Karnataka SSLC Question Paper 2021 Maths for Kannada Medium

CÈÉí¨Ü PÜñܤÄÔ
Question Booklet Serial No. : 11-

®æãàí¨Ü~ ÓÜíTæ :
Register Number :
±Ü£ÅPæ - 01 / Paper – 01
GÓ….GÓ….GÇ….Ô. ÊÜááS ±ÜÄàûæ – 2021
SSLC MAIN EXAMINATION – 2021
+ +
Subjects : MATHEMATICS + SCIENCE + SOCIAL SCIENCE
PܮܰvÜ ÊÜáñÜᤠCíXÉÐ… ÊÜÞ«ÜÂÊÜá / Kannada and English Medium
CCE-RF / CCE-RR / CCE-PF / CCE-PR / NSR / NSPR

TEAR HERE TO OPEN THE QUESTION BOOKLET
: 10-30 1-30 ] [ Time : 10-30 A.M. to 1-30 P.M.
: 40 + 40 + 40 = 120 ] [ Total No. of Questions : 40 + 40 + 40 = 120
: 40 + 40 + 40 = 120 ] [ Max. Marks : 40 + 40 + 40 = 120
81-K/E — /Mathematics
˨ݦìWÜÚWæ ÓÜãaÜ®æWÜÙÜá / Instructions to the Students :
1. ¯ÜÅÊæàÍÜ ¯ÜñÜŨÜÈÉ¬Ü Öܬæã®í¨Üá AíQWÜÙÜ ¬æãàí¨Ü~ ÓÜíTæ¿á¬Üá® ¯ÜÅÍ殯ÜâÔ¤Pæ¿á ŸÆ¯ÝÍÜÌì¨Ü
ÊæáàÆᤩ¿áÈÉ ÓܱÐÜrÊÝX ŸÃæÀáÄ.
Write your eleven digit Register Number on the Question Booklet as
allotted in the admission ticket in the space provided at the top right
corner of this front page.
2. D ¯ÜÅÍ殯ÜâÔ¤Pæ¿á¬Üá® ×ÊÜáá¾S hÝPæp… ÊÜáãÆPÜ ÊæãÖÜÃÜá ÔàÇ… ÊÜÞvÜÇÝX¨æ. ±ÜÄàûæ
±ÝÅÃÜí»ÜÊÝWÜáÊÜ ÓÜÊÜá¿áPæR ­ÊÜá¾ ¯ÜÅÍ殯ÜâÔ¤Pæ¿á ŸÆŸ© ¯ÝÍÜÌìÊܬÜá® PÜñܤÄÔ,
±ÜÅÍæ°±ÜâÔ¤Pæ¿áÈÉ GÇÝÉ ±ÜâoWÜÙÜá CÊæÁáà Gí¨Üá ±ÜÄàüÔPæãÚÛ.
This Question Booklet has been sealed by reverse jacket. You have to cut
on the right side to open the Question Booklet at the time of
commencement of the examination. Check whether all the pages of the
Question Booklet are intact.
3. ËÐÜ¿áÊÝÃÜá OMR ±ÜâoÊÜ®Üá° ±ÜÅñæÂàPÜÊÝX ¯àvÜÇÝWÜáÊÜâ¨Üá.
OMR Sheet will be provided subject-wise separately.
4. D ±ÜÅÍæ°±ÜâÔ¤Pæ¿áá ÊÜáãÃÜá PæãàÃ… ËÐÜ¿áWÜÙܬÜá® Öæãí©¨Üáª, ¯ÜÅ£ ËÐÜ¿áÊÜä ¯ÜÅñæÂàPÜÊݨÜ
±ÜâÔ¤Pæ¿á®Üá° Öæãí©¨æ.
This set of Question Booklets consists of three core subjects and each
Tear here

subject has separate Question Booklet.

1111 () 1 of 32

5. ±ÜÅ£ ËÐÜ¿áPæR 40 ±ÜÅÍæ°WÜÚ¨Üáª, D ±ÜÅÍæ°±ÜâÔ¤Pæ¿áá Joár 120 ±ÜÅÍæ°WÜÙÜ®Üá° Öæãí©¨æ.
(i) WÜ~ñÜ & ±ÜÅÍæ°WÜÙÜ ÓÜíTæ 1 Äí¨Ü 40
(ii) ËþÝ®Ü & ±ÜÅÍæ°WÜÙÜ ÓÜíTæ 41 Äí¨Ü 80
(iii) ÓÜÊÜÞg ËþÝ®Ü & ±ÜÅÍæ°WÜÙÜ ÓÜíTæ 81 Äí¨Ü 120
40 questions are provided against each subject. This set of Question
Booklets contains 120 questions in all.
(i) Mathematics – Question Numbers 1 to 40
(ii) Science – Question Numbers 41 to 80
(iii) Social Science – Question Numbers 81 to 120
6. ±ÜÅ£à ±ÜÅÍæ°Wæ Jí¨Üá AíPÜ˨Üáª, GÇÝÉ ±ÜÅÍæ°WÜÚWÜã EñܤÄÓÜáÊÜâ¨Üá PÜvÝx¿á ÖÝWÜã ±ÜÅ£
ÓÜÄ¿Þ¨Ü EñܤÃÜPæR Jí¨Üá AíPÜ˨Üáª, ñܱݳ¨Ü EñܤÃÜPæR ¿ÞÊÜâ¨æà MáOÝñܾPÜ AíPÜWÜÙÜá
CÃÜáÊÜâ©ÆÉ.
Each question carries one mark. Answering all the questions is
compulsory and each correct answer will be awarded one mark. There will
be no negative marking for wrong answers.
7. ¯ÜÄàûÝ AÊܘ¿áÈÉ,
G ±ÜÅÍæ°WÜÙÜ®Üá° hÝWÜÃÜãPÜñæÀáí¨Ü K©Ä.
¹ K.Gí.BÃ…. ( OMR ) ±Üâo¨ÜÈÉ ±ÜÅ£ ±ÜÅÍæ°ÓÜíTæÂWæ ÓÜÄ Öæãí¨ÜáÊÜ EñܤÃÜÊÜ®Üá°
WÜáÃÜá£ÓÜÆá ¯àvÜÇÝXÃÜáÊÜ ®ÝÆáR ÊÜêñܤWÜÙÜ ±æçQ ÓÜÄ¿Þ¨Ü EñܤÃÜ¨Ü Jí¨Üá ÊÜêñܤÊÜ®Üá°
¯àÈ/PܯÜâ± ÍÝÀá¿á ¸ÝÇ… ¯ÝÀáíp… ¯æ¬… ÊÜÞñÜÅ E¯ÜÁãàXÔ ÓÜí¯Üä|ìÊÝX
Íæàv… ÊÜÞw. JÊæá¾ EñܤÃÜÊܬÜá® Íæàv… ÊÜÞw¨Ü ÊæáàÇæ Ÿ¨ÜÇÝÀáÓÜÆá AÊÜPÝÍÜËÆÉ
ÊÜáñÜᤠ¿ÞÊÜâ¨æà A¬ÜWÜñÜ WÜáÃÜáñÜáWÜÙܬÜá® K.Gí.BÃ…. ( OMR ) ÊæáàÇæ ÊÜÞvܸÝÃܨÜá.
E¨ÝÖÜÃÜOæ ±ÜÅÍæ° ÓÜíTæ 20PæR EñܤÃÜ¨Ü BÁáR ÓÜíTæ C BX¨ÜªÈÉ K.Gí.BÃ….
( OMR ) ±Üâo¨ÜÈÉ BÁáR C ¿á®Üá° ¯àÈ/PܯÜâ± ÍÝÀá¿á ¸ÝÇ… ¯ÝÀáíp… ¯æ¬…
E¯ÜÁãàXÔ D PæÙÜWæ ñæãàÄÔ¨Üíñæ ÊÜêñܤÊܬÜá® ÓÜí¯Üä|ìÊÝX Íæàv… ÊÜÞvܸæàPÜá.
±ÜÅÍæ° ÓÜíTæ 20) A B C D (C¨Üá E¨ÝÖÜÃÜOæWæ ÊÜÞñÜÅ)

Ô K.Gí.BÃ…. ( OMR ) ÖÝÙæ¿á¬Üá® ÊÜávÜaÜáÊÜâ¨Üá, ÖÜÄ¿ááÊÜâ¨Üá A¥ÜÊÝ Óærà¯ÜÇ… °¬…
ÊÜÞvܸÝÃܨÜá.

1111 () 2 of 32

During the examination,

a) Read the questions carefully.

b) Completely darken / shade the relevant circle against Question

Number in the OMR Sheet using blue / black ball point pen. Do not

try to alter the entry and not to do any stray marks on OMR Sheet.

Example : In the question booklet, if C is the correct answer for

Question No. 20, then in the OMR Sheet shade the option C using

blue / black ball point pen as follows.

Question No. 20) A B C D ( This is an example only )

c) Do not fold, tear, wrinkle or staple on the OMR Sheet.

8. Jí¨Üá ¯ÜÅÍæ®Wæ Jí¨ÜQRíñÜ ÖæaÜác ÊÜêñܤWÜÙܬÜá® Íæàv… ÊÜÞw¨ÜªÈÉ AíñÜÖÜ EñܤÃÜWÜÙܬÜá® ñܯæ±í¨Üá
±ÜÄWÜ~Ô AíPÜWÜÙÜ®Üá° ¯àvÜÇÝWÜáÊÜâ©ÆÉ.

If more than one circle is shaded for a given question, such answer is

treated as wrong and no marks will be given.

9. K.Gí.BÃ…. ( OMR ) ±Üâo¨ÜÈÉ ¯WÜ©ñÜ ÓܧÙܨÜÈÉ Ë¨Ý¦ì ÖÝWÜã PæãsÜw ÊæáàÈÌaÝÃÜPÜÃÜá
ñܱܳ¨æà ÓÜ× ÊÜÞvܸæàPÜá.

Student and Room Invigilator should sign in the OMR Sheet in the space

provided.

1111 () 3 of 32

10. ¯ÜÄàûÝ AÊܘ ÊÜááX¨Ü ¬ÜíñÜÃÜ ËÐÜ¿áÊÝÃÜá EñܤÄst K.Gí.BÃ…. ( OMR )®Üá° PæãsÜw
ÊæáàÈÌaÝÃÜPÜÄWæ ñܱܳ¨æà J²³ÓܸæàPÜá.

Candidate should return the subject-wise answered OMR Sheet to the

Room Invigilator before leaving the examination hall.

11. PÜaÝc PÝ¿áìÊÜ®Üá° ±ÜÅÍæ°±ÜâÔ¤Pæ¿áÈÉ ¯àwÃÜáÊÜ PÜaÝc PÝ¿áì¨Ü ÖÝÙæ¿áÈÉÁáà ÊÜÞvÜáÊÜâ¨Üá.

Rough work can be done in the space provided at the end of the Question

Booklet.

12. ±ÜÄàûÝ PæãsÜwÁãÙÜWæ PÝÂÆáRÇæàoÃ…, Êæã¸æçÇ… ¶æäଅ, Óݾp…ì ÊÝa… ÊÜáñÜᤠCñÜÃæ
¿ÞÊÜâ¨æà GÇæPÝó­P… E¯ÜPÜÃÜ|WÜÙܬÜá® ñÜÃÜáÊÜâ¨Ü¬Üá® ­Ðæà˜ÓÜÇÝX¨æ.

Calculators, Mobiles, Smart Watches and any other electronic equipment
are not allowed inside the examination hall.

1111 () 4 of 32

Subject : MATHEMATICS
D ±ÜÅ£Áãí¨Üá ±ÜÅÍæ°WÜÚWæ A¥ÜÊÝ A±Üä|ì ÖæàÚPæWÜÚWæ ®ÝÆáR BÁáRWÜÙÜ®Üá° ¯àvÜÇÝX¨æ.
AÊÜâWÜÙÜÈÉ ÓÜÄ¿Þ¨Ü EñܤÃÜÊÜ®Üá° BÄÔ ¯ÊÜáWæ ¯àvÜÇÝXÃÜáÊÜ K.Gí.BÃ…. ( OMR ) EñܤÃÜ
±Ü£ÅPæ¿áÈÉ ¯àÈ A¥ÜÊÝ PܱÜâ³ ÍÝÀá¿á ¸ÝÇ… ±ÝÀáíp… ±æ®…¯í¨Ü ÓÜÄ¿Þ¨Ü BÁáR¿á®Üá°
Íæàv… ÊÜÞw 40 × 1 = 40

Four choices are given for each of the following questions / incomplete

statements. Choose the correct answer among them and shade the correct

option in the OMR Answer Sheet given to you with a black / blue ball point
pen. 40 × 1 = 40

1. Jí¨Üá ÓÜÊÜÞíñÜÃÜ ÍæÅà{¿á n®æà ±Ü¨Ü a n = 4n + 5 B¨ÝWÜ, A¨ÜÃÜ 5®æà ±Ü¨ÜÊÜâ
(A) 20 (B) 14

(C) 25 (D) 24
The nth term of an Arithmetic Progression is a n = 4n + 5. Then its 5th

term is

(A) 20 (B) 14

(C) 25 (D) 24
2. 5 x 2 = 2 ( 2x + 3 ) ÊÜWÜìÓÜËáàPÜÃÜ|ÊܬÜá® B¨ÜÍÜìÃÜã¯Ü¨ÜÈÉ ŸÃæ¨ÝWÜ, ¨æãÃÜPÜáÊÜ Ô§ÃÝíPÜ

(A) 5 (B) 6

(C) 4 (D) –6

When the quadratic equation 5 x 2 = 2 ( 2x + 3 ) is expressed in the
standard form, the constant term obtained is

(A) 5 (B) 6

(C) 4 (D) –6

1111 () 5 of 32

3. x – 2y = 0 ÊÜáñÜᤠ3x + 4y – 20 = 0 ÓÜËáàPÜÃÜ|WÜÙÜá

(A) ±ÜÃÜÓܳÃÜ dæà©ÓÜáñܤÊæ (B) IPÜÂWæãÙÜáÛñܤÊæ
(C) ÓÜÊÜÞíñÜÃÜÊÝXÃÜáñܤÊæ (D) ±ÜÃÜÓܳÃÜ ÆíŸÊÝXÃÜáñܤÊæ

x – 2y = 0 and 3x + 4y – 20 = 0 are

(A) Intersecting lines (B) Coincident lines

(C) Parallel lines (D) Perpendicular lines
4. bñÜŨÜÈÉ ñæãàÄÔÃÜáÊÜ ®Üûæ¿áÈÉ®Ü ÃæàTÝñܾPÜ ÓÜËáàPÜÃÜ|WÜÙÜ hæãàwWÜÙÜá

(A) x+y=1 ÊÜáñÜᤠ2x – y = 1

(B) 2x + y = 2 ÊÜáñÜᤠx+y=2

(C) 2x – y = 2 ÊÜáñÜᤠ4x – y = 4

(D) y–x=0 ÊÜáñÜᤠx–y=1

1111 () 6 of 32

The pair of equations of lines as shown in the graph are

(A) x + y = 1 and 2x – y = 1

(B) 2x + y = 2 and x+y=2

(C) 2x – y = 2 and 4x – y = 4

(D) y – x = 0 and x–y=1

5. a1x  b1y  c1  0 ÊÜáñÜᤠa 2x  b2y  c 2  0 ÃæàTÝñܾPÜ hæãàw ÃæàTæWÜÙÜá
ÓÜÊÜÞíñÜÃÜÊݨÜÃæ AÊÜâWÜÙÜ ÓÜÖÜWÜá|WÜÙÜ ÓÜÄ¿Þ¨Ü ÓÜíŸí«ÜÊÜâ

a1 b1 c1 a1 b1 c1
(A)   (B)  
a2 b2 c2 a2 b2 c2

a1 b1 a1 b
(C)  (D)  1
a2 b2 b2 a2

1111 () 7 of 32

If the pair of linear equations in two variables a1x  b1y  c1  0 and

a 2 x  b2y  c 2  0 are parallel lines then the correct relation of their

coefficients is
a1 b1 c1 a1 b1 c1
(A)   (B)  
a2 b2 c2 a2 b2 c2

a1 b1 a1 b
(C)  (D)  1
a2 b2 b2 a2

6. 2x + 3y + 7 = 0 ÊÜáñÜᤠax + by + 14 = 0 ÃæàTæWÜÙÜ hæãàw¿áá ±ÜÃÜÓܳÃÜ IPÜÂWæãÙÜáÛÊÜ

ÃæàTæWÜÙݨÜÃæ, ‘a’ ÊÜáñÜᤠ‘b’ ¸æÇæWÜÙÜá PÜÅÊÜáÊÝX

(A) 2 ÊÜáñÜᤠ3 (B) 3 ÊÜáñÜᤠ2

(C) 4 ÊÜáñÜᤠ6 (D) 1 ÊÜáñÜᤠ2

If the pair of lines 2x + 3y + 7 = 0 and ax + by + 14 = 0 are coincident

lines then the values of ‘a’ and ‘b’ are respectively equal to

(A) 2 and 3 (B) 3 and 2

(C) 4 and 6 (D) 1 and 2

7. D PæÙÜX®ÜÊÜâWÜÙÜÈÉ ¿ÞÊÜâ¨Üá ÓÜÊÜÞíñÜÃÜ ÍæÅà{¿ÞX¨æ ?

(A) 1, – 1, – 2, ..........

(B) 1, 5, 9, ..............

(C) 2, – 2, 2, – 2, ............

(D) 1, 2, 4, 8, ..........

1111 () 8 of 32

Which of the following is an Arithmetic Progression ?

(A) 1, – 1, – 2, ..........

(B) 1, 5, 9, ..............

(C) 2, – 2, 2, – 2, ............

(D) 1, 2, 4, 8, ..........

8. – 3, – 1, 1, 3, ....... ÓÜÊÜÞíñÜÃÜ ÍæÅà{¿á 11®æà ±Ü¨ÜÊÜâ

(A) 23 (B) – 23

(C) – 17 (D) 17

The 11th term of the Arithmetic Progression – 3, – 1, 1, 3, ....... is

(A) 23 (B) – 23

(C) – 17 (D) 17

9. Jí¨Üá ÓÜÊÜÞíñÜÃÜ ÍæÅà{¿á Êæã¨ÜÆ 10 ±Ü¨ÜWÜÙÜ ÊæãñܤÊÜâ 155 BX¨æ ÊÜáñÜᤠA¨æà ÍæÅà{¿á
Êæã¨ÜÆ 9 ±Ü¨ÜWÜÙÜ ÊæãñܤÊÜâ 126 B¨ÝWÜ ÍæÅà{¿á 10®æà ±Ü¨ÜÊÜâ

(A) 27 (B) 126

(C) 29 (D) 25

The sum of the first 10 terms of an Arithmetic Progression is 155 and the
sum of the first 9 terms of the same progression is 126 then the 10th term
of the progression is

(A) 27 (B) 126

(C) 29 (D) 25

1111 () 9 of 32

10. 2 x 2 + ax + 6 = 0 ÊÜWÜìÓÜËáàPÜÃÜ|¨Ü Jí¨Üá ÊÜáãÆÊÜâ 2 B¨ÝWÜ, ‘a’ ¿á ¸æÇæ

7
(A) 7 (B)
2
7
(C) –7 (D) 
2

If one root of the equation 2 x 2 + ax + 6 = 0 is 2, then the value of ‘a’

is
7
(A) 7 (B)
2
7
(C) –7 (D) 
2

11. px 2  qx  r  0 ÊÜWÜì ÓÜËáàPÜÃÜ|¨Ü Íæãà«ÜPÜÊÜâ

(A) q 2  4 pr (B) q 2  4 pr

(C) p 2  4 pr (D) p 2  4qr

The discriminant of the Quadratic equation px 2  qx  r  0 is

(A) q 2  4 pr (B) q 2  4 pr

(C) p 2  4 pr (D) p 2  4qr

12. 4, x, 10 ÓÜÊÜÞíñÜÃÜ ÍæÅà{¿áÈɨܪÃæ x ®Ü ¸æÇæ¿áá

(A) 14 (B) –6

(C) –7 (D) 7

If 4, x, 10 are in Arithmetic Progression the value of x is

(A) 14 (B) –6

(C) –7 (D) 7

1111 () 10 of 32

13. ax 2 + bx + c = 0 ÊÜWÜìÓÜËáàPÜÃÜ|¨Ü ÊÜáãÆWÜÙÜá

b  b 2  4ac
(A) x =
2a

b  b 2  4ac
(B) x =
2a

b  b 2  4c
(C) x =
2a

b  b 2  4ac
(D) x =
2a

The roots of the quadratic equation ax 2 + bx + c = 0 are

b  b 2  4ac
(A) x =
2a

b  b 2  4ac
(B) x =
2a

b  b 2  4c
(C) x =
2a

b  b 2  4ac
(D) x =
2a

14. ( x – 3 ) ( x + 2 ) = 0 ÓÜËáàPÜÃÜ|¨Ü ÊÜáãÆWÜÙÜá

(A) – 3, 2 (B) 3, – 2

(C) – 3, – 2 (D) 3, 2

The roots of the equation ( x – 3 ) ( x + 2 ) = 0 are

(A) – 3, 2 (B) 3, – 2

(C) – 3, – 2 (D) 3, 2

1111 () 11 of 32

15. GÃÜvÜá A®ÜáPÜÅÊÜá ±ÜäOÝìíPÜWÜÙÜ ÊæãñܤÊÜâ 27 B¨ÜÃæ, B ±ÜäOÝìíPÜWÜÙÜá
(A) 7 ÊÜáñÜᤠ20 (B) 13 ÊÜáñÜᤠ14

(C) 1 ÊÜáñÜᤠ26 (D) – 13 ÊÜáñÜᤠ– 14

If the sum of two consecutive integers is 27, then the integers are

(A) 7 and 20 (B) 13 and 14

(C) 1 and 26 (D) – 13 and – 14
16. PæãqrÃÜáÊÜ bñÜŨÜÈÉ sin  ¨Ü ¸æÇæ¿áá

1 3
(A) (B)
2 2
2
(C) 3 (D)
3

In the figure, the value of sin  is

1 3
(A) (B)
2 2
2
(C) 3 (D)
3

1111 () 12 of 32

17. ( sin 30° + cos 60° – tan 45° ) ¿á ¸æÇæ¿áá

(A) 1 (B) –1

(C) 2 (D) 0

The value of ( sin 30° + cos 60° – tan 45° ) is

(A) 1 (B) –1

(C) 2 (D) 0

18. 3 + sec 2  C¨ÜPæR ÓÜÊÜá®Ý¨Üá¨Üá

(A) 4 + tan 2  (B) 4 + cot 2 

(C) 2 + cot 2  (D) 3 + cot 2 

3 + sec 2  is equal to

(A) 4 + tan 2  (B) 4 + cot 2 

(C) 2 + cot 2  (D) 3 + cot 2 

19. Wæãà±ÜâÃÜ¨Ü ±Ý¨Ü©í¨Ü 30 Ëáà. ¨ÜãÃÜ¨Ü ®æÆ¨Ü Êæáà騆 Jí¨Üá ¹í¨Üá˯í¨Ü Wæãà±ÜâÃܨÜ
ñÜá©¿á®Üá° ËàüÔ¨ÝWÜ EípÝWÜáÊÜ E®Ü°ñÜ Pæãà®ÜÊÜâ 30° B¨ÜÃæ, B Wæãà±ÜâÃÜ¨Ü GñܤÃÜÊÜâ

(A) 10 m (B) 30 m

(C) 10 3 m (D) 30 3 m

The angle of elevation of the top of a tower from a point on the ground,

which is 30 metres away from the foot of the tower, is 30°. Then the height

of the tower is

(A) 10 m (B) 30 m

(C) 10 3 m (D) 30 3 m

1111 () 13 of 32

20. ( sin   cosec  ) ¨Ü ¸æÇæ¿áá

(A) 2 (B) 1

1 3
(C) – (D)
2 2

The value of ( sin   cosec  ) is

(A) 2 (B) 1

1 3
(C) – (D)
2 2

21. A ( x1 , y1 ) ÊÜáñÜᤠB ( x 2 , y 2 ) ¹í¨ÜáWÜÙÜ®Üá° ÓæàÄÓÜáÊÜ ÃæàTÝSívÜ¨Ü ÊÜá«Ü¹í¨ÜáÊÜ®Üá°

PÜívÜá×w¿ááÊÜ ÓÜãñÜÅ

 x 2  x1 y 2  y1   x 2  x1 y 2  y1 
(A)  ,  (B)  , 
 2 2   2 2 
   

 x 2  y2 x1  y1   x 2  x1 y 2  y1 
(C)  ,  (D)  , 
 3 3   3 3 
   

The formula to find the mid-point of the line segment joining the points
A ( x1 , y1 ) and B ( x 2 , y 2 ) is

 x 2  x1 y 2  y1   x 2  x1 y 2  y1 
(A)  ,  (B)  , 
 2 2   2 2 
   

 x 2  y2 x1  y1   x 2  x1 y 2  y1 
(C)  ,  (D)  , 
 3 3   3 3 
   

1111 () 14 of 32

22. ( x1 , y1 ) ÊÜáñÜᤠ( x 2 , y 2 ) ¹í¨ÜáWÜÚXÃÜáÊÜ ¨ÜãÃÜÊÜâ

(A) ( x1  x 2 )2  ( y1  y 2 )2 (B) ( x 2  x1 )2  ( y 2  y1 )2

(C) ( x1  x 2 )2  ( y1  y 2 )2 (D) ( x 2  x1 )2  ( y 2  y1 )2

The distance between the points ( x1 , y1 ) and ( x 2 , y 2 ) is

(A) ( x1  x 2 )2  ( y1  y 2 )2 (B) ( x 2  x1 )2  ( y 2  y1 )2

(C) ( x1  x 2 )2  ( y1  y 2 )2 (D) ( x 2  x1 )2  ( y 2  y1 )2

23. ¨Üñܤ ±ÝűݤíPÜWÜÙÜÈÉ A£ ÖæaÜác ÓÜÆ ±Üâ®ÜÃÝÊÜ£ìÓÜáÊÜ ÓÜíTæ¿á ÊÜåèÆÂÊÜâ ±ÝűݤíPÜWÜÙÜ
(A) ÓÜÃÝÓÜÄ¿ÞX¨æ (B) ŸÖÜáÆPÜ BX¨æ
(C) ÊÜÞ«ÝÂíPÜÊÝX¨æ (D) Êݲ¤ BX¨æ
The value among the observations of most repeated scores of the data is

(A) the mean (B) the mode

(C) the median (D) the range
24. D PæÙÜX®Ü ¨ÜñݤíÍÜWÜÙÜ ÓÜÃÝÓÜÄ ¿áá
AíPÜWÜÙÜá 1 3 5 7

(A) 16 (B) 5

(C) 1.6 (D) 4

The Mean of the following scores is

Marks 1 3 5 7

(A) 16 (B) 5

(C) 1.6 (D) 4

1111 () 15 of 32

25. PæÆÊÜâ ¨ÜñݤíÍÜWÜÙÜ ÓÜÃÝÓÜÄ ÊÜáñÜᤠŸÖÜáÆPÜ ÖÝWÜã ÊÜá«ÝÂíPÜWÜÙÜ ÓÜíŸí«ÜÊÜâ

(A) 3 ÊÜá«ÝÂíPÜ = 2 ÓÜÃÝÓÜÄ + ŸÖÜáÆPÜ

(B) 3 ÓÜÃÝÓÜÄ = 2 ÊÜá«ÝÂíPÜ + ŸÖÜáÆPÜ

(C) ÓÜÃÝÓÜÄ = 3 ÊÜá«ÝÂíPÜ + ŸÖÜáÆPÜ

(D) ŸÖÜáÆPÜ = 3 ÓÜÃÝÓÜÄ + 2 ÊÜá«ÝÂíPÜ

The relation among the Mean, Mode and Median is

(A) 3 Median = 2 Mean + Mode (B) 3 Mean = 2 Median + Mode

(C) Mean = 3 Median + Mode (D) Mode = 3 Mean + 2 Median

26. Êæáà|©í¨Ü ÊÜÞvÜƳor Jí¨Üá ÔÈívÜÃÜ®Üá° PÜÃÜXÔ A¨Ü®Üá° ÓÜí±Üä|ìÊÝX Jí¨Üá WæãàÙܨÜ
BPÝÃÜPæR Ÿ¨ÜÇÝÀáÔ¨ÝWÜ ¨æãÃÜPÜáÊÜ WæãàÙÜ¨Ü Z®Ü¶ÜÆÊÜâ

(A) ÔÈívÜÃ…¬Ü Z¬Ü¶ÜÆ¨Ü GÃÜvÜÃÜÐÝrWÜáñܤ¨æ

(B) ÔÈívÜÃ…¬Ü Z¬Ü¶ÜÆ¨Ü A«Üì¨ÜÐÝrWÜáñܤ¨æ

(C) ÔÈívÜÃ…¬Ü Z¬Ü¶ÜÆ¨Ü ÊÜáãÃÜÃÜÐÝrWÜáñܤ¨æ

(D) ÔÈívÜÃ…¬Ü Z¬Ü¶ÜƨÜÐræ à CÃÜáñܤ¨æ

A cylinder made of wax is melted and recast completely into a sphere.
Then the volume of the sphere is

(A) two times the volume of the cylinder

(B) half the volume of the cylinder

(C) 3 times the volume of the cylinder

(D) equal to the volume of the cylinder

1111 () 16 of 32

27. ÊÜWÝìíñÜÃÜ ÊÜá«Ü¹í¨Üá (AíPÜ)ÊÜ®Üá° PÜívÜá×w¿ááÊÜ ÓÜãñÜÅ
ÊæáàȾ£ – PæÙÜËá£
(A) 2
ÊæáàȾ£ × PæÙÜËá£
(B)
3
ÊæáàȾ£ + PæÙÜËá£
(C)
2
ÊæáàȾ£ + PæÙÜËá£
(D) 3
The formula to find the mid-point of the class interval is
Upper limit  low er limit
(A)
2
Upper limit  low er limit
(B)
3
Upper limit  low er limit
(C)
2
Upper limit  low er limit
(D)
3
28.  ABC ¿áÈÉ XY || BC B¨ÝWÜ

AX AC
(A) 
AB AY
AX AY
(B) 
BX CY
AX XY
(C) 
BX AY
AB AC
(D) 
BX AY

1111 () 17 of 32

In the  ABC, XY || BC then

AX AC
(A) 
AB AY
AX AY
(B) 
BX CY
AX XY
(C) 
BX AY
AB AC
(D) 
BX AY
29. PæãqrÃÜáÊÜ GÃÜvÜá £Å»ÜágWÜÙÜ®Üá° WÜÊÜá¯Ô, ®ÜíñÜÃÜ DF ®Ü AÙÜñæ¿á®Üá° WÜáÃÜá£Ô

(A) 6 2 cm (B) 3 2 cm
(C) 4.2 cm (D) 8.4 cm
Observe the given two triangles and then identify the length of DF in the
following :

(A) 6 2 cm (B) 3 2 cm
(C) 4.2 cm (D) 8.4 cm

1111 () 18 of 32

30.  ABC ~  PQR,  ABC ËÔ¤à|ì = 64 cm 2 ÊÜáñÜᤠ PQR ËÔ¤à|ì = 100 cm 2

BX¨æ. AB = 8 cm B¨ÝWÜ PQ ®Ü E¨ÜªÊÜâ

(A) 12 cm (B) 15 cm

(C) 10 cm (D) 8 cm

 ABC ~  PQR. Area of  ABC = 64 cm 2 and the area of  PQR = 100 cm 2 .

If AB = 8 cm then the length of PQ is

(A) 12 cm (B) 15 cm

(C) 10 cm (D) 8 cm

31.  ABC ¿áÈÉ, B = 90° ÊÜáñÜᤠBD  AC, AB = 6 cm, BC = 8 cm B¨ÝWÜ,

CD ¿á E¨ÜªÊÜâ

(A) 10 cm (B) 6.4 cm

(C) 4.8 cm (D) 3.6 cm

1111 () 19 of 32

In the  ABC, B = 90° and BD  AC. If AB = 6 cm, BC = 8 cm

then the length of CD is

(A) 10 cm (B) 6.4 cm

(C) 4.8 cm (D) 3.6 cm

32. bñÜŨÜÈÉ ñæãàÄÔÃÜáÊÜíñæ ‘O’ Pæàí¨ÜÅÊÜâÙÜÛ ÊÜêñܤPæR A ¹í¨ÜáË®ÜÈÉ AT ÓܳÍÜìPÜÊÜ®Üá°
GÙæ¿áÇÝX¨æ. OTA = 30° ÊÜáñÜᤠOT = 4 cm B¨ÜÃæ, AT ¿á E¨Üª

(A) 4 cm (B) 2 cm

(C) 2 3 cm (D) 4 3 cm

1111 () 20 of 32

In the given figure AT is a tangent drawn at the point A to the circle with

centre O such that OT = 4 cm. If OTA = 30° then AT is

(A) 4 cm (B) 2 cm

(C) 2 3 cm (D) 4 3 cm

33. bñÜŨÜÈÉ PA, PBC ÊÜáñÜᤠCD WÜÙÜá ‘O’ Pæàí¨ÜÅÊÜâÙÜÛ ÊÜêñܤPæR GÙæ¨Ü ÓܳÍÜìPÜWÜÙÝXÊæ.
PC = 8 cm ÊÜáñÜᤠAP = 5 cm B¨ÝWÜ, CD ÓܳÍÜìPÜ¨Ü E¨ÜªÊÜâ

(A) 5 cm (B) 3 cm

(C) 8 cm (D) 13 cm

1111 () 21 of 32

In the given figure PA, PBC and CD are the tangents to a circle with
centre O. If PC = 8 cm and AP = 5 cm, the length of the tangent CD is

(A) 5 cm (B) 3 cm

(C) 8 cm (D) 13 cm
34. D PæÙÜX®Ü ÖæàÚPæWÜÙÜÈÉ ñܱÜâ³ ÖæàÚPæ¿á®Üá° WÜáÃÜá£Ô
(A) ÊÜêñܤPæR GÙæ¨Ü ÓܳÍÜìPÜÊÜâ ÊÜêñܤÊÜ®Üá° Jí¨æà ¹í¨ÜáË®ÜÈÉ ÓܳÎìÓÜáñܤ¨æ
(B) ÊÜêñܤPæR Jí¨Üá ÓÜÃÜÙÜ ÃæàTæ¿á®Üá° GÙæ¨ÝWÜ A¨Üá ¿ÞÊÝWÜÆá ÊÜêñܤ¨Ü Jí¨æà Jí¨Üá
¹í¨Üá˯í¨Ü ÖݨÜá ÖæãàWÜáñܤ¨æ
(C) ÊÜêñܤPæR Jí¨Üá ÓÜÃÜÙÜ ÃæàTæ¿á®Üá° GÙæ¨ÝWÜ A¨Üá ÊÜêñܤÊÜ®Üá° ÓܳÎìÓÜáÊÜ ¹í¨ÜáÊÜ®Üá°
ÓܳÍÜì¹í¨Üá Gí¨Üá PÜÃæ¿ááñæ¤àÊæ
(D) ÓܱÍÜì¹í¨ÜáË­í¨Ü ÊÜêñܤPæR GÙæ¨Ü £ÅgÂÊÜâ ÓܱÍÜìÃæàTæWæ ÆíŸÊÝXÃÜáñܤ¨æ
The wrong statement in the following is

(A) a tangent to a circle touches the circle exactly at one point

(B) when a straight line is drawn to a circle it always passes through a
point on the circle

(C) the point common to the circle and its tangent is called the point of
contact

(D) the tangent drawn at any point to a circle is perpendicular to the
radius drawn at the point of contact

1111 () 22 of 32

35. ¨Üñܤ ÊÜêñܤPæR A¨ÜÃÜ ÖæãÃÜX®Ü ¹í¨Üá ‘T ’ Àáí¨Ü GÃÜvÜá ÓܳÍÜìPÜWÜÙÜ®Üá° ÃÜbÓÜáÊÝWÜ bñÜŨÜÈÉ
ñæãàÄÔÃÜáÊÜ ÃÜaÜ®æ¿á ÖÜíñÜ¨Ü ÊÜááí©®Ü ÖÜíñÜÊÜ®Üá° WÜáÃÜá£Ô

(A)

(B)

(C)

(D)

1111 () 23 of 32

Which is the next step of construction while constructing a pair of
tangents to a circle from an external point ‘T ’, given in the figure ?

(A)

(B)

(C)

(D)

1111 () 24 of 32

36. Jí¨Üá WæãàÙÜ¨Ü ÊæáàÇ澄 ËÔ¤à|ì 616 cm 2 BX¨æ. A¨æà WæãàÙÜ¨Ü £ÅgÂÊÜâ
(A) 49 cm (B) 14 cm

(C) 21 cm (D) 7 cm

The surface area of a sphere is 616 sq.cm. Then the radius of the same
sphere is

(A) 49 cm (B) 14 cm

(C) 21 cm (D) 7 cm
37. PæãqrÃÜáÊÜ ÍÜíPÜá訆 Z®Ü¶ÜÆ PÜívÜá×w¿ááÊÜ ÓÜãñÜÅÊÜâ

(A) r 2 h (B) r ( r + l )
1
(C) r 2 h (D) r l
3

The volume of a cone as shown in the figure is

(A) r 2 h (B) r ( r + l )
1
(C) r 2 h (D) r l
3

1111 () 25 of 32

38. GÃÜvÜá ±Ý¨ÜWÜÙÜÈÉ Jí¨Üá ±Ý¨Ü ñæÃæ¿áƳqrÃÜáÊÜ ®æàÃÜ ÔÈívÜÄ®Ü ±Ý¨Ü¨Ü £Åg r cm ÊÜáñÜá¤
A¨ÜÃÜ GñܤÃÜ h cm B¨ÝWÜ ÔÈívÜÄ¬Ü ¯Üä|ì ÊæáàÇ澄 ËÔ¤à|ìÊܬÜá® PÜívÜá×w¿ááÊÜ ÓÜãñÜÅ

(A) (  r 2 + 2rh ) cm 2 (B) 2rh cm 2

1
(C)  r 2h cm 3 (D) (  r 2 + h ) cm 2
3

The formula to find the total surface area of a right circular based

cylindrical vessel of base radius r cm and height h cm opened at one end is

(A) (  r 2 + 2rh ) cm 2 (B) 2rh cm 2

1
(C)  r 2h cm 3 (D) (  r 2 + h ) cm 2
3

39. bñÜŨÜÈÉ ñæãàÄÔÃÜáÊÜ ¹¬Ü®PÜ ÍÜíPÜáË¬Ü ÊÜPÜÅÊæáàÇ澄 ËÔ¤à|ì PÜívÜá×w¿ááÊÜ ÓÜãñÜÅÊÜâ

1 1
(A)  l ( r1  r2 ) (B)  h ( r12  r22  r1 r2 )
3 3

(C) l ( r1  r2 ) (D) l ( r1  r2 )

1111 () 26 of 32

To find the curved surface area of a frustum of a cone as shown in the

figure the formula used is

1 1
(A)  l ( r1  r2 ) (B)  h ( r12  r22  r1 r2 )
3 3

(C) l ( r1  r2 ) (D) l ( r1  r2 )

40. Jí¨Üá Z¬Ü A«ÜìWæãàÙÜ¨Ü ¯Üä|ì ÊæáàÇ澄 ËÔ¤à|ìÊÜâ 462 cm 2 BX¨æ ÊÜáñÜᤠA¨ÜÃÜ
ÊÜPÜÅÊæáàÇ澄 ËÔ¤à|ìÊÜâ 308 cm 2 B¨ÝWÜ A«ÜìWæãàÙÜ¨Ü ±Ý¨Ü¨Ü ËÔ¤à|ìÊÜâ

(A) 308 cm 2 (B) 231 cm 2

(C) 154 cm 2 (D) 1078 cm 2

The total surface area of solid hemisphere is 462 cm 2 . If the curved

surface area of it is 308 cm 2 , then the area of the base of the hemisphere

is

(A) 308 cm 2 (B) 231 cm 2

(C) 154 cm 2 (D) 1078 cm 2

1111 () 27 of 32

PÜaÝc PÝ¿áìPÝRX
( SPACE FOR ROUGH WORK )

1111 () 28 of 32

PÜaÝc PÝ¿áìPÝRX
( SPACE FOR ROUGH WORK )

1111 () 29 of 32

PÜaÝc PÝ¿áìPÝRX
( SPACE FOR ROUGH WORK )

1111 () 30 of 32

PÜaÝc PÝ¿áìPÝRX
( SPACE FOR ROUGH WORK )

1111 () 31 of 32

1111 () 32 of 32