USz öuõhº Á›ø\
(B) J¸ Tmkz öuõhº Á›øP
(C) J¸ Tmkz öuõhº Á›ø\²©À», ö£¸USz öuõhº Á›ø\²©À»
(D) J¸ ©õÔ¼z öuõhº Á›ø\
If the sequence t1, t2, t3 ...... are in A.P., then the sequence t6, t12, t18, ...... is :

(a) a Geometric Progression
(b) an Arithmetic Progression
(c) neither an Arithmetic Progression nor a Geometric Progression

(d) a constant sequence

3 6822

3y − 3 7y − 7
5. ÷ Gߣx :
y 3y 2

9y 9y 3
(A) (B)
7 (21y − 21)

(C)
21y 2 − 42y + 21
(D)
(
7 y 2 − 2y + 1 )
3 2
3y y

3y − 3 7y − 7
÷ is :
y 3y 2

9y 9y 3
(a) (b)
7 (21y − 21)

(c)
21y 2 − 42y + 21
(d)
(
7 y 2 − 2y + 1 )
3 2
3y y

6. J¸ C¸£i \©ß£õmiß Áøµ£h® J¸ __________.
(A) ÷|ºU÷Põk (B) Ámh® (C) £µÁøͯ® (D) Av£µÁøͯ®
Graph of a Quadratic equation is a __________.

(a) straight line (b) circle (c) parabola (d) hyperbola

AB BC
7. = GÛÀ, ∆ABC ©ØÖ® ∆EDF G¨ö£õÊx ÁiöÁõzuøÁ¯õP
DE FD
Aø©²® ?
(A) B = E (B) A = D (C) B= D (D) A= F

AB BC
If in triangles ABC and EDF, = then they will be similar, when :
DE FD

(a) B= E (b) A= D (c) B= D (d) A= F

[ v¸¨¦P / Turn over

6822 4

8. Ámhzvß öuõk÷Põk® Auß Bµ•® ö\[SzuõP Aø©²® Ch® :
(A) ø©¯® (B) öuõk¦ÒÎ
(C) •i¼ (D) |õs
A tangent of a circle is perpendicular to the radius at the :
(a) centre (b) point of contact
(c) infinity (d) chord

9. x-Aa_US ö\[SzuõP EÒÍ ÷|ºU÷Põmiß \õ´Ä :
(A) 1 (B) 0 (C) ∞ (D) −1
The slope of the straight line perpendicular to x-axis is :
(a) 1 (b) 0 (c) ∞ (d) −1

10. sinθ=cosθ GÛÀ 2tan2θ+sin2θ−1 &ß ©v¨¦ :

3 −3 2 −2
(A) (B) (C) (D)
2 2 3 3
If sinθ=cosθ, then the value of 2tan2θ+sin2θ−1 is :

3 −3 2 −2
(a) (b) (c) (d)
2 2 3 3

11. Bµ® 5 ö\.« ©ØÖ® \õ²¯µ® 13 ö\.« Eøh¯ ÷|ºÁmhU T®¤ß E¯µ® :
(A) 12 ö\.« (B) 10 ö\.« (C) 13 ö\.« (D) 5 ö\.«
The height of a right circular cone whose radius is 5 cm and slant height is 13 cm
will be :
(a) 12 cm (b) 10 cm (c) 13 cm (d) 5 cm

12. \©©õÚ Âmh® ©ØÖ® E¯µ® Eøh¯ Kº E¸øÍ, J¸ T®¦ ©ØÖ® J¸
÷PõÍzvß PÚ AÍÄPÎß ÂQu® :
(A) 1 : 2 : 3 (B) 2 : 1 : 3 (C) 1 : 3 : 2 (D) 3 : 1 : 2
The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same
diameter and same height is :

(a) 1:2:3 (b) 2:1:3 (c) 1:3:2 (d) 3:1:2

5 6822

13. SÔ¨¤mh uµÄ¨ ¦ÒÎPÎß TkuÀ ©ØÖ® \µõ\› BQ¯øÁ •øÓ÷¯ 407 ©ØÖ®
11 GÛÀ, uµÄ¨ ¦ÒÎPÎß GsoUøP¯õÚx :
(A) 37 (B) 4477 (C) 396 (D) 418
If the sum and mean of a data are 407 and 11 respectively, then the number of
observations in the data are :
(a) 37 (b) 4477 (c) 396 (d) 418

14. B[Q» GÊzxPÒ {a, b, ....., z } &¼¸¢x J¸ GÊzx \©Áõ´¨¦ •øÓ°À ÷uºÄ
ö\´¯¨£kQÓx. A¢u GÊzx x &US •¢øu¯ GÊzxPÎÀ JßÓõP
C¸¨£uØPõÚ {PÌuPÄ :
12 1 23 3
(A) (B) (C) (D)
13 13 26 26
If a letter is chosen at random from the English alphabets {a, b, ....., z }, then the
probability that the letter chosen precedes x :

12 1 23 3
(a) (b) (c) (d)
13 13 26 26

£Sv & II / PART - II
SÔ¨¦ : GøÁ÷¯Ý® 10 ÂÚõUPÐUS Âøh¯ÎUPÄ®. ÂÚõ Gs 28 &US
Pmhõ¯©õP Âøh¯ÎUPÄ®. 10x2=20
Note : Answer any 10 questions. Question No. 28 is compulsory.

15. B×A={(−2, 3), (−2, 4), (0, 3), (0, 4), (3, 3), (3, 4)} GÛÀ A ©ØÖ® B BQ¯ÁØøÓU
PõsP.
If B×A={(−2, 3), (−2, 4), (0, 3), (0, 4), (3, 3), (3, 4)} find A and B.

16. fof (k)=5, f (k)=2k−1 GÛÀ, k &ß ©v¨ø£U PõsP.
Find k if f of (k)=5 where f (k)=2k−1.

17. x+6, x+12 ©ØÖ® x+15 Gß£Ú J¸ ö£¸USz öuõhº Á›ø\°ß öuõhºa]¯õÚ
‰ßÖ EÖ¨¦PÒ GÛÀ, x &ß ©v¨ø£U PõsP.
Find x so that x+6, x+12 and x+15 are consecutive terms of a Geometric

Progression.

[ v¸¨¦P / Turn over

6822 6

x +2 x2 − x − 6
18. _¸USP : ÷
4y 12y 2

x +2 x2 − x − 6
Simplify : ÷
4y 12y 2

19. ¤ßÁ¸® C¸£ia \©ß£õmiß ‰»[PÎß ußø©ø¯U PõsP.
2x2−x−1=0
Determine the nature of roots for the following quadratic equation.
2x2−x−1=0

20. £hzvÀ AD Gߣx ∠BAC &°ß C¸\©öÁmi¯õS®.
AB=10 ö\.«

AC=14 ö\.« ©ØÖ®

BC=6 ö\.« GÛÀ, BD ©ØÖ® DC&IU PõsP.

In the figure AD is the bisector of ∠BAC, if AB=10 cm, AC=14 cm and BC=6 cm.
Find BD and DC.

7 6822

21. J¸ §øÚ xy uÍzvÀ (−6, −4) GßÓ ¦ÒΰÀ EÒÍx. (5, 11) GßÓ ¦ÒΰÀ
J¸ £õÀ ¦mi øÁUP¨£mkÒÍx. §øÚ ªPU SÖQ¯ yµ® £¯ozx¨ £õÀ
A¸¢u ¸®¦QÓx GÛÀ, £õø»¨ £¸SÁuØSz ÷uøÁ¯õÚ £õøu°ß
\©ß£õmøhU PõsP.
A cat is located at the point (−6, −4) in xy plane. A bottle of milk is kept at
(5, 11). The cat wishes to consume the milk travelling through shortest possible
distance. Find the equation of the path it needs to take the milk.

22. 12y=−(P+3)x+12, 12x−7y=16 BQ¯ ÷|ºU÷PõkPÒ JßÖUöPõßÖ ö\[Szx
GÛÀ, P &°ß ©v¨ø£U PõsP.
If the straight lines 12y=−(P+3)x+12, 12x−7y=16 are perpendicular then
find ‘P’.

secθ sinθ
23. − = cotθ Gߣøu {¹¤UPÄ®.
sinθ cosθ

secθ sinθ
Prove that − = cotθ .
sinθ cosθ

24. QzuõøÚU öPõsk 7 « Bµ•®, 24 « E¯µ•® Eøh¯ J¸ T®¦ ÁiÁU Thõµ®
E¸ÁõUP¨£kQÓx. ö\ÆÁP ÁiÁU QzuõÛß AP»® 4 « GÛÀ, Auß }Í®
PõsP.
The radius of a conical tent is 7 m and height is 24 m. Calculate the length of the
canvas used to make the tent if the width of the rectangular canvas is 4 m.

25. C¸ ÷PõÍ[PÎß Bµ[PÒ ÂQu® 4 : 7 GÛÀ AÁØÔß PÚ AÍÄPÎß ÂQu®
PõsP.
If the ratio of radii of two spheres is 4 : 7, find the ratio of their volumes.

26. öPõkUP¨£mh uµÄ¨ ¦ÒÎPÐUS Ãa_ ©ØÖ® Ãa_U öPÊøÁU PõsP.
63, 89, 98, 125, 79, 108, 117, 68
Find the range and co-efficient of range of the following data.

63, 89, 98, 125, 79, 108, 117, 68

[ v¸¨¦P / Turn over

6822 8

27. A ©ØÖ® B BQ¯ C¸ Âsn¨£uõµºPÒ IIT &°À ÷\ºÁuØPõPU Põzv¸¨£ÁºPÒ.
CÁºPÎÀ A ÷uº¢öukUP¨£kÁuØPõÚ {PÌuPÄ 0.5. A ©ØÖ® B C¸Á¸®
÷uº¢öukUP¨£kÁuØPõÚ {PÌuPÄ 0.3 GÛÀ, B ÷uº¢öukUP¨£kÁuØPõÚ
AvP£m\ {PÌuPÄ 0.8 GÚ {¹¤UPÄ®.
A and B are two candidates seeking admission to IIT. The probability that A
getting selected is 0.5 and the probability that both A and B getting selected is
0.3. Prove that probability of B being selected is at the most 0.8.

28. p2×q1×r4×s3=3,15,000 GßÓÁõÖ Aø©²® GÛÀ p, q, r ©ØÖ® s BQ¯ÁØÔß
©v¨¦PøÍU PõsP.
If p2×q1×r4×s3=3,15,000 then find p, q, r and s.

£Sv & III / PART - III

SÔ¨¦ : GøÁ÷¯Ý® 10 ÂÚõUPÐUS Âøh¯ÎUPÄ®. ÂÚõ Gs 42 &US
Pmhõ¯©õP Âøh¯ÎUPÄ®. 10x5=50

Note : Answer any 10 questions. Question No. 42 is compulsory.

29. f : A → B GßÓ \õº£õÚx f (x ) = x − 1, GÚ Áøµ¯ÖUP¨£kQÓx. C[S
2
A={2, 4, 6, 10, 12}, B={0, 1, 2, 4, 5, 9} BP C¸US® ÷£õx \õº¦ f &I ¤ßÁ¸®
•øÓPÎÀ SÔUPÄ®.
(i) Á›ø\ ÷\õiPÎß Pn® (ii) AmhÁøn
(iii) A®¦USÔ £h® (iv) Áøµ£h®

x
Let f : A → B be a function defined by f (x ) = − 1, where A={2, 4, 6, 10, 12},
2
B={0, 1, 2, 4, 5, 9} Represent f by :

(i) set of ordered pairs (ii) a table

(iii) an arrow diagram (iv) a graph

9 6822

30. J¸ öu¸Â¾ÒÍ ÃkPÐUS 1 •uÀ 49 Áøµ öuõhºa]¯õPU Pu»UP®
ÁÇ[P¨£mkÒÍx. ö\¢v¼ß ÃmiØS •ßÚuõP EÒÍ ÃkPÎß
Pu»UP[PÎß Tmkz öuõøP¯õÚx ö\¢v¼ß ÃmiØS¨ ¤ßÚuõP EÒÍ
ÃkPÎß Pu»UP[PÎß Tmkz öuõøPUSa \©® GÛÀ ö\¢v¼ß ÃmkU
Pu»UPzøuU PõsP.

The houses of a street are numbered from 1 to 49. Senthil’s house is numbered
such that the sum of numbers of the houses prior to Senthil’s house is equal to
the sum of numbers of the houses following Senthil’s house. Find Senthil’s
house number.

31. 5+55+555+..... GßÓ öuõhºÁ›ø\°ß •uÀ n EÖ¨¦PÎß TkuÀ PõsP.

Find the sum to n terms of the series 5+55+555+.....

32. RÌUPõq® ‰ßÖ ©õÔPÎÀ Aø©¢u J¸[Pø© ÷|›¯À \©ß£õmkz
öuõS¨¦PøÍ wºUP.

3y
x+20= +10=2z+5=110−(y+z)
2

Solve the following system of linear equations in three variables.
3y
x+20= +10=2z+5=110−(y+z)
2

1 7 
5 2 9  
 , B =  1 2  GÛÀ (AB) =B A Gߣøua \›£õºUPÄ®.
33. A=  T T T
 1 2 8   5 −1
 

1 7 
5 2 9   T T T
If A =   , B =  1 2  verify that (AB) =B A

1 2 8  5 −1
 

[ v¸¨¦P / Turn over

6822 10

34. ‘P’ «mhº CøhöÁΰÀ ‘a’ «mhº ©ØÖ® ‘b’ «mhº E¯µ•ÒÍ Cµsk ysPÒ
EÒÍÚ. ysPÎß Ea]°¼¸¢x Gv÷µ²ÒÍ ysPÎß AiUS Áøµ¯¨£k®
ab
÷PõkPÒ \¢vUS® ¦Ò롧 E¯µ©õÚx «mhº Gߣøu {¹¤UPÄ®.
a+b
Two poles of height ‘a’ metres and ‘b’ metres are ‘P’ metres apart. Prove that the
height of the point of intersection of the lines joining the top of each pole to the
ab
foot of the opposite pole is given by metres.
a+b

35. ÷Põn C¸\©öÁmi ÷uØÓzøu GÊv {¹¤UPÄ®.
State and prove Angle Bisector theorem.

36. (8, 6) (5, 11) (−5, 12) ©ØÖ® (−4, 3) BQ¯ ¦ÒÎPøÍ •øÚPÍõP öPõsh
|õØPµzvß £µ¨ø£U PõsP.
Find the area of the quadrilateral formed by points (8, 6) (5, 11) (−5, 12) and
(−4, 3).

37. 7x−3y=−12, 2y=x+3 BQ¯ ÷|ºU÷PõkPÒ \¢vUS® ¦ÒÎ ÁÈ ö\ÀÁx®
X&Aa_US Cøn¯õÚx©õÚ ÷|ºU÷Põmiß \©ß£õmøhU PõsP.

Find the equation of a straight line parallel to X-axis and passing through the
point of intersection of the lines 7x−3y=−12 and 2y=x+3.

38. J¸ P»[Pøµ ÂÍUPzvß Ea]°¼¸¢x Gvöµvº £UP[PÎÀ EÒÍ Cµsk
P¨£ÀPÒ 308 ©ØÖ® 608 CÓUPU ÷PõnzvÀ £õºUP¨£kQßÓÚ. P»[Pøµ
ÂÍUPzvß E¯µ® h «. C¸ P¨£ÀPÒ ©ØÖ® P»[Pøµ ÂÍUPzvß Ai¨£Sv
BQ¯øÁ J÷µ ÷|ºU÷PõmiÀ Aø©QßÓÚ GÛÀ, Cµsk P¨£ÀPÐUS
Cøh¨£mh öuõø»Ä 4h «. GÚ {¹¤UPÄ®.
3
From the top of a lighthouse, the angle of depression of two ships on the opposite
sides of it are observed to be 308 and 608. If the height of the lighthouse is ‘h’
metres and the line joining the ships passes through the foot of the lighthouse,

4h
show that the distance between the ships is m.
3

11 6822

39. Kº E¸øÍ°ß Bµ® ©ØÖ® E¯µ[PÎß ÂvP® 5 : 7 BS®. Auß ÁøÍ£µ¨¦
5500 \.ö\.« GÛÀ, E¸øÍ°ß Bµ® ©ØÖ® E¯µ® PõsP.

The radius and height of a cylinder are in the ratio 5 : 7 and its curved surface
area is 5500 sq.cm. Find its radius and height.

40. A¸Ò uÚx Sk®£ ÂÇõÂØS 150 |£ºPÒ u[SÁuØS J¸ Thõµ® Aø©UQÓõº.
Thõµzvß Ai¨£Sv E¸øÍ Ái¾® ÷©Ø£Sv T®¦ Ái¾® EÒÍx.
J¸Áº u[SÁuØS 4 \.« Ai¨£Sv £µ¨¦® 40 P.« PõØÖ® ÷uøÁ¨£kQÓx.
ThõµzvÀ E¸øÍ°ß E¯µ® 8 « GÛÀ T®¤ß E¯µ® PõsP.
Arul has to make arrangements for the accommodation of 150 persons for his
family function. For this purpose, he plans to build a tent which is in the shape of
cylinder surmounted by a cone. Each person requires 4 sq.m. of the space on
ground and 40 cu. meter of air to breathe. Find the height of the conical part of
the tent if the height of cylindrical part is 8 m.

41. Cµsk ^µõÚ £PøhPÒ •øÓ¯õP J÷µ ÷|µzvÀ E¸mh¨£kQßÓÚ.
(i) Cµsk £PøhPξ® J÷µ•P ©v¨¦ QøhUP
(ii) •P ©v¨¦PÎß ö£¸UPØ£»ß £Põ GsnõP QøhUP
(iii) •P ©v¨¦PÎß TkuÀ £Põ GsnõP QøhUP
(iv) •P ©v¨¦PÎß TkuÀ 1 &BP C¸UP
BQ¯ {PÌa]PÎß {PÌuPÄPøÍU PõsP.
Two unbiased dice are rolled once. Find the probability of getting :
(i) a doublet (equal numbers on both dice)
(ii) the product as a prime number
(iii) the sum as a prime number

(iv) the sum as 1

42. A={x∈W/x < 3}, B={x∈N/1 < x ≤ 5} ©ØÖ® C={3, 5, 7} GÛÀ A×(B∪C)=(A×B)∪(A×C)
Gߣøu \›£õºUPÄ®.

Let A={x∈W/x < 3}, B={x∈N/1 < x ≤ 5} and C={3, 5, 7} verify that
A×(B∪C)=(A×B)∪(A×C).

[ v¸¨¦P / Turn over

6822 12
12345
12345
12345
12345
12345
£Sv & IV / PART - IV 12345
12345
12345
12345
12345
SÔ¨¦ : AøÚzx ÂÚõUPÐUS® Âøh¯ÎUPÄ®. 2x8=16 12345
12345
12345
12345
12345
Note : Answer all the questions. 12345
12345
12345
12345
12345
43. (A) 4 ö\.« Bµ•ÒÍ Ámh® Áøµ¢x, Auß ø©¯zv¼¸¢x 11 ö\.«
öuõø»Â¾ÒÍ J¸ ¦ÒÎø¯U SÔzx, A¨¦Òΰ¼¸¢x ÁmhzvØS
Cµsk öuõk÷PõkPÒ ÁøµP.
AÀ»x
(B) Ai¨£UP® BC=8 ö\.« ∠A=608 ©ØÖ® ∠A &ß C¸ \©öÁmi¯õÚx
BC &I D GßÓ ¦ÒΰÀ BD=6 ö\.« GßÓÁõÖ \¢vUQÓx GÛÀ,
•U÷Põn® ABC ÁøµP.
(a) Take a point which is 11 cm away from the centre of a circle of radius 4 cm
and draw two tangents to the circle from that point.
OR
(b) Draw a triangle ABC of base BC=8 cm, ∠A=608 and the bisector of ∠A meets
BC at D such that BD=6 cm.

44. (A) ÁºæPõ öÁÆ÷ÁÖ AÍÄPÎÀ 6 Ámh[PøÍ Áøµ¢uõÒ. AmhÁøn°À
EÒÍÁõÖ, JÆöÁõ¸ Ámhzvß ÂmhzvØS®, Auß _ØÓÍÂØS® EÒÍ
÷uõµõ¯z öuõhº¦US J¸ Áøµ£h® Áøµ¯Ä®. AuøÚ £¯ß£kzv
Âmh©õÚx 6 ö\.« BP C¸US® ÷£õx Ámhzvß _ØÓÍøÁU PõsP.
Âmh® (x ) ö\.« 1 2 3 4 5
_ØÓÍÄ ( y ) ö\.« 3.1 6.2 9.3 12.4 15.5

AÀ»x
(B) y=x2−5x−6 &ß Áøµ£h® Áøµ¢x, AuøÚ¨ £¯ß£kzv x2−5x−14=0
GßÓ \©ß£õmøhz wºUPÄ®.
(a) Varshika drew 6 circles with different sizes. Draw a graph for the relationship
between the diameter and circumference (approximately related) of each
circle as shown in the table and use it to find the circumference of a circle
when its diameter is 6 cm.

Diame ter ( x ) cm 1 2 3 4 5
Circumference ( y ) cm 3.1 6.2 9.3 12.4 15.5

OR
(b) Draw the graph of y=x2−5x−6 and hence solve x2−5x−14=0.

-o0o-