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LMN

: MATHEMATICS, PHYSICS & CHEMISTRY 1 : »ç‡æÌ, ÖæñçÌ·¤ çߙææÙ ÌÍæ ÚUâæØÙ çߙææÙ

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1. Immediately fill in the particulars on this page of the Test Booklet with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited. 2. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer Sheet and fill in the particulars carefully. 3. The test is of 3 hours duration. 4. The Test Booklet consists of 90 questions. The maximum marks are 360. 5. There are three parts in the question paper A, B, C consisting of Mathematics, Physics and Chemistry having 30 questions in each part of equal weightage. Each question is allotted 4 (four) marks for correct response. 6. Candidates will be awarded marks as stated above in instruction No. 5 for correct response of each question. ¼ (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 7. There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above. 8. Use Blue/Black Ball Point Pen only for writing particulars/ marking responses on Side-1 and Side–2 of the Answer Sheet. Use of pencil is strictly prohibited. 9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination room/hall. 10. Rough work is to be done on the space provided for this purpose in the Test Booklet only. This space is given at the bottom of each page and in one page (i.e. Page 39) at the end of the booklet. 11. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them. 12. The CODE for this Booklet is C. Make sure that the CODE printed on Side–2 of the Answer Sheet and also tally the serial number of the Test Booklet and Answer Sheet are the same as that on this booklet. In case of discrepancy, the candidate should immediately report the matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet. 13. Do not fold or make any stray mark on the Answer Sheet.

ÂÚèÿææÍèü ·¤æ Ùæ× (ÕǸð ¥ÿæÚæð´ ×ð´) Ñ ¥Ùé·¤ý ×æ´·¤

: in figures

Ñ ¥´·¤æð´ ×ð´

: in words

Ñ àæŽÎæð´ ×ð´

Examination Centre Number :

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Name of Examination Centre (in Capital letters) :

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Test Booklet Code

ÂÚèÿææ ÂéçSÌ·¤æ â´·ð¤Ì

C

×ãžßÂê‡æü çÙÎðüàæ Ñ 1. ÂÚUèÿææ ÂéçSÌ·¤æ ·ð¤ §â ÂëcÆU ÂÚU ¥æßàØ·¤ çßßÚU‡æ ÙèÜð / ·¤æÜð ÕæòÜ Œß槴ÅU ÂðÙ âð ̈·¤æÜ ÖÚð´Ð Âðç‹âÜ ·¤æ ÂýØæð» çÕË·é¤Ü ßçÁüÌ ãñÐ 2. ©žæÚU Â˜æ §â ÂÚUèÿææ ÂéçSÌ·¤æ ·ð¤ ¥‹ÎÚU ÚU¹æ ãñÐ ÁÕ ¥æ·¤æð ÂÚUèÿææ ÂéçSÌ·¤æ ¹æðÜÙð ·¤æð ·¤ãæ Áæ°, Ìæ𠩞æÚU ˜æ çÙ·¤æÜ ·¤ÚU âæßÏæÙèÂêß·ü ¤ çßßÚU‡æ ÖÚðU´Ð 3. ÂÚUèÿææ ·¤è ¥ßçÏ 3 ƒæ´ÅðU ãñÐ 4. §â ÂÚUèÿææ ÂéçSÌ·¤æ ×ð´ 90 ÂýàÙ ãñ´Ð ¥çÏ·¤Ì× ¥´·¤ 360 ãñ´Ð 5. §â ÂÚUèÿææ ÂéçSÌ·¤æ ×ð´ ÌèÙ Öæ» A, B, C ãñ´, çÁâ·ð¤ ÂýˆØð·¤ Öæ» ×ð´ »ç‡æÌ, ÖæñçÌ·¤ çߙææÙ °ß´ ÚUâæØÙ çߙææÙ ·ð¤ 30 ÂýàÙ ãñ´ ¥æñÚU âÖè ÂýàÙæ𴠷𤠥´·¤ â×æÙ ãñ´Ð ÂýˆØð·¤ ÂýàÙ ·ð¤ âãè ©žæÚU ·ð¤ çÜ° 4 (¿æÚU) ¥´·¤ çÙÏæüçÚUÌ ç·¤Øð »Øð ãñ´Ð 6. ¥ØçÍüØæð´ ·¤æð ÂýˆØð·¤ âãè ©žæÚU ·ð¤ çÜ° ©ÂÚUæð€Ì çÙÎðüàæ٠ⴁØæ 5 ·ð¤ çÙÎðüàææÙéâæÚU ¥´·¤ çÎØð ÁæØð´»ðÐ ÂýˆØð·¤ ÂýàÙ ·ð¤ »ÜÌ ©žæÚU ·ð¤ çÜØð ¼ ßæ´ Öæ» ·¤æÅU çÜØæ ÁæØð»æÐ ØçÎ ©žæÚU ˜æ ×ð´ ç·¤âè ÂýàÙ ·¤æ ©žæÚU Ùãè´ çÎØæ »Øæ ãæð Ìæð ·é¤Ü Âýæ#æ´·¤ âð ·¤æð§ü ·¤ÅUæñÌè Ùãè´ ·¤è ÁæØð»èÐ 7. ÂýˆØð·¤ ÂýàÙ ·¤æ ·ð¤ßÜ °·¤ ãè âãè ©žæÚU ãñÐ °·¤ âð ¥çÏ·¤ ©žæÚU ÎðÙð ÂÚU ©âð »ÜÌ ©žæÚU ×æÙæ ÁæØð»æ ¥æñÚU ©ÂÚUæð€Ì çÙÎðüàæ 6 ·ð¤ ¥ÙéâæÚU ¥´·¤ ·¤æÅU çÜØð ÁæØð´»ðÐ 8. ©žæÚU Â˜æ ·ð¤ ÂëcÆU-1 °ß´ ÂëcÆU-2 ÂÚU ßæ´çÀUÌ çßßÚU‡æ °ß´ ©žæÚU ¥´ç·¤Ì ·¤ÚUÙð ãðÌé ·ð¤ßÜ ÙèÜð/·¤æÜð ÕæòÜ Œß槴ÅU ÂðÙ ·¤æ ãè ÂýØæð» ·¤Úð´UÐ Âðç‹âÜ ·¤æ ÂýØæð» çÕË·é¤Ü ßçÁüÌ ãñÐ 9. ÂÚUèÿææÍèü mæÚUæ ÂÚUèÿææ ·¤ÿæ/ãæòÜ ×ð´ Âýßðàæ ·¤æÇüU ·ð¤ ¥Üæßæ ç·¤âè Öè Âý·¤æÚU ·¤è ÂæÆ÷UØ âæ×»ýè, ×éçÎýÌ Øæ ãSÌçÜç¹Ì, ·¤æ»Á ·¤è Âç¿üØæ¡, ÂðÁÚU, ×æðÕæ§Ü ȤæðÙ Øæ ç·¤âè Öè Âý·¤æÚU ·ð¤ §Üð€ÅþUæòçÙ·¤ ©Â·¤ÚU‡ææð´ Øæ ç·¤âè ¥‹Ø Âý·¤æÚU ·¤è âæ×»ýè ·¤æð Üð ÁæÙð Øæ ©ÂØæð» ·¤ÚUÙð ·¤è ¥Ùé×çÌ Ùãè´ ãñÐ 10. ÚUȤ ·¤æØü ÂÚUèÿææ ÂéçSÌ·¤æ ×ð´ ·ð¤ßÜ çÙÏæüçÚUÌ Á»ã ÂÚU ãè ·¤èçÁ°Ð Øã Á»ã ÂýˆØð·¤ ÂëcÆU ÂÚU Ùè¿ð ·¤è ¥æðÚU ¥æñÚU ÂéçSÌ·¤æ ·ð¤ ¥´Ì ×ð´ °·¤ ÂëcÆU ÂÚU (ÂëcÆU 39) Îè »§ü ãñÐ 11. ÂÚUèÿææ â×æŒÌ ãæðÙð ÂÚU, ÂÚUèÿææÍèü ·¤ÿæ/ãæòÜ ÀUæðǸÙð âð Âêßü ©žæÚU Â˜æ ·¤ÿæ çÙÚUèÿæ·¤ ·¤æð ¥ßàØ âæñ´Â Îð´Ð ÂÚUèÿææÍèü ¥ÂÙð âæÍ §â ÂÚUèÿææ ÂéçSÌ·¤æ ·¤æð Üð Áæ â·¤Ìð ãñ´Ð 12. §â ÂéçSÌ·¤æ ·¤æ â´·ð¤Ì C ãñÐ Øã âéçÙçà¿Ì ·¤ÚU Üð´ ç·¤ §â ÂéçSÌ·¤æ ·¤æ â´·ð¤Ì, ©žæÚU Â˜æ ·ð¤ ÂëcÆU-2 ÂÚU ÀUÂð â´·ð¤Ì âð ç×ÜÌæ ãñ ¥æñÚU Øã Öè âéçÙçà¿Ì ·¤ÚU Üð´ ç·¤ ÂÚUèÿææ ÂéçSÌ·¤æ, ©žæÚU ˜æ ÂÚU ·ý¤× ⴁØæ ç×ÜÌè ãñÐ ¥»ÚU Øã çÖóæ ãæð Ìæð ÂÚUèÿææÍèü ÎêâÚUè ÂÚUèÿææ ÂéçSÌ·¤æ ¥æñÚU ©žæÚU ˜æ ÜðÙð ·ð¤ çÜ° çÙÚUèÿæ·¤ ·¤æð ÌéÚU‹Ì ¥ß»Ì ·¤ÚUæ°¡Ð 13. ©žæÚU Â˜æ ·¤æð Ù ×æðǸ𴠰ߴ Ù ãè ©â ÂÚU ¥‹Ø çÙàææ٠ܻ氡Ð

Name of the Candidate (in Capital letters ) : Roll Number

No. :

1. Invigilator’s Signature :

çÙÚèÿæ·¤ ·ð¤ ãSÌæÿæÚ Ñ

2. Invigilator’s Signature :

çÙÚèÿæ·¤ ·ð¤ ãSÌæÿæÚ Ñ

Öæ» A — »ç‡æÌ

PART A — MATHEMATICS 1.

A complex number z is said to be

1.

unimodular if ?z?51. Suppose z1 and z2 z1 2 2 z2 are complex numbers such that 2 2 z1 z2

ç·¤

z1 2 2 z2 2 2 z1 z2

°·¤×æÂæ´·¤è ãñ ÌÍæ

z2 °·¤×æÂæ´·¤è

Ùãè´ ãñ, Ìæð çÕ´Îé z1 çSÍÌ ãñ Ñ

is unimodular and z2 is not unimodular. Then the point z1 lies on a :

2.

°·¤ âç×Ÿæ ⴁØæ z °·¤×æÂæ´·¤è ·¤ãÜæÌè ãñ ØçÎ ?z?51 ãñÐ ×æÙæ z1 ÌÍæ z2 °ðâè âç×Ÿæ ⴁØæ°¡ ãñ´

(1)

circle of radius

(2)

straight line parallel to x-axis.

(2)

ç˜æ’Øæ ßæÜð ßëžæ ÂÚUÐ x-¥ÿæ ·ð¤ â×æ´ÌÚU °·¤ ÚðU¹æ ÂÚUÐ

(3)

straight line parallel to y-axis.

(3)

y-¥ÿæ

(4)

circle of radius 2.

(4)

2 ç˜æ’Øæ

2.

(1)

2

·ð¤ â×æ´ÌÚU °·¤ ÚðU¹æ ÂÚUÐ ßæÜð ßëžæ ÂÚUÐ

at (1, 1) :

ß·ý ¤ x 2 12xy23y 250 ·ð ¤ çÕ´ Î é ¥çÖÜÕ Ñ

(1)

(1)

ß·ý¤ ·¤æð ÎæðÕæÚUæ ¿ÌéÍü ¿ÌéÍæZàæ ×ð´ ç×ÜÌæ ãñÐ

The normal to the curve, x212xy23y250,

2.

meets the curve again in the fourth

(1, 1)

ÂÚU

quadrant. (2)

does not meet the curve again.

(2)

ß·ý¤ ·¤æð ÎæððÕæÚUæ Ùãè´ ç×ÜÌæÐ

(3)

meets the curve again in the second

(3)

ß·ý¤ ·¤æð ÎæðÕæÚUæ çmÌèØ ¿ÌéÍæZàæ ×ð´ ç×ÜÌæ ãñÐ

(4)

ß·ý¤ ·¤æð ÎæðÕæÚUæ ÌëÌèØ ¿ÌéÍæZàæ ×ð´ ç×ÜÌæ ãñÐ

quadrant. (4)

meets the curve again in the third quadrant.

3.

The sum of first 9 terms of the series

3.

13 1 2 3 13 1 2 3 1 3 3 13 1 1 1 .... is : 1 113 11 31 5

Ÿæð‡æè 13 1 2 3 13 1 2 3 1 3 3 13 1 1 1 .... 1 113 11 31 5

Âý‰æ× 9 ÂÎæð´ ·¤æ Øæð» ãñ Ñ (1)

192

(1)

192

(2)

71

(2)

71

(3)

96

(3)

96

(4)

142

(4)

142

C/Page 2

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

·ð ¤

4.

Let f (x) be a polynomial of degree four

4.

×æÙæ

f (x)

ÌÍæ

ƒææÌ

4

·¤æ °·¤ Õãé  Πãñ çÁâ·ð ¤ ÂÚU ¿ÚU× ×æÙ ãñ´Ð ØçÎ

having extreme values at x51 and x52.

x51

f ( x )  If lim 1 1  5 3 , then f (2) is equal x →0  x2 

f ( x )  lim 1 1 53 x →0  x2 

x52

ãñ, Ìæð f (2) ÕÚUæÕÚU ãñ Ñ

to :

5.

(1)

4

(1)

4

(2)

28

(2)

28

(3)

24

(3)

24

(4)

0

(4)

0

The negation of ~ s Ú (~ r Ù s ) is equivalent

5.

~ s Ú (~ r Ù s ) ·¤æ

çÙáðÏ â×ÌéËØ ãñ Ñ

to :

6.

(1)

sÙr

(1)

sÙr

(2)

sÙ~r

(2)

sÙ~r

(3)

s Ù (r Ù ~ s)

(3)

s Ù (r Ù ~ s)

(4)

s Ú (r Ú ~ s)

(4)

s Ú (r Ú ~ s)

1 2 2    If A 5  2 1 22  is a matrix satisfying  a 2 b 

6.

ØçÎ

1 2 2  A 5  2 1 22  °·¤  a 2 b 

°ðâæ ¥æÃØêã ãñ Áæð

(a, b) is equal to :

¥æÃØêã â×è·¤ÚU‡æ AAT59I, ·¤æð â´ÌécÅU ·¤ÚUÌæ ãñ, Áãæ¡ I, 333 ·¤æ ̈â×·¤ ¥æÃØêã ãñ, Ìæð ·ý¤ç×Ì Øé‚× (a, b) ·¤æ ×æÙ ãñ Ñ

(1)

(22, 21)

(1)

(22, 21)

(2)

(2, 21)

(2)

(2, 21)

(3)

(22, 1)

(3)

(22, 1)

(4)

(2, 1)

(4)

(2, 1)

the equation AA T 59I, where I is 333 identity matrix, then the ordered pair

C/Page 3

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

7.

The integral

dx

∫ x 2 ( x 4 1 1)3 4

equals :

7.

â×æ·¤Ü ∫

1

(1)

 x 41 1  4 2  1c  x4   

(2)

 x4 1 1  4   1c  x4   

(3)

( x 411) 4 1 c

(4)

2( x 4 1 1) 4 1 c

9.

3

4

x ( x 1 1)

4

ÕÚUæÕÚU ãñ Ñ

1

(1)

 x 41 1  4 2  1c  x4   

(2)

 x4 1 1  4   1c  x4   

(3)

( x 411) 4 1 c

(4)

2( x 4 1 1) 4 1 c

1

8.

dx 2

1

1

1

1

1

numbers l and n (l, n > 1) and G1, G2 and G3 are three geometric means between l

ØçÎ Îæð çßç֋٠ßæSÌçß·¤ â´  Øæ¥æð ´ l ÌÍæ n (l, n > 1) ·¤æ â×æ´ÌÚU ×æŠØ (A.M.) m ãñ ¥æñÚU l ÌÍæ n ·ð¤ Õè¿ ÌèÙ »é‡ææðžæÚU ×æŠØ (G.M.) G1, G2 ÌÍæ

and n, then G14 1 2G24 1 G 34 equals.

G3 ãñ´,

Ìæð

If m is the A.M. of two distinct real

8.

4

(1)

4 l2m2n2

(1)

4 l2m2n2

(2)

4 l2mn

(2)

4 l2mn

(3)

4 lm2n

(3)

4 lm2n

(4)

4 lmn2

(4)

4 lmn2

Let y(x) be the solution of the differential

9.

4

4

G1 1 2G2 1 G3

ÕÚUæÕÚU ãñ Ñ

×æÙæ ¥ß·¤Ü â×è·¤ÚU‡æ

equation

dy 1 y 5 2 x log x , ( x / 1). dx Then y(e) is equal to :

·¤æ ãÜ

(1)

2e

(1)

2e

(2)

e

(2)

e

(3)

0

(3)

0

(4)

2

(4)

2

( x log x )

C/Page 4

SPACE FOR ROUGH WORK /

dy 1 y 5 2 x log x , ( x / 1) dx y(x) ãñ, Ìæð y(e) ÕÚUæÕÚU ãñ Ñ

( x log x )

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

10.

The number of integers greater than 6,000

10.

that can be formed, using the digits 3, 5, 6,

¥´·¤æð´ 3, 5, 6, 7 ÌÍæ 8 ·ð¤ ÂýØæð» âð, çÕÙæ ÎæðãÚUæØð, ÕÙÙð ßæÜð 6,000 âð ÕǸð Âê‡ææZ·¤æð´ ·¤è ⴁØæ ãñ Ñ

7 and 8, without repetition, is :

11.

(1)

72

(1)

72

(2)

216

(2)

216

(3)

192

(3)

192

(4)

120

(4)

120

The number of points, having both

11.

co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0),

ç˜æÖéÁ, çÁâ·ð¤ àæèáü (0, 0), (0, 41) ÌÍæ (41, 0) ãñ´, ·ð¤ ¥æ´ÌçÚU·¤ Öæ» ×ð´ çSÍÌ ©Ù çÕ´Îé¥æð´ ·¤è ⴁØæ çÁÙ·ð¤ ÎæðÙæð´ çÙÎðüàææ´·¤ Âê‡ææZ·¤ ãñ´, ãñ Ñ

(0, 41) and (41, 0), is :

12.

(1)

780

(1)

780

(2)

901

(2)

901

(3)

861

(3)

861

(4)

820

(4)

820

Let a and b be the roots of equation

12.

x 2 26x2250. If a n 5a n 2b n , for n/1, a 2 2a8 then the value of 10 is equal to : 2a9

×æÙæ a ÌÍæ b çmƒææÌ â×è·¤ÚU‡æ x226x2250 ·ð¤ ×êÜ ãñ´Ð ØçÎ n/1 ·ð¤ çÜ°, an5an2bn ãñ, Ìæð a10 2 2a8 2a9

(1)

23

(1)

23

(2)

6

(2)

6

(3)

26

(3)

26

(4)

3

(4)

3

C/Page 5

SPACE FOR ROUGH WORK /

·¤æ ×æÙ ãñ Ñ

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

13.

Let

13.

 2x tan21 y 5 tan21 x 1 tan21   1 2 x2

where ? x ? <

 2x tan21 y 5 tan21 x 1 tan21   1 2 x2

1 . Then a value of y is : 3

Áãæ¡

3 x 1 x3

(1)

(1)

1 1 3 x2

3 x 2 x3

(2)

(2)

1 2 3 x2

3 x 1 x3

(3)

(3)

1 2 3 x2

3 x 2 x3

(4)

14.

 , 

(4)

1 1 3 x2

The distance of the point (1, 0, 2) from the point

of

×æÙæ

intersection

of

the

14.

line

?x? <

1 1 3 x2

3 x 2 x3 1 2 3 x2

3 x 1 x3 1 2 3 x2

3 x 2 x3 1 1 3 x2

y 11 x 22 z 22 5 5 3 4 12 x2y1z516 ·ð¤ Âýç̑ÀðUÎ çÕ´Îé ·¤è,

Úð U ¹ æ

âð ÎêÚUè ãñ Ñ

(1)

13

(1)

13

(2)

2 14

(2)

2 14

(3)

8

(3)

8

(4)

3 21

(4)

3 21

SPACE FOR ROUGH WORK /

ãñ, Ìæð y ·¤æ °·¤ ×æÙ ãñ Ñ

3 x 1 x3

y 11 x 22 z 22 5 5 and the plane 3 4 12 x2y1z516, is :

C/Page 6

1 3

 , 

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

ÌÍæ â×ÌÜ çÕ´Îé (1, 0, 2)

15.

The area (in sq. units) of the region

15.

described by

{(x, y) : y2[ 2x ÌÍæ y / 4x 2 1} mæÚUæ

ÿæð˜æ ·¤æ ÿæð˜æÈ¤Ü (ß»ü §·¤æ§Øæð´) ×ð´ ãñ Ñ

ÂçÚUÖæçáÌ

{(x, y) : y2 [ 2x and y / 4x 2 1} is :

16.

(1)

9 32

(1)

9 32

(2)

7 32

(2)

7 32

(3)

5 64

(3)

5 64

(4)

15 64

(4)

15 64

Let O be the vertex and Q be any point on

16.

the parabola, x258y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

17.

×æÙæ ÂÚUßÜØ x258y ·¤æ àæèáü O ÌÍæ ©â ÂÚU ·¤æð§ü çÕ´ Î é Q ãñ Ð ØçÎ çÕ´ Î é P, Úð U ¹ æ¹´ Ç U OQ ·¤æð 1 : 3 ·ð¤ ¥æ´ÌçÚU·¤ ¥ÙéÂæÌ ×ð´ Õæ¡ÅUÌæ ãñ, Ìæð P ·¤æ çÕ´ÎéÂÍ ãñ Ñ

(1)

x 2 52y

(1)

x 2 52y

(2)

x 2 5y

(2)

x 2 5y

(3)

y 2 5x

(3)

y 2 5x

(4)

y 2 52x

(4)

y 2 52x

The mean of the data set comprising of 16

17.

observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added

Âýðÿæ‡ææð´ ßæÜð ¥æ¡·¤Ç¸æð´ ·¤æ ×æŠØ 16 ãñÐ ØçÎ °·¤ Âýðÿæ‡æ çÁâ·¤æ ×æÙ 16 ãñ, ·¤æð ãÅUæ ·¤ÚU, 3 ÙØð Âýðÿæ‡æ çÁÙ·ð¤ ×æÙ 3, 4 ÌÍæ 5 ãñ´, ¥æ¡·¤Ç¸æð´ ×ð´ ç×Üæ çÎØð ÁæÌð ãñ´, Ìæð ÙØð ¥æ¡·¤Ç¸æð´ ·¤æ ×æŠØ ãñ Ñ 16

to the data, then the mean of the resultant data, is : (1)

14.0

(1)

14.0

(2)

16.8

(2)

16.8

(3)

16.0

(3)

16.0

(4)

15.8

(4)

15.8

C/Page 7

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

18.

The area (in sq. units) of the quadrilateral

18.

y2 x2 1 51 9 5

Îèƒæüßëžæ

·ð¤ ÙæçÖܐÕæð´ ·ð¤ çâÚUæð´ ÂÚU

¹è´¿è »§ü SÂàæü ÚðU¹æ¥æð´ mæÚUæ çÙç×üÌ ¿ÌéÖéüÁ ·¤æ ÿæð˜æÈ¤Ü (ß»ü §·¤æ§Øæð´ ×ð´) ãñ Ñ

formed by the tangents at the end points of the latera recta to the ellipse

y2 x2 1 5 1 , is : 9 5

19.

(1)

27

(1)

27

(2)

27 4

(2)

27 4

(3)

18

(3)

18

(4)

27 2

(4)

27 2

parallel to the plane, x13y16z51, is :

ÚðU¹æ 2x25y1z53, x1y14z55 ·¤æð ¥´ÌçßücÅU ·¤ÚUÙð ßæÜð â×ÌÜ, Áæð â×ÌÜ x13y16z51 ·ð¤ â×æ´ÌÚU ãñ, ·¤æ â×è·¤ÚU‡æ ãñ Ñ

(1)

2x16y112z5213

(1)

2x16y112z5213

(2)

2x16y112z513

(2)

2x16y112z513

(3)

x13y16z527

(3)

x13y16z527

(4)

x13y16z57

(4)

x13y16z57

The equation of the plane containing the

19.

line 2x25y1z53; x1y14z55, and

20.

The number of common tangents to the circles

x 2 1y 2 24x26y21250

x21y216x118y12650,

20.

and

is :

ßëžææð´

x21y216x118y12650

ÚðU¹æ¥æð´ ·¤è ⴁØæ ãñ Ñ

(1)

4

(1)

4

(2)

1

(2)

1

(3)

2

(3)

2

(4)

3

(4)

3

C/Page 8

SPACE FOR ROUGH WORK /

ÌÍæ ·¤è ©ÖØçÙcÆU SÂàæü

x21y224x26y21250

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

21.

system of linear equations :

·ð¤ âÖè ×æÙæð´ ·¤æ â×鑿Ø, çÁÙ·ð¤ çÜ° ÚñUç¹·¤ â×è·¤ÚU‡æ çÙ·¤æØ

2x 122x21x 35lx 1

2x 122x21x 35lx 1

2x112x2

2x112x2

The set of all values of l for which the

21.

2x 123x 212x 35lx 2

2x 123x 212x 35lx 2

5lx3

22.

contains more than two elements.

(2)

is an empty set.

(3)

is a singleton.

(4)

contains two elements.

If 12 identical balls are to be placed in 3

5lx3

·¤æ °·¤ ¥Ìé‘ÀU ãÜ ãñ, (1) ×ð´ Îæð âð ¥çÏ·¤ ¥ßØß ãñ´Ð (2) °·¤ çÚU€Ì â×é‘¿Ø ãñÐ (3) °·¤ °·¤Ü â×é‘¿Ø ãñÐ (4) ×ð´ Îæð ¥ßØß ãñ´Ð

has a non-trivial solution, (1)

l

22.

identical boxes, then the probability that one of the boxes contains exactly 3 balls

ØçÎ 12 °·¤ Áñâè »ðδ ,´ð 3 °·¤ Áñâð Հâæð´ ×ð´ ÚU¹è ÁæÌè ãñ´, Ìæð §Ù×ð´ âð °·¤ Հâð ×ð´ ÆUè·¤ 3 »ð´Îð´ ãæðÙð ·¤è ÂýæçØ·¤Ìæ ãñ Ñ

is :

23.

11

(1)

1 22   3

(2)

55  2 11   3 3

(3)

2 55   3

(4)

1 220   3

50

(3)

2 55   3

(4)

1 220   3

23.

(1 2 2 x )

10

50

12

·ð¤ çmÂÎ ÂýâæÚU ×ð´

ƒææÌæ𴠷𤠻é‡ææ´·¤æð´ ·¤æ Øæð» ãñ Ñ

is :

(

)

(1)

1 50 2 11 2

(

)

(2)

1 50 3 11 2

(3)

1 50 3 2

(4)

1 50 3 21 2

(1)

1 50 2 11 2

(2)

1 50 3 11 2

(3)

1 50 3 2

(4)

1 50 3 21 2

C/Page 9

(2)

55  2 11   3 3

12

of x in the binomial expansion of

(1 2 2 x )

(1)

10

The sum of coefficients of integral powers

11

1 22   3

( ) (

) SPACE FOR ROUGH WORK /

(

)

(

)

( ) (

)

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

x

·¤è Âê‡ææZ·¤èØ

24.

24.

The integral 4

log x 2

∫ log x 2 1 log (36 2 12 x 1 x 2 )

4

26.

2

is equal to :

ÕÚUæÕÚU ãñ Ñ

(1)

6

(1)

6

(2)

2

(2)

2

(3)

4

(3)

4

(4)

1

(4)

1

If the function.

25.

ØçΠȤÜÙ

 k x 1 1 , 0 [ x [ 3 g( x ) 5   m x 1 2 , 3 < x [ 5

 k x 1 1 , 0 [ x [ 3 g( x ) 5   m x 1 2 , 3 < x [ 5

is differentiable, then the value of k1m is :

¥ß·¤ÜÙèØ ãñ, Ìæð k1m ·¤æ ×æÙ ãñ Ñ

(1)

4

(1)

4

(2)

2

(2)

2

(3)

16 5

(3)

16 5

(4)

10 3

(4)

10 3

çÕ´Îé

(2, 3) ·ð¤

Locus of the image of the point (2, 3) in

26.

ÚðU¹æ

(2x23y14)1k (x22y13)50, k e R

the line (2x23y14)1k (x22y13)50, k e R, is a :

ÂýçÌçÕ´Õ ·¤æ çÕ´ÎéÂÍ °·¤ Ñ

(1)

(1) (2)

circle of radius

(3)

3. straight line parallel to x-axis. straight line parallel to y-axis.

(4)

circle of radius

(2)

27.

log x 2

∫ log x 2 1 log (36 2 12 x 1 x 2 ) d x

dx

2

25.

â×æ·¤Ü

lim

x→0

is equal to :

27.

lim

x→0

( 1 2 cos 2 x )( 3 1 cos x ) ÕÚUæÕÚU ãñ Ñ x tan 4 x

(2)

3

(3)

3

2

(4)

2

(2) (3) (4) C/Page 10

(4)

1 2 4

1 2 4

(1)

2.

( 1 2 cos 2 x )( 3 1 cos x ) x tan 4 x

(3)

ç˜æ’Øæ ·¤æ ßëžæ ãñÐ x-¥ÿæ ·ð¤ â×æ´ÌÚU ÚðU¹æ ãñÐ y-¥ÿæ ·ð¤ â×æ´ÌÚU ÚðU¹æ ãñÐ 2 ç˜æ’Øæ ·¤æ ßëžæ ãñÐ 3

(1)

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

×ð ´

28.

If the angles of elevation of the top of a

28.

tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 308, 458 and 608 respectively,

ÌèÙ â´ÚðU¹ çÕ´Îé¥æð´ A, B ÌÍæ C, °·¤ °ðâè ÚðU¹æ ÂÚU çSÍÌ ãñ´ Áæð °·¤ ×èÙæÚU ·ð¤ ÂæÎ ·¤è çÎàææ ×ð´ Üð ÁæÌè ãñ, âð °·¤ ×èÙæÚU ·ð¤ çàæ¹ÚU ·ð¤ ©‹ÙØÙ ·¤æð‡æ ·ý¤×àæÑ 308, 458 ÌÍæ 608 ãñ´, Ìæð AB : BC ·¤æ ¥ÙéÂæÌ ãñ Ñ

then the ratio, AB : BC, is : (1)

2:3

3:1

(2)

3:1

(3)

3: 2

(3)

3: 2

(4)

1: 3

1: 3

having at least three elements is :

×æÙæ A ÌÍæ B Îæð â×é‘¿Ø ãñ´ çÁÙ×ð´ ·ý¤×àæÑ ¿æÚU ÌÍæ Îæð ¥ßØß ãñ´, Ìæð â×é‘¿Ø A3B ·ð¤ ©Ù ©Ââ×鑿Øæð´ ·¤è ⴁØæ, çÁÙ×ð´ ÂýˆØð·¤ ×ð´ ·¤× âð ·¤× ÌèÙ ¥ßØß ãñ´, ãñ Ñ

(1)

510

(1)

510

(2)

219

(2)

219

(3)

256

(3)

256

(4)

275

(4)

275

Let A and B be two sets containing four

29.

and two elements respectively. Then the number of subsets of the set A3B, each

30.

2:3

(2)

(4) 29.

(1)

→ →

→

Let a , b and c be three non-zero vectors

30.

such that no two of them are collinear and →

→

→

( a 3 b )3 c 5

1 → → → b c a . If u is the 3 →

→

angle between vectors b and c , then a value of sin u is :

→ →

→

×æÙæ a , b ÌÍæ c ÌèÙ àæê‹ØðÌÚU °ðâð âçÎàæ ãñ´ ç·¤ ð Ùãè´ ã´ñ ÌÍæ ©Ù×ð´ âð ·¤æð§ü Îæð â´ ÚU¹ →

→

→

( a 3 b )3 c 5 →

→

ÌÍæ ×æÙ ãñ Ñ b

c

22 3 3

(1)

22 3 3

(2)

2 2 3

(2)

2 2 3

(3)

2 2 3

(3)

2 2 3

(4)

2 3

(4)

2 3

SPACE FOR ROUGH WORK /

ãñÐ ØçÎ âçÎàææð´

·ð¤ Õè¿ ·¤æ ·¤æð‡æ u ãñ, Ìæð sin u ·¤æ °·¤

(1)

C/Page 11

1 → → → b c a 3

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

Öæ» B — ÖæñçÌ·¤ çߙææÙ

PART B — PHYSICS 31.

31.

resistor is :

ÎàææüØð »Øð ÂçÚUÂÍ ×ð´ ãæð»è Ñ

(1)

0.13 A, from P to Q

(1)

0.13 A, P

âð Q ·¤æð

(2)

1.3 A, from P to Q

(2)

1.3 A, P

âð Q ·¤è ¥æðÚU

(3)

0A

(3)

0 (àæê‹Ø) A

(4)

0.13 A, from Q to P

(4)

0.13 A, Q

In the circuit shown, the current in the 1V

32.

Distance of the centre of mass of a solid

32.

uniform cone from its vertex is z0. If the radius of its base is R and its height is h then z0 is equal to :

3h 2 8R

(1)

3h 2 8R

(2)

h2 4R

(2)

h2 4R

(3)

3h 4

(3)

3h 4

(4)

5h 8

(4)

5h 8

SPACE FOR ROUGH WORK /

âð ÂýßæçãÌ ÏæÚUæ

âð P ·¤æð

ç·¤âè °·¤â×æÙ ÆUæðâ àæ´·é¤ ·ð¤ ÎýÃØ×æÙ ·ð¤‹Îý ·¤è ©â·ð¤ àæèáü âð ÎêÚUè z0 ãñÐ ØçÎ àæ´·é¤ ·ð¤ ¥æÏæÚU ·¤è ç˜æ’Øæ R ÌÍæ àæ´·é¤ ·¤è ª¡¤¿æ§ü h ãæð Ìæð z0 ·¤æ ×æÙ çِÙæ´ç·¤Ì ×ð´ âð ç·¤â·ð¤ ÕÚUæÕÚU ãæð»æ?

(1)

C/Page 12

1V ÂýçÌÚUæðÏ·¤

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

33.

Match List - I (Fundamental Experiment)

33.

with List - II (its conclusion) and select the correct option from the choices given

âê¿è - I (×êÜ ÂýØæð») ·¤æ âê¿è - II (©â·ð¤ ÂçÚU‡ææ×) ·ð¤ âæÍ âé×ðÜÙ (×ñ¿) ·¤èçÁØð ¥æñÚU çِÙæ´ç·¤Ì çß·¤ËÂæð´ ×ð´ âð âãè çß·¤Ë ·¤æ ¿ØÙ ·¤èçÁØð Ñ

below the list : List - I

34.

ÇÏ¤Í - I

List - II

(A)

Franck-Hertz Experiment.

(i)

Particle nature of light

(A) ­âՙ‰œ‰

(B)

Photo-electric experiment.

(ii)

Discrete energy levels of atom

(B)

§âœ‰ËÅË ÌÄlα §â½ËÕ 

(ii)

(C)

Wave nature of Davison - Germer (iii) electron Experiment.

(C)

¬ÕUÄÍǾ ¦¼á¿U §â½ËÕ 

(iii)

(iv)

Structure of atom

ȪÜáÇ §â½ËÕ 

(i)

(iv)

ÇÏ¤Í - II §âœ‰ËÅË œ‰Í œ‰Ìø˜‰Ë §âœÐ‰Ì± ŠøËÎ œÕ‰ ÌÄÌÄþ± ‰¦Ëá S±¿U ŒÁÕþªãUË×¾ œ‰Í ±¿™U  §âœÐ‰Ì± §¿U¼ËøËÎ œ‰Í Ǚ¿U¤¾Ë

(1)

(A) -(iv)

(B) - (iii)

(C) - (ii)

(1)

(A) -(iv)

(B) - (iii)

(C)- (ii)

(2)

(A) - (i)

(B) - (iv)

(C) - (iii)

(2)

(A) - (i)

(B) - (iv)

(C) - (iii)

(3)

(A) - (ii)

(B) - (iv)

(C) - (iii)

(3)

(A) - (ii)

(B) - (iv)

(C) - (iii)

(4)

(A) - (ii)

(B) - (i)

(C) - (iii)

(4)

(A) - (ii)

(B) - (i)

(C) - (iii)

The period of oscillation of a simple pendulum is T 5 2p

34.

L . Measured value g

of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist

ç·¤âè âÚUÜ ÜæðÜ·¤ ·¤æ ¥æßÌü, L

·¤æ ×æçÂÌ ×æÙ

20.0 cm

the determination of g is : (1)

5%

(1)

5%

(2)

2%

(2)

2%

(3)

3%

(3)

3%

(4)

1%

(4)

1%

SPACE FOR ROUGH WORK /

L g

ãñÐ

ãñ, çÁâ·¤è ØÍæÍüÌæ

ãñÐ §â ÜæðÜ·¤ ·ð¤ 100 ÎæðÜÙæð´ ·¤æ â×Ø 90 s ãñ, çÁâð 1s çßÖðÎÙ ·¤è ƒæǸè âð ÙæÂæ »Øæ ãñÐ Ìæð, g ·ð¤ çÙÏæüÚU‡æ ×ð´ ØÍæÍüÌæ ãæð»è Ñ 1 mm

watch of 1s resolution. The accuracy in

C/Page 13

T 5 2p

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

35.

the diode is :

°·¤ ÜæÜ Ú´U» ·¤æ °Ü.§ü.ÇUè. (Âý·¤æàæ ©ˆâÁü·¤ ÇUæØæðÇU) 0.1 ßæÅU ÂÚU, °·¤â×æÙ Âý·¤æàæ ©ˆâçÁüÌ ·¤ÚUÌæ ãñÐ ÇUæØæðÇU âð 1 m ÎêÚUè ÂÚU, §â Âý·¤æàæ ·ð¤ çßléÌ ÿæð˜æ ·¤æ ¥æØæ× ãæð»æ Ñ

(1)

7.75 V/m

(1)

7.75 V/m

(2)

1.73 V/m

(2)

1.73 V/m

(3)

2.45 V/m

(3)

2.45 V/m

(4)

5.48 V/m

(4)

5.48 V/m

A red LED emits light at 0.1 watt uniformly

35.

around it. The amplitude of the electric field of the light at a distance of 1 m from

36.

and are not to scale)

çÎØð »Øð ÂçÚUÂÍ ×ð´, C ·ð¤ ×æÙ ·ð¤ 1mF âð 3mF ÂçÚUßçÌüÌ ãæðÙð âð, 2mF â´ÏæçÚU˜æ ÂÚU ¥æßðàæ Q2 ×ð´ ÂçÚUßÌüÙ ãæðÌæ ãñÐ ‘C’ ·ð¤ ȤÜÙ ·ð¤ M¤Â ×ð´ Q2 ·¤æð ·¤æñÙ âæ ¥æÜð¹ âãè ÎàææüÌæ ãñ? (¥æÜð¹ ·ð¤ßÜ ÃØßSÍæ ¥æÚðU¹ ãñ´ ¥æñÚU S·ð¤Ü ·ð¤ ¥ÙéâæÚU Ùãè´ ãñ´Ð)

(1)

(1)

(2)

(2)

(3)

(3)

(4)

(4)

In the given circuit, charge Q2 on the 2mF capacitor changes as C is varied from 1mF

36.

to 3mF. Q2 as a function of ‘C’ is given properly by : (figures are drawn schematically

C/Page 14

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

37.

37.

Îæð ÂÌÜð ܐÕð ÌæÚUæð´ ×ð´ ÂýˆØð·¤ âð I ÏæÚUæ ÂýßæçãÌ ãæð ÚUãè ãñÐ §‹ãð´ L ܐÕæ§ü ·ð¤ çßléÌÚUæðÏè Ïæ»æð´ âð ÜÅU·¤æØæ »Øæ ãñÐ §Ù Ïæ»æð´ ×ð´ ÂýˆØð·¤ ·ð¤ mæÚUæ ª¤ŠßæüÏÚU çÎàææ âð ‘u’ ·¤æð‡æ ÕÙæÙð ·¤è çSÍçÌ ×ð´, Øð ÎæðÙæð´ ÌæÚU âæØæßSÍæ ×ð´ ÚUãÌð ãñ´Ð ØçÎ §Ù ÌæÚUæð´ ·¤è ÂýçÌ §·¤æ§ü ܐÕæ§ü ÎýÃØ×æÙ l ãñ ÌÍæ g »éL¤ˆßèØ ˆßÚU‡æ ãñ Ìæð, I ·¤æ ×æÙ ãæð»æ Ñ

Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle ‘u’ with the vertical. If wires have mass l per unit length then the value of I is : (g5gravitational acceleration)

plgL tan u m0

(1)

38.

(2)

sinu

(3)

2sinu

(4)

2

plgL m0 cosu plgL m0 cosu

pgL tan u m0

A particle of mass m moving in the

plgL tan u m0

(1)

38.

x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in

(2)

sinu

(3)

2sinu

(4)

2

x-çÎàææ

×ð´

plgL m0 cosu plgL m0 cosu

pgL tan u m0 2v ¿æÜ âð ¿ÜÌð ãé° m ÎýÃØ×æÙ ·ð¤ °·¤

·¤‡æ âð, y-çÎàææ ×ð´ v ßð» âð ¿ÜÌæ ãé¥æ 2m ÎýÃØ×æÙ ·¤æ °·¤ ·¤‡æ, ÅU·¤ÚUæÌæ ãñÐ ØçÎ Øã ⴃæÅ÷UÅU (ÅU€·¤ÚU) Âê‡æüÌÑ ¥ÂýˆØæSÍ ãñ Ìæð, ÅU€·¤ÚU ·ð¤ ÎæñÚUæÙ ª¤Áæü ·¤æ ÿæØ (ãæçÙ) ãæð»è Ñ

the energy during the collision is close to : (1)

62%

(1)

62%

(2)

44%

(2)

44%

(3)

50%

(3)

50%

(4)

56%

(4)

56%

C/Page 15

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

39.

39.

Øãæ¡ ¥æÚðU¹ ×ð´ Îæð ŽÜæò·¤ (»éÅU·ð¤) A ¥æñÚU B ÎàææüØð »Øð ãñ´ çÁÙ·ð¤ ÖæÚU ·ý¤×àæÑ 20 N ÌÍæ 100 N ãñ´Ð §‹ãð´, °·¤ ÕÜ F mæÚUæ ç·¤âè ÎèßæÚU ÂÚU ÎÕæØæ Áæ ÚUãæ ãñÐ ØçÎ ƒæáü‡æ »é‡ææ´·¤ ·¤æ ×æÙ, A ÌÍæ B ·ð¤ Õè¿ 0.1 ÌÍæ B ¥æñÚU ÎèßæÚU ·ð¤ Õè¿ 0.15 ãñ Ìæð, ÎèßæÚU mæÚUæ ŽÜæò·¤ B ÂÚU Ü»æ ÕÜ ãæð»æ Ñ

Given in the figure are two blocks A and B of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is :

40.

(1)

150 N

(1)

150 N

(2)

100 N

(2)

100 N

(3)

80 N

(3)

80 N

(4)

120 N

(4)

120 N

Consider an ideal gas confined in an

40.

isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between q

molecules increases as V , where V is the volume of the gas. The value of q is : Cp   g 5  Cv  

°·¤ ¥æÎàæü »ñ â ç·¤âè ՋΠ(â´ ß ë Ì ), çßØé € Ì (çßÜç»Ì) ·¤ÿæ ×ð´ âèç×Ì (ÚU¹è) ãñÐ §â »ñâ ×´ð´ L¤Î÷Ïæðc× ÂýâæÚU ãæðÙð ÂÚU, §â·ð¤ ¥‡æé¥æð´ ·ð¤ Õè¿ ÅU€·¤ÚU ·¤æ ¥æñâÌ ·¤æÜ (â×Ø) Vq ·ð¤ ¥ÙéâæÚU Õɸ ÁæÌæ ãñ, Áãæ¡ V »ñâ ·¤æ ¥æØÌÙ ãñÐ Ìæð q ·¤æ ×æÙ ãæð»æ : Cp   g 5  Cv  

(1)

g 21 2

(1)

g21 2

(2)

3g 1 5 6

(2)

3g 1 5 6

(3)

3g 2 5 6

(3)

3g 2 5 6

(4)

g 11 2

(4)

g11 2

C/Page 16

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

41.

figures below :

ÌÍæ 5 cm ÖéÁæ¥æ𴠷𤠰·¤ ¥æØÌæ·¤æÚU Üê (Âæàæ) âð °·¤ çßléÌ ÏæÚUæ, I 5 12 A, ÂýßæçãÌ ãæðU ÚUãè ãñÐ §â Âæàæ ·¤æð ¥æÚðU¹ ×ð´ ÎàææüØð »Øð ¥ÙéâæÚU çßçÖóæ ¥çÖçߋØæâæð´ (çSÍçÌØæð´) ×ð´ ÚU¹æ »Øæ ãñÐ

(a)

(a)

(b)

(b)

(c)

(c)

(d)

(d)

If there is a uniform magnetic field of

equilibrium and (ii) unstable equilibrium ?

ØçÎ ßãæ¡ 0.3 T ÌèßýÌæ ·¤æ ·¤æð§ü °·¤â×æÙ ¿éÕ·¤èØ ÿæð˜æ, ÏÙæˆ×·¤ z çÎàææ ×ð´ çßl×æÙ ãñ Ìæð, ÎàææüØð »Øð 緤⠥çÖçߋØæâ ×ð´, Øã Âæàæ (ÜêÂ) (i) SÍæØè â´ÌéÜÙ ÌÍæ (ii) ¥SÍæØè â´ÌéÜÙ ×ð´, ãæð»æ?

(1)

(b) and (c), respectively

(1)

·ý¤×àæÑ

(b) ÌÍæ (c) ×ð´

(2)

(a) and (b), respectively

(2)

·ý¤×àæÑ

(a) ÌÍæ (b) ×ð´

(3)

(a) and (c), respectively

(3)

·ý¤×àæÑ

(a) ÌÍæ (c) ×ð´

(4)

(b) and (d), respectively

(4)

·ý¤×àæÑ (b) ÌÍæ (d) ×ð´

A rectangular loop of sides 10 cm and

41.

5 cm carrying a current I of 12 A is placed in different orientations as shown in the

0.3 T in the positive z direction, in which orientations the loop would be in (i) stable

C/Page 17

SPACE FOR ROUGH WORK /

10 cm

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

42.

Consider a spherical shell of radius R at

42.

temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume

u5

U ; T4 V

and

ç·¤âè »æðÜèØ ·¤æðàæ (àæñÜ) ·¤è ç˜æ’Øæ R ãñ ¥æñÚU §â·¤æ Ìæ T ãñÐ §â·ð¤ ÖèÌÚU ·ë¤çc‡æ·¤æ çßç·¤ÚU‡ææð´ ·¤æð ȤæðÅUæòÙæð´ ·¤è °·¤ °ðâè ¥æÎàæü »ñâ ×æÙæ Áæ â·¤Ìæ ãñ çÁâ·¤è ÂýçÌ §·¤æ§ü ¥æØÌÙ ¥æ‹ÌçÚU·¤ ª¤Áæü,

pressure

ÌÍæ ÎæÕ,

1 U p 5   . If the shell now undergoes 3 V

p5

1 U   ãñÐ 3 V

u5

U ; T4 V

ØçÎ §â ·¤æðàæ ×ð´ L¤Î÷Ïæðc×

ÂýâæÚU ãæð Ìæð, T ÌÍæ R ·ð¤ Õè¿ â´Õ´Ï ãæð»æ Ñ

an adiabatic expansion the relation between T and R is :

43.

(1)

T;

(2)

1

1

(1)

T;

T ; e2R

(2)

T ; e2R

(3)

T ; e23R

(3)

T ; e23R

(4)

T;

(4)

T;

R

3

1 R

R3

1 R

hydrogen - like atom/ion :

ÁÕ ·¤æð§ü §Üð€ÅþUæòÙ, ãæ§ÇþUæðÁÙ Áñâð ÂÚU×æ‡æé /¥æØÙ ·¤è ©žæðçÁÌ ¥ßSÍæ âð ‹ØêÙÌ× ª¤Áæü ¥ßSÍæ ×ð´ â´·ý¤×‡æ ·¤ÚUÌæ ãñ Ìæð ©â·¤è Ñ

(1)

(1)

»çÌÁ ª¤Áæü ß ·é¤Ü ª¤Áæü ·¤× ãæð ÁæÌè ãñ´ ç·¤‹Ìé, çSÍçÌÁ ª¤Áæü Õɸ ÁæÌè ãñÐ

(2)

»çÌÁ ª¤Áæü ×ð´ ßëçh ÌÍæ çSÍçÌÁ ª¤Áæü ÌÍæ ·é¤Ü ª¤Áæü ×ð´ ·¤×è ãæðÌè ãñÐ

(3)

»çÌÁ ª¤Áæü, çSÍçÌÁ ª¤Áæü ÌÍæ ·é¤Ü ª¤Áæü ×ð´ ·¤×è ãæð ÁæÌè ãñÐ

(4)

»çÌÁ ª¤Áæü ·¤× ãæðÌè ãñ, çSÍçÌÁ ª¤Áæü ÕɸÌè ãñ ¥æñÚU ·é¤Ü ª¤Áæü ßãè ÚUãÌè ãñÐ

As an electron makes a transition from an

43.

excited state to the ground state of a

kinetic energy and total energy decrease but potential energy increases

(2)

its kinetic energy increases but potential energy and total energy decrease

(3)

kinetic energy, potential energy and total energy decrease

(4)

kinetic energy decreases, potential energy increases but total energy remains same

C/Page 18

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

44.

that as it travels, the light beam :

»ýèc× «¤Ìé ·¤è »×ü ÚUæç˜æ ×ð´, Öê-ÌÜ ·ð¤ çÙ·¤ÅU, ßæØé ·¤æ ¥ÂßÌüÙæ´·¤ ‹ØêÙÌ× ãæðÌæ ãñ ¥æñÚU Öê-ÌÜ â𠪡¤¿æ§ü ·ð¤ âæÍ ÕɸÌæ ÁæÌæ ãñÐ ØçÎ, ·¤æð§ü Âý·¤æàæ-ç·¤ÚU‡æ-´éÁ ÿæñçÌÁ çÎàææ ×ð´ Áæ ÚUãæ ãæð Ìæð, ã槻ð‹â ·ð¤ çâhæ‹Ì âð Øã ÂçÚU‡ææ× Âý æ ŒÌ ãæð Ì æ ãñ ç·¤, ¿ÜÌð ãé ° Âý·¤æàæ-ç·¤ÚU‡æ ´éÁ Ñ

(1)

bends upwards

(1)

ª¤ÂÚU ·¤è ¥æðÚU Ûæé·¤ ÁæØð»æÐ

(2)

becomes narrower

(2)

â´·é¤ç¿Ì (â´·¤è‡æü) ãæð ÁæØð»æÐ

(3)

goes horizontally without any

(3)

çÕÙæ çßÿæðçÂÌ ãé°, ÿæñçÌÁ çÎàææ ×ð´ ¿ÜÌæ ÚUã»ð æÐ

(4)

Ùè¿ð ·¤è ¥æðÚU Ûæé·¤ ÁæØð»æÐ

On a hot summer night, the refractive

44.

index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens’ principle leads us to conclude

deflection (4)

45.

bends downwards

From a solid sphere of mass M and radius R R, a spherical portion of radius is 2 removed, as shown in the figure. Taking

45.

gravitational potential V50 at r5:, the potential at the centre of the cavity thus formed is : (G5 gravitational constant)

°·¤ ÆUæðâ »æðÜð ·¤æ ÎýÃØ×æÙ R

2 2GM R

(1)

2 2GM R

(2)

2 GM 2R

(2)

2 GM 2R

(3)

2 GM R

(3)

2 GM R

(4)

2 2GM 3R

(4)

2 2GM 3R

SPACE FOR ROUGH WORK /

ÌÍæ ç˜æ’Øæ

R

ãñÐ

§ââð ç˜æ’Øæ ·¤æ °·¤ »æðÜèØ Öæ», ¥æÚðU¹ ×ð´ ÎàææüØð 2 »Øð ¥ÙéâæÚU ·¤æÅU çÜØæ ÁæÌæ ãñÐ r5:(¥Ù‹Ì) ÂÚU »éL¤ˆßèØ çßÖß ·ð¤ ×æÙ V ·¤æð àæê‹Ø (V50) ×æÙÌð ãé°, §â Âý·¤æÚU ÕÙð ·¤æðÅUÚU (·ñ¤çßÅUè) ·ð¤ ·ð¤‹Îý ÂÚU, »éL¤ˆßèØ çßÖß ·¤æ ×æÙ ãæð»æ Ñ (G5 »éL¤ˆßèØ çSÍÚUæ¡·¤ ãñ )

(1)

C/Page 19

M

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

46.

Monochromatic light is incident on a glass

46.

prism of angle A. If the refractive index of the material of the prism is m, a ray, incident at an angle u, on the face AB would get transmitted through the face AC

·¤æ¡¿ ·ð¤ ç·¤âè çÂý’× ·¤æ ·¤æð‡æ ‘A’ ãñÐ §â ÂÚU °·¤ß‡æèü Âý·¤æàæ ¥æÂçÌÌ ãæðÌæ ãñÐ ØçÎ, çÂý’× ·ð¤ ÂÎæÍü ·¤æ ¥ÂßÌüÙæ´·¤ m ãñ Ìæð, çÂý’× ·ð¤ AB Ȥܷ¤ ÂÚU, u ·¤æð‡æ ¥æÂçÌÌ Âý·¤æàæ ·¤è ç·¤ÚU‡æ, çÂý’× ·ð¤ Ȥܷ¤ AC âð ÂæÚU»Ì ãæð»è ØçÎ Ñ

of the prism provided :

(1)

   1   u < cos21 m sin  A 1 sin21      m     

(1)

   1   u < cos21 m sin  A 1 sin21      m     

(2)

   1   u > sin21 m sin  A 2 sin21      m     

(2)

   1   u > sin21 m sin  A 2 sin21      m     

(3)

   1   u < sin21 m sin  A 2 sin21      m     

(3)

   1   u < sin21 m sin  A 2 sin21       m    

(4)

   1   u > cos21 m sin  A 1 sin21      m     

(4)

   1   u > cos21 m sin  A 1 sin21      m     

C/Page 20

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

47.

Two stones are thrown up simultaneously

47.

from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with

ç·¤âè 240 m ª¡¤¿è ¿æðÅUè ·ð¤ °·¤ ç·¤ÙæÚðU âð, Îæð ˆÍÚUæð´ ·¤æð °·¤âæÍ ª¤ÂÚU ·¤è ¥æðÚU Èð´¤·¤æ »Øæ ãñ, §Ù·¤è ÂýæÚ´UçÖ·¤ ¿æÜ ·ý¤×àæÑ 10 m/s ÌÍæ 40 m/s ãñ, Ìæð, çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙâæ »ýæȤ (¥æÜð¹) ÂãÜð ˆÍÚU ·ð¤ âæÂðÿæ ÎêâÚðU ˆÍÚU ·¤è çSÍçÌ ·ð¤ â×Ø çß¿ÚU‡æ (ÂçÚUßÌüÙ) ·¤æð âßæüçÏ·¤ âãè ÎàææüÌæ ãñ?

respect to the first ? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g510 m/s2)

(×æÙ ÜèçÁ° ç·¤, ˆÍÚU Á×èÙ âð ÅU·¤ÚUæÙð ·ð¤ Âà¿æÌ ª¤ÂÚU ·¤è ¥æðÚU Ùãè´ ©ÀUÜÌð ãñ´ ÌÍæ ßæØé ·¤æ ÂýçÌÚUæðÏ Ù»‡Ø ãñ, çÎØæ ãñ g510 m/s2)

scale)

(Øãæ¡ »ýæȤ ·ð¤ßÜ ÃØßSÍæ ¥æÚðU¹ ãñ´ ¥æñÚU S·ð¤Ü ·ð¤ ¥ÙéâæÚU Ùãè´ ãñ´)

(1)

(1)

(2)

(2)

(3)

(3)

(4)

(4)

(The figures are schematic and not drawn to

C/Page 21

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

48.

(graphs are schematic and not drawn to scale)

ç·¤âè âÚUÜ ÜæðÜ·¤ ·ð¤ çÜØð, ©â·ð¤ çßSÍæÂÙ d ÌÍæ ©â·¤è »çÌÁ ª¤Áæü ·ð¤ Õè¿ ¥æñÚU çßSÍæÂÙ d ÌÍæ ©â·¤è çSÍçÌÁ ª¤Áæü ·ð¤ Õè¿ »ýæȤ ¹è´¿ð »Øð ãñ´Ð çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙ âæ »ýæȤ (¥æÜð¹) âãè ãñ? (Øãæ¡ »ýæȤ ·ð¤ßÜ ÃØßSÍæ ¥æÚðU¹ ãñ´ ¥æñÚU S·ð¤Ü ·ð¤ ¥ÙéâæÚU Ùãè´ ãñ´)

(1)

(1)

(2)

(2)

(3)

(3)

(4)

(4)

For a simple pendulum, a graph is plotted

48.

between its kinetic energy (KE) and potential

energy

(PE)

against

its

displacement d. Which one of the following represents these correctly ?

49.

A train is moving on a straight track with

49.

speed 20 ms21. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound5320 ms21) close to :

°·¤ ÅþðUÙ (ÚðUÜ»æǸè) âèÏè ÂÅUçÚUØæð´ ÂÚU 20 ms21 ·¤è ¿æÜ âð »çÌ ·¤ÚU ÚUãè ãñÐ §â·¤è âèÅUè ·¤è ŠßçÙ ·¤è ¥æßëçžæ 1000 Hz ãñÐ ØçÎ ŠßçÙ ·¤è ßæØé ×ð´ ¿æÜ 320 ms21 ãæð Ìæð, ÂÅUçÚUØæð´ ·ð¤ çÙ·¤ÅU ¹Ç¸ð ÃØç€Ì ·ð¤ Âæâ âð ÅþðUÙ ·ð¤ »éÁÚUÙð ÂÚU, ©â ÃØç€Ì mæÚUæ âéÙè »§ü âèÅUè ·¤è ŠßçÙ ·¤è ¥æßëçžæ ×ð´ ÂýçÌàæÌ ÂçÚUßÌüÙ ãæð»æ ֻܻ Ñ

(1)

24%

(1)

24%

(2)

6%

(2)

6%

(3)

12%

(3)

12%

(4)

18%

(4)

18%

C/Page 22

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

50.

An LCR circuit is equivalent to a damped

50.

pendulum. In an LCR circuit the capacitor is charged to Q0 and then connected to the L and R as shown below :

If a student plots graphs of the square of

2 maximum charge ( QMax ) on the capacitor

with time(t) for two different values L1 and

L2 (L1>L2) of L then which of the following

represents this graph correctly ? (plots are schematic and not drawn to scale)

(1)

·ð¤ ÌéËØ ãæðÌæ ãñÐ ç·¤âè LCR ÂçÚUÂÍ ×ð´ â´ÏæçÚU˜æ ·¤æð Q0 Ì·¤ ¥æßðçàæÌ ç·¤Øæ »Øæ ãñ, ¥æñÚU çȤÚU §âð ¥æÚðU¹ ×ð´ ÎàææüØð »Øð ¥ÙéâæÚU L ß R âð ÁæðÇ¸æ »Øæ ãñÐ

ØçÎ °·¤ çßlæÍèü L ·ð¤, Îæð çßçÖóæ ×æÙæð´, L1 ÌÍæ L2 (L 1 >L 2 ) ·ð ¤ çÜØð , â×Ø t ÌÍæ â´ Ï æçÚU ˜ æ ÂÚU 2 ¥çÏ·¤Ì× ¥æßðàæ ·ð¤ ß»ü QMax ·ð¤ Õè¿ Îæð »ýæȤ ÕÙæÌæ ãñ Ìæð çِÙæ´ç·¤Ì ×ð´ âð ·¤æñÙ âæ »ýæȤ âãè ãñ? (ŒÜæòÅU ·ð¤ßÜ ÃØßSÍæ ŒÜæòÅU ãñ´ ÌÍæ S·ð¤Ü ·ð¤ ¥ÙéâæÚU Ùãè´ ãñ´)

(1)

(2)

(2)

(3)

(3)

(4)

C/Page 23

LCR (°Ü.âè.¥æÚU) ÂçÚUÂÍ ç·¤âè ¥ß×´çÎÌ ÜæðÜ·¤

(4)

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

51.

A solid body of constant heat capacity

51.

1 J/8C is being heated by keeping it in contact with reservoirs in two ways : (i)

Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat.

(ii)

Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat.

In both the cases body is brought from initial temperature 1008C to final temperature 2008C. Entropy change of the

°·¤ ÆUæðâ ç´ÇU (ßSÌé) ·¤è çSÍÚU ª¤c×æ ÏæçÚUÌæ 1 J/8C ãñÐ §â·¤æ𠪤c×·¤æð´ (ª¤c×æ Ö´ÇUæÚUæð´) ·ð¤ âÂ·ü¤ ×ð´ ÚU¹·¤ÚU çِ٠Îæð Âý·¤æÚU âð »×ü ç·¤Øæ ÁæÌæ ãñ, (i) ¥Ùé·ý¤ç×·¤ M¤Â âð 2 ª¤c×·¤æð´ ·ð¤ âÂ·ü¤ ×ð´ §â Âý·¤æÚU ÚU¹·¤ÚU ç·¤ ÂýˆØð·¤ ª¤c×·¤ â×æÙ ×æ˜ææ ×ð´ ª¤c×æ ÎðÌæ ãñ, (ii) ¥Ùé·ý¤ç×·¤ M¤Â âð 8 ª¤c×·¤æð´ ·ð¤ âÂ·ü¤ ×ð´ §â Âý·¤æÚU ÚU¹·¤ÚU ç·¤ ÂýˆØð·¤ ª¤c×·¤ â×æÙ ×æ˜ææ ×ð´ ª¤c×æ ÎðÌæ ãñ, ÎæðÙæð´ çSÍçÌØæð´ ×ð´ ç´ÇU ·¤æ ÂýæÚ´UçÖ·¤ Ìæ 1008C ÌÍæ ¥ç‹Ì× Ìæ 2008C ãñÐ Ìæð, §Ù Îæð çSÍçÌØæð´ ×ð´ ç´ÇU ·¤è °‹ÅþUæòÂè ×ð´ ÂçÚUßÌüÙ ãæð»æ, ·ý¤×àæÑ

body in the two cases respectively is :

52.

(1)

2ln2, 8ln2

(1)

2ln2, 8ln2

(2)

ln2, 4ln2

(2)

ln2, 4ln2

(3)

ln2, ln2

(3)

ln2, ln2

(4)

ln2, 2ln2

(4)

ln2, 2ln2

An inductor (L50.03H) and a resistor

52.

(R50.15 kV) are connected in series to a battery of 15V EMF in a circuit shown below. The key K1 has been kept closed for a long time. Then at t50, K1 is opened

and key K 2 is closed simultaneously. At t51ms, the current in the circuit will be : (e5@150)

ÎàææüØð »Øð ÂçÚUÂÍ ×ð´, °·¤ ÂýðÚU·¤ (L50.03H) ÌÍæ °·¤ ÂýçÌÚUæðÏ·¤ (R50.15 kV) ç·¤âè 15V çßléÌ ßæã·¤ ÕÜ (§ü.°×.°È¤) ·¤è ÕñÅUÚUè âð ÁéǸð ãñ´Ð ·é´¤Áè K1 ·¤æð ÕãéÌ â×Ø Ì·¤ ՋΠÚU¹æ »Øæ ãñÐ §â·ð¤ Âà¿æÌ÷ â×Ø t50 ÂÚU, K1 ·¤æð ¹æðÜ ·¤ÚU âæÍ ãè âæÍ, K2 ·¤æð ՋΠ緤Øæ ÁæÌæ ãñÐ â×Ø t51ms ÂÚU, ÂçÚUÂÍ ×ð´ çßléÌ ÏæÚUæ ãæð»è Ñ (e5@150)

(1)

0.67 mA

(1)

0.67 mA

(2)

100 mA

(2)

100 mA

(3)

67 mA

(3)

67 mA

(4)

6.7 mA

(4)

6.7 mA

C/Page 24

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

53.

R has potential V0 (measured with respect

·ð¤ ç·¤âè °·¤â×æÙ ¥æßðçàæÌ ÆUæðâ »æðÜð ·ð¤ ÂëcÆU ·¤æ çßÖß V0 ãñ (: ·ð¤ âæÂðÿæ ×æÂæ »Øæ)Ð §â

equipotential surfaces with potentials

»æðÜð ·ð¤ çÜØð,

A uniformly charged solid sphere of radius

53.

to :) on its surface. For this sphere the

3V0 5V0 3V0 , , 2 4 4

ÌÍæ

V0 4

çßÖßæð´

V 3V0 5V0 3V0 and 0 have radius R1, , , 4 2 4 4 R2, R3 and R4 respectively. Then

ßæÜð â×çßÖßè Âë c ÆU æ ð ´ ·¤è ç˜æ’ØæØð ´ , ·ý ¤ ×àæÑ R1, R2, R3 ÌÍæ R4 ãñ´Ð Ìæð,

(1)

(1)

(2) (3) (4) 54.

R ç˜æ’Øæ

2R < R4 R150 and R2 > (R42R3) R1 ¹ 0 and (R22R1) > (R42R3)

(2) (3) (4)

R150 and R2 < (R42R3)

A long cylindrical shell carries positive

54.

surface charge s in the upper half and negative surface charge 2s in the lower half. The electric field lines around the cylinder will look like figure given in : (figures are schematic and not drawn to scale)

(1)

(2)

(2)

(3)

(3)

(4)

(4)

SPACE FOR ROUGH WORK /

R150

ÌÍæ R2 < (R42R3)

ç·¤âè ܐÕð ÕðÜÙæ·¤æÚU ·¤æðàæ ·ð¤ ª¤ÂÚUè Öæ» ×ð´ ÏÙæˆ×·¤ ÂëcÆU ¥æßðàæ s ÌÍæ çÙ¿Üð Öæ» ×ð´ «¤‡ææˆ×·¤ ÂëcÆU ¥æßðàæ 2s ãñ´Ð §â ÕðÜÙ (çâç܋ÇUÚU) ·ð¤ ¿æÚUæð´ ¥æðÚU çßléÌ ÿæð˜æ-ÚðU¹æØð´, Øãæ¡ ÎàææüØð »Øð ¥æÚð¹æð´ ×ð´ âð 緤⠥æÚðU¹ ·ð¤ â×æÙ ãæð´»è? (Øã ¥æÚðU¹ ·ð¤ßÜ ÃØßSÍæ ¥æÚðU¹ ãñ ¥æñÚU S·ð¤Ü ·ð¤ ¥ÙéâæÚU Ùãè´ ãñ)

(1)

C/Page 25

2R < R4 R150 ÌÍæ R2 > (R42R3) R1 ¹ 0 ÌÍæ (R22R1) > (R42R3)

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

55.

resolve at 500 nm wavelength is :

ØçÎ ×æÙß Ùð˜æ ·¤è ÂéÌÜè ·¤è ç˜æ’Øæ 0.25 cm, ¥æñÚU SÂcÅU âéçßÏæ ÁÙ·¤ Îð¹Ùð ·¤è ÎêÚUè 25 cm ãæð Ìæð, 500 nm ÌÚ´U»ÎñƒØü ·ð¤ Âý·¤æàæ ×ð´, Îæð ßSÌé¥æð´ ·ð¤ Õè¿ ç·¤ÌÙè ‹ØêÙÌ× ÎêÚUè Ì·¤ ×æÙß Ùð˜æ ©Ù ÎæðÙæð´ ·ð¤ Õè¿ çßÖðÎÙ ·¤ÚU â·ð¤»æ?

(1)

300 mm

(1)

300 mm

(2)

1 mm

(2)

1 mm

(3)

30 mm

(3)

30 mm

(4)

100 mm

(4)

100 mm

Assuming human pupil to have a radius

55.

of 0.25 cm and a comfortable viewing distance of 25 cm, the minimum separation between two objects that human eye can

56.

signal is/are :

¥æßëçžæ ·ð¤ ç·¤âè â´·ð¤Ì (çâ‚ÙÜ) ·¤æ 2 MHz ¥æßëçžæ ·¤è ßæã·¤ ÌÚ´U» ÂÚU ¥æØæ× ×æòÇéUÜÙ ç·¤Øæ »Øæ ãñÐ Ìæð, ÂçÚU‡ææ×è çâ‚ÙÜ (â´·ð¤Ì) ·¤è ¥æßëçžæ ãæð»è Ñ

(1)

2000 kHz and 1995 kHz

(1)

2000 kHz

(2)

2 MHz only

(2)

2 MHz

(3)

2005 kHz, and 1995 kHz

(3)

2005 kHz,

(4)

2005 kHz, 2000 kHz and 1995 kHz

(4)

2005 kHz, 2000 kHz

A signal of 5 kHz frequency is amplitude

56.

modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant

C/Page 26

SPACE FOR ROUGH WORK /

5 kHz

ÌÍæ 1995 kHz

·ð¤ßÜ ÌÍæ 1995 kHz

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

ÌÍæ 1995 kHz

57.

Two coaxial solenoids of different radii

57.

carry current I in the same direction. Let →

F1

be the magnetic force on the inner → F2

solenoid due to the outer one and

Îæð â×æÿæè ÂçÚUÙæçÜ·¤æ¥æð´ ×ð´, ÂýˆØð·¤ âð I ÏæÚUæ °·¤ ãè çÎàææ ×ð´ ÂýßæçãÌ ãæð ÚUãè ãñÐ ØçÎ, ÕæãÚUè ÂçÚUÙæçÜ·¤æ ·ð¤ ·¤æÚU‡æ, ÖèÌÚUè ÂçÚUÙæçÜ·¤æ ÂÚU ¿éÕ·¤èØ ÕÜ →

F1

be

ÌÍæ ÖèÌÚUè ÂçÚUÙæçÜ·¤æ ·ð¤ ·¤æÚU‡æ, ÕæãÚUè ÂçÚUÙæçÜ·¤æ

ÂÚU ¿éÕ·¤èØ ÕÜ

the magnetic force on the outer solenoid

→

ãæð Ìæð Ñ

F2

due to the inner one. Then : →

→

(1)

F1 is radially outwards and F2 50

(2)

F1 5 F25 0

(3)

F1 is radially inwards and F2 is

→

(1)

→

→

→

58.

→

F1

A pendulum made of a uniform wire of

(4) 58.

cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to TM. If the Young’s modulus of the material of the 1 is equal to : Y (g5gravitational acceleration)

wire is Y then

(2)

 TM   T

2  A  1 2     Mg

(3)

 TM   T

2  Mg   21   A

(4)

 T 1 2  M  T 

C/Page 27

  

A   Mg 

2

A  Mg 

SPACE FOR ROUGH WORK /

→

F1

ãñÐ

ÖèÌÚU ·¤è ¥æðÚU ß ¥ÚUèØ (ç˜æ’Ø) ãñ ¥æñÚU ÕæãÚU ·¤è ¥æðÚU ß ¥ÚUèØ ãñÐ ÖèÌÚU ·¤è ¥æðÚU ß ¥ÚUèØ ãñ ÌÍæ

→

F2 50

ç·¤âè °·¤â×æÙ ÌæÚU ·¤è ¥ÙéÂýSÍ·¤æÅU ·¤æ ÿæð˜æÈ¤Ü ‘A’ ãñÐ §ââð ÕÙæØð »Øð °·¤ ÜæðÜ·¤ ·¤æ ¥æßÌü·¤æÜ T ãñÐ §â ÜæðÜ·¤ ·ð¤ »æðÜ·¤ âð °·¤ ¥çÌçÚU€Ì M ÎýÃØ×æÙ ÁæðǸ ÎðÙð âð ÜæðÜ·¤ ·¤æ ¥æßÌü·¤æÜ ÂçÚUßçÌüÌ ãæð·¤ÚU TM ãæð ÁæÌæ ãñÐ ØçÎ §â ÌæÚU ·ð¤ ÂÎæÍü ·¤æ Ø´» »é‡ææ´·¤ ‘Y’ ãæð Ìæð (g5»éL¤ˆßèØ

2

(1)

→

→

F2 50

→

(3)

→

→

  

→

F1 5 F25 0

F2

F1 is radially inwards and F2 50

  T 1 2    TM 

ãñÐ

ÕæãÚU ·¤è ¥æðÚU ß ¥ÚUèØ ãñ ÌÍæ

(2)

radially outwards (4)

→

F1

1 Y

·¤æ ×æÙ ãæð»æ Ñ

ˆßÚU‡æ) 2

(1)

  T 1 2    TM 

(2)

 TM   T

2  A   21    Mg

(3)

 TM   T

2  Mg   21    A

(4)

 T 1 2  M  T 

  

  

A  Mg  

2

A   Mg

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

59.

From a solid sphere of mass M and radius

59.

R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is :

60.

ç·¤âè ÆUæðâ »æðÜð ·¤æ ÎýÃØ×æÙ M ÌÍæ §â·¤è ç˜æ’Øæ R ãñÐ §â×ð´ âð ¥çÏ·¤Ì× â´Öß ¥æØÌÙ ·¤æ °·¤ €ØêÕ (ƒæÙ) ·¤æÅU çÜØæ ÁæÌæ ãñÐ §â €ØêÕ ·¤æ ÁǸˆß ¥æƒæê‡æü ç·¤ÌÙæ ãæð»æ, ØçÎ, §â·¤è ƒæê‡æüÙ-¥ÿæ, §â·ð¤ ·ð¤‹Îý âð ãæð·¤ÚU »é$ÁÚUÌè ãñ ÌÍæ §â·ð¤ ç·¤âè °·¤ Ȥܷ¤ ·ð¤ ܐÕßÌ÷U ãñ?

(1)

4MR 2 3 3p

(1)

4MR 2 3 3p

(2)

MR 2 32 2p

(2)

MR 2 32 2p

(3)

MR 2 16 2p

(3)

MR 2 16 2p

(4)

4MR 2 9 3p

(4)

4MR 2 9 3p

When 5V potential difference is applied

60.

across a wire of length 0.1 m, the drift speed of electrons is 2.531024 ms21. If the electron density in the wire is 831028 m23, the resistivity of the material

0.1 m Ü´Õð

ç·¤âè ÌæÚU ·ð¤ çâÚUæð´ ·ð¤ Õè¿ 5V çßÖßæ´ÌÚUU ¥æÚUæðçÂÌ ·¤ÚUÙð âð §Üð€ÅþUæòÙæð´ ·¤è ¥Âßæã ¿æÜ 2.531024 ms21 ãæðÌè ãñÐ ØçÎ §â ÌæÚU ×ð´ §Üð€ÅþUæòÙ ƒæÙˆß 831028 m23 ãæð Ìæð, §â ·ð¤ ÂÎæÍü ·¤è ÂýçÌÚUæðÏ·¤Ìæ ãæð»è, ֻܻ Ñ

is close to : (1)

1.631025 Vm

(1)

1.631025 Vm

(2)

1.631028 Vm

(2)

1.631028 Vm

(3)

1.631027 Vm

(3)

1.631027 Vm

(4)

1.631026 Vm

(4)

1.631026 Vm

C/Page 28

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

Öæ» C — ÚUâæØÙ çߙææÙ

PART C — CHEMISTRY 61.

The vapour pressure of acetone at 208C is

61.

185 torr. When 1.2 g of a non-volatile substance was dissolved in 100 g of acetone at 208C, its vapour pressure was 183 torr. The molar mass (g mol21) of the substance

208C ÂÚU

°ðçâÅUæðÙ ·¤è ßæc ÎæÕ 185 torr ãñÐ ÁÕ 208C ÂÚU, 1.2 g ¥ßæcÂàæèÜ ÂÎæÍü ·¤æð 100 g °ðçâÅUæðÙ ×𴠃ææðÜæ »Øæ, ÌÕ ßæc ÎæÕ 183 torr ãæð »ØæÐ §â ÂÎæÍü ·¤æ ×æðÜÚU ÎýÃØ×æÙ (g mol21 ×ð´) ãñ Ñ

is :

62.

(1)

488

(1)

488

(2)

32

(2)

32

(3)

64

(3)

64

(4)

128

(4)

128

adsorbed (per gram of charcoal) is :

°·¤ ÜæS·¤ ×ð´ 0.06N °çâçÅU·¤ ¥Ü ·ð¤ 50 mL çßÜØÙ ×ð´ 3 g âç·ý¤çØÌ÷ ·¤æcÆU ·¤æðØÜæ ç×ÜæØæ »ØæÐ °·¤ ƒæ´ÅðU ·ð¤ Âà¿æÌ÷ ©âð ÀUæÙæ »Øæ ¥æñÚU çÙSØ´Î ·¤è ÂýÕÜÌæ 0.042 N Âæ§ü »§üÐ ¥çÏàææðçáÌ °çâçÅU·¤ ¥Ü ·¤è ×æ˜ææ (·¤æcÆU-·¤æðØÜæ ·ð¤ ÂýçÌ »ýæ× ÂÚU) ãñ Ñ

(1)

54 mg

(1)

54 mg

(2)

18 mg

(2)

18 mg

(3)

36 mg

(3)

36 mg

(4)

42 mg

(4)

42 mg

3 g of activated charcoal was added to

62.

50 mL of acetic acid solution (0.06N) in a flask. After an hour it was filtered and the strength of the filtrate was found to be 0.042 N.

63.

64.

The amount of acetic acid

possible excited state of hydrogen ?

çِÙçÜç¹Ì ×ð´ âð ãæ§üÇþUæðÁÙ ·¤è â´Öß ©žæðçÁÌ ¥ßSÍæ ·¤è ª¤Áæü ·¤æñÙ âè ãñ?

(1)

16.8 eV

(1)

16.8 eV

(2)

113.6 eV

(2)

113.6 eV

(3)

26.8 eV

(3)

26.8 eV

(4)

23.4 eV

(4)

23.4 eV

Which of the following is the energy of a

Which among the following is the most

63.

64.

çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ âßæüçÏ·¤ ¥çÖç·ý¤ØæàæèÜ ãñ?

reactive ? (1)

ICl

(1)

ICl

(2)

Cl2

(2)

Cl2

I2

(4)

(3) (4) C/Page 29

Br2

(3)

SPACE FOR ROUGH WORK /

Br2 I2

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

65.

66.

of paints and lacquers ?

ç·¤â ÕãéÜ·¤ ·¤æ ©ÂØæð» ÂýÜð ¥æñÚU ÂýÜæÿæ ÕÙæÙð ×ð´ ãæðÌæ ãñ?

(1)

Poly vinyl chloride

(1)

ÂæòçÜ ßæ§çÙÜ €ÜæðÚUæ§ÇU

(2)

Bakelite

(2)

Õð·ð¤Üæ§ÅU

(3)

Glyptal

(3)

ç‚ÜŒÅUæÜ

(4)

Polypropene

(4)

ÂæòçÜÂýæðÂèÙ

Which polymer is used in the manufacture

The molecular formula of a commercial

65.

66.

resin used for exchanging ions in water softening is C8H7SO3Na (Mol. wt. 206). What would be the maximum uptake of Ca21 ions by the resin when expressed in

°·¤ ßæç‡æ’Ø ÚðUç$ÁÙ ·¤æ ¥æç‡ß·¤ âê˜æ C8H7SO3Na ãñ (¥æç‡ß·¤ ÖæÚU = 206) §â ÚðUç$ÁÙ ·¤è Ca21 ¥æØÙ ·¤è ¥çÏ·¤Ì× ¥´Ì»ýüã‡æ ÿæ×Ìæ (×æðÜ ÂýçÌ »ýæ× ÚðUç$ÁÙ) €Øæ ãñ?

mole per gram resin ?

67.

(1)

1 412

(1)

1 412

(2)

1 103

(2)

1 103

(3)

1 206

(3)

1 206

(4)

2 309

(4)

2 309

In Carius method of estimation of

67.

halogens, 250 mg of an organic compound gave 141 mg of AgBr. The percentage of bromine in the compound is :

ãñÜæðÁÙ ·ð¤ ¥æ·¤ÜÙ ·¤è ·ñ¤çÚU¥â çßçÏ ×ð´ 250 mg ·¤æÕüçÙ·¤ Øæñç»·¤ 141 mg AgBr ÎðÌæ ãñÐ Øæñç»·¤ ×ð´ Õýæð×èÙ ·¤è ÂýçÌàæÌÌæ ãñ : (ÂÚU×æç‡ß·¤ ÎýÃØ×æÙ Ag5108; Br580)

(at. mass Ag5108; Br580) (1)

60

(1)

60

(2)

24

(2)

24

(3)

36

(3)

36

(4)

48

(4)

48

C/Page 30

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

68.

Assertion : Nitrogen and Oxygen are the

68.

main components in the atmosphere but these do not

¥çÖ·¤ÍÙ Ñ Ùæ§ÅþUæðÁÙ ¥æñÚU ¥æò€âèÁÙ ßæÌæßÚU‡æ ·ð¤ ×éØ ƒæÅU·¤ ãñ´ ÂÚU‹Ìé Øã ç·ý¤Øæ ·¤ÚU·ð¤ Ùæ§ÅþUæðÁÙ ·ð¤ ¥æò€âæ§ÇU Ùãè´ ÕÙæÌðÐ

react to form oxides of nitrogen. Reason :

Ì·ü¤ Ñ

The reaction between nitrogen and oxygen requires high temperature.

(1)

Both the assertion and reason are

Ùæ§ÅþUæðÁÙ ¥æñÚU ¥æò€âèÁÙ ·ð¤ Õè¿ ¥çÖç·ý ¤ Øæ ·ð ¤ çÜ° ©“æ Ìæ ·¤è ¥æßàØ·¤Ìæ ãñÐ

(1)

¥çÖ·¤ÍÙ ß Ì·ü¤ ÎæðÙæð´ »ÜÌ ãñ´Ð

(2)

¥çÖ·¤ÍÙ ¥æñÚU Ì·ü¤ ÎæðÙæð´ âãè ãñ´ ¥æñÚU Ì·ü¤ ¥çÖ·¤ÍÙ ·¤æ âãè SÂcÅUè·¤ÚU‡æ ãñÐ

(3)

¥çÖ·¤ÍÙ ¥æñÚU Ì·ü¤ ÎæðÙæð´ âãè ãñ´ ÂÚU‹Ìé Ì·ü¤ ¥çÖ·¤ÍÙ ·¤æ âãè SÂcÅUè·¤ÚU‡æ Ùãè´ ãñÐ

(4)

¥çÖ·¤ÍÙ »ÜÌ ãñ ÂÚU‹Ìé Ì·ü¤ âãè ãñÐ

incorrect (2)

Both assertion and reason are correct, and the reason is the correct explanation for the assertion

(3)

Both assertion and reason are correct, but the reason is not the correct explanation for the assertion

(4)

The assertion is incorrect, but the reason is correct

69.

The following reaction is performed at

69.

çِÙçÜç¹Ì ¥çÖç·ý¤Øæ ·¤æð 298 K ÂÚU ç·¤Øæ »ØæÐ

298 K.

2NO(g) 1 O 2 (g) ì 2NO 2 (g) The standard free energy of formation of NO(g) is 86.6 kJ/mol at 298 K. What is the standard free energy of formation of NO2(g) at 298 K? (Kp51.631012)

2NO(g) 1 O 2 (g) ì 2NO 2 (g) 298 K ÂÚU NO(g) ·ð¤

â´ÖßÙ ·¤è ×æÙ·¤ ×é€Ì ª¤Áæü 86.6 kJ/mol ãñÐ 298 K ÂÚU NO2(g) ·¤è ×æÙ·¤ ×é€Ì ª¤Áæü €Øæ ãñ? (Kp51.631012)

(1)

0.5[2386,6002R(298) ln(1.631012)]

(1)

0.5[2386,6002R(298) ln(1.631012)]

(2)

R(298) ln(1.6310 12)286600

(2)

R(298) ln(1.631012)286600

(3)

866001R(298) ln(1.6310 12)

(3)

866001R(298) ln(1.631012)

(4)

86600 2

(4)

86600 2

C/Page 31

ln (1.6 3 1012 ) R (298) SPACE FOR ROUGH WORK /

ln (1.6 3 1012 ) R (298)

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

70.

greater than its lattice enthalpy ?

çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ âð ÿææÚUèØ ×ëÎæ ÏæÌé âËÈð¤ÅU ·¤è ÁÜØæðÁÙ °ð‹ÍæËÂè ©â·ð¤ ÁæÜ·¤ °ð‹ÍæËÂè âð ¥çÏ·¤ ãñ?

(1)

SrSO 4

(1)

SrSO 4

(2)

CaSO 4

(2)

CaSO 4

(3)

BeSO4

(3)

BeSO4

(4)

BaSO4

(4)

BaSO4

Which one of the following alkaline earth

70.

metal sulphates has its hydration enthalpy

71.

72.

73.

exist for square planar [Pt (Cl) (py) (NH3)

(NH2OH)]1 is (py 5 pyridine) :

ß»ü â×ÌÜèØ [Pt (Cl) (py) (NH3) (NH2OH)]1 (py 5 pyridine) ·ð¤ ’Øæç×ÌèØ â×æßØçßØæð´ ·¤è ⴁØæ ãñ Ñ

(1)

6

(1)

6

(2)

2

(2)

2

(3)

3

(3)

3

(4)

4

(4)

4

The number of geometric isomers that can

71.

accomplished by :

¥Ë·¤æ§Ü ÜæðÚUæ§ÇU ·ð¤ â´àÜðá‡æ ·ð¤ çÜ° âÕâð ÕðãÌÚUèÙ çßçÏ ãñ Ñ

(1)

Swarts reaction

(1)

SßæÅüUâ ¥çÖç·ý¤Øæ

(2)

Free radical fluorination

(2)

×é€Ì ×êÜ·¤ ÜæðçÚUÙðàæÙ

(3)

Sandmeyer’s reaction

(3)

âñ‹ÇU×æØÚU ¥çÖç·ý¤Øæ

(4)

Finkelstein reaction

(4)

çÈ´¤·¤ÜSÅUæ§Ù ¥çÖç·ý¤Øæ

The synthesis of alkyl fluorides is best

The intermolecular interaction that is

72.

73.

dependent on the inverse cube of distance

ßã ¥´ÌÚUæ-¥‡æé·¤ ¥‹Øæð‹Ø ç·ý¤Øæ Áæ𠥇æé¥æð´ ·ð¤ Õè¿ ·¤è ÎêÚUè ·ð¤ ÂýçÌÜæð× ƒæÙ ÂÚU çÙÖüÚU ãñ, ãñ Ñ

between the molecules is : (1)

hydrogen bond

(1)

ãæ§üÇþUæðÁÙ Õ´Ï·¤

(2)

ion - ion interaction

(2)

¥æØÙ - ¥æØÙ ¥‹Øæð‹Ø

(3)

ion - dipole interaction

(3)

¥æØÙ - çmÏýéß ¥‹Øæð‹Ø

(4)

London force

(4)

Ü´ÇUÙ ÕÜ

C/Page 32

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

74.

In the context of the Hall - Heroult process

74.

for the extraction of Al, which of the

ãæòÜ-ãðÚUæòËÅU Âý·ý¤× âð °ðÜéç×çÙØ× ·ð¤ çÙc·¤áü‡æ ·ð¤ â´ÎÖü ×ð´ ·¤æñÙ âæ ·¤ÍÙ »ÜÌ ãñ?

following statements is false ? (1)

Na3AlF6 serves as the electrolyte

(1)

(2)

CO and CO2 are produced in this process

(2)

(3)

Al 2O 3 is mixed with CaF 2 which lowers the melting point of the

(3)

mixture and brings conductivity (4)

Al31 is reduced at the cathode to

(4)

form Al 75.

Which of the following compounds will

76.

77.

1, 1 - Diphenyl - 1 - propane

(2)

1 - Phenyl - 2 - butene

(3)

3 - Phenyl - 1 - butene

(4)

2 - Phenyl - 1 - butene

The ionic radii (in Å) of N32, O22 and F2

çßléÌ ¥ÂƒæÅ÷UØ ·¤æ ·¤æ× ·¤ÚUÌæ

ãñÐ §â Âý·ý¤× ×ð´ CO ÌÍæ CO2 ·¤æ ©ˆÂæÎÙ ãæðÌæ ãñÐ CaF2 ·¤æð Al2O3 ×ð´ ç×ÜæÙð ÂÚU çןæ‡æ ·¤æ »ÜÙæ´·¤ ·¤× ãæðÌæ ãñ ¥æñÚU ©â×ð´ ¿æÜ·¤Ìæ ¥æÌè ãñÐ ·ñ¤ÍæðÇU ÂÚU Al31 ¥Â¿çØÌ ãæð ·¤ÚU Al ÕÙæÌæ ãñÐ

75.

çِÙçÜç¹Ì ×ð ´ âð ·¤æñ Ù âæ Øæñ ç »·¤ ’Øæç×ÌèØ â×æßØßÌæ ÎàææüÌæ ãñ? (1) 1, 1 - ÇUæ§üÈð¤çÙÜ - 1 - ÂýæðÂðÙ (2) 1 - Èð¤çÙÜ - 2 - ŽØêÅUèÙ (3) 3 - Èð¤çÙÜ - 1 - ŽØêÅUèÙ (4) 2 - Èð¤çÙÜ - 1 - ŽØêÅUèÙ

76.

N32, O22 ÌÍæ F2 ·¤è

exhibit geometrical isomerism ? (1)

Na3AlF6

are respectively :

·ý¤×àæÑ ãñ´ Ñ

(1)

1.71, 1.36 and 1.40

(1)

1.71, 1.36

(2)

1.36, 1.40 and 1.71

(2)

1.36, 1.40

(3)

1.36, 1.71 and 1.40

(3)

1.36, 1.71

(4)

1.71, 1.40 and 1.36

(4)

1.71, 1.40

From the following statements regarding

77.

H2O2, choose the incorrect statement : (1)

It has to be kept away from dust

(2)

It can act only as an oxidizing agent

(3)

It decomposes on exposure to light

(4)

It has to be stored in plastic or wax lined glass bottles in dark

C/Page 33

SPACE FOR ROUGH WORK /

ÌÍæ ÌÍæ ÌÍæ ÌÍæ

H2O2 ·ð¤

¥æØçÙ·¤ ç˜æ’ØæØð´ (Å ×ð´)

1.40 1.71 1.40 1.36

â´ÎÖü ×ð´, çِÙçÜç¹Ì ·¤ÍÙæð´ ×ð´ âð »ÜÌ ·¤ÍÙ ¿éçÙ° Ñ (1) §âð ÏêÜ âð ÎêÚU ÚU¹Ùæ ¿æçã° (2) Øã ·ð¤ßÜ ¥æò€âè·¤æÚU·¤ ãñ (3) Âý·¤æàæ ×ð´ §â·¤æ ¥ÂƒæÅUÙ ãæðÌæ ãñ (4) §âð ŒÜæçSÅU·¤ Øæ ×æð×¥ÅðU ·¤æ´¿ ÕæðÌÜæð´ ×ð´ ¥´ÏðÚðU ×ð´ â´»ýçãÌ ç·¤Øæ ÁæÌæ ãñ ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

78.

Higher order (>3) reactions are rare due

78.

©‘¿ ·¤æðçÅU ¥çÖç·ý¤Øæ (>3) ÎéÜüÖ ãñ €Øæð´ç·¤ Ñ

to : (1)

loss of active species on collision

(1)

ÅU·¤ÚUæß âð âç·ý¤Ø SÂèàæè$Á ·¤æ ÿæØ ãæðÌæ ãñÐ

(2)

low probability of simultaneous

(2)

ÂýçÌç·ý¤Øæ ×ð´ âÖè ÂýÁæçÌØæ𴠷𤠰·¤ âæÍ ÅU€·¤ÚU ·¤è â´ÖæßÙæ ·¤× ãæðÌè ãñÐ

(3)

¥çÏ·¤ ¥‡æé¥æð´ ·ð¤ àææç×Ü ãæðÙð âð °´ÅþUæÂè ¥æñÚU â´ç·ý¤Ø‡æ ª¤Áæü ×ð´ ßëçh ãæðÌè ãñÐ

(4)

Üæð¿ÎæÚU ÅU·¤ÚUæß ·ð¤ ·¤æÚU‡æ ¥çÖ·¤æÚU·¤æð´ ·¤è çÎàææ ×ð´ âæØ ·¤æ SÍæÙæ´ÌÚU‡æ ãæðÌæ ãñÐ

collision of all the reacting species (3)

increase in entropy and activation energy as more molecules are involved

(4)

shifting of equilibrium towards reactants due to elastic collisions

79.

Match the catalysts to the correct

79.

processes : Catalyst

80.

çΰ »° ©ˆÂýðÚU·¤æð´ ·¤æð âãè Âý·ý¤× ·ð¤ âæÍ âé×ðçÜÌ ·¤Úð´U Ñ ©ˆÂýðÚU·¤

Process

Âý·ý¤×

(A)

TiCl3

(i)

Wacker process

(A)

TiCl3

(i)

ßæò·¤ÚU Âý·ý¤×

(B)

PdCl2

(ii)

Ziegler - Natta

(B)

PdCl2

(ii)

ˆâè‚ÜÚ-Ù^æ ÕãéÜ·¤è·¤ÚU‡æU

(C)

CuCl2

(iii)

Contact process

(C)

CuCl2

(iii)

â´SÂàæü Âý·ý¤×

(D)

V 2O 5

(iv)

Deacon’s process

(D)

V 2O 5

(iv)

ÇUè·¤Ù Âý·ý¤×

(1)

(A) - (iii), (B) - (i), (C) - (ii), (D) - (iv)

(1)

(A) - (iii), (B) - (i), (C) - (ii), (D) - (iv)

(2)

(A) - (iii), (B) - (ii), (C) - (iv), (D) - (i)

(2)

(A) - (iii), (B) - (ii), (C) - (iv), (D) - (i)

(3)

(A) - (ii), (B) - (i), (C) - (iv), (D) - (iii)

(3)

(A) - (ii), (B) - (i), (C) - (iv), (D) - (iii)

(4)

(A) - (ii), (B) - (iii), (C) - (iv), (D) - (i)

(4)

(A) - (ii), (B) - (iii), (C) - (iv), (D) - (i)

polymerization

Which one has the highest boiling point ?

80.

çِÙçÜç¹Ì ×ð´ âð âßæüçÏ·¤ €ßÍÙæ´·¤ 緤ⷤæ ãñ?

(1)

Xe

(1)

Xe

(2)

He

(2)

He

(3)

Ne

(3)

Ne

(4)

Kr

(4)

Kr

C/Page 34

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

81.

In the reaction

81.

NaNO /HCl 0258 C

çΰ »° ¥çÖç·ý¤Øæ ×ð´ ©ˆÂæÎ E ãñ Ñ

CuCN/KCN D

NaNO /HCl 0258 C

2  → D → E 1 N 2

CuCN/KCN D

2  → D  → E 1 N2

the product E is :

82.

(1)

(1)

(2)

(2)

(3)

(3)

(4)

(4)

colored yellow ?

çΰ »° Øæñç»·¤æð´ ×ð´ ·¤æñÙ âð Øæñç»·¤ ·¤æ Ú´U» ÂèÜæ Ùãè´ ãñ?

(1)

BaCrO 4

(1)

BaCrO 4

(2)

Zn2[Fe(CN)6]

(2)

Zn2[Fe(CN)6]

(3)

K3[Co(NO2)6]

(3)

K3[Co(NO2)6]

(4)

(NH4)3 [As (Mo3 O10)4]

(4)

(NH4)3 [As (Mo3 O10)4]

Which of the following compounds is not

C/Page 35

82.

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

83.

Sodium metal crystallizes in a body centred

83.

cubic lattice with a unit cell edge of 4.29Å. The

radius

of

sodium

atom

is

âæðçÇUØ× ÏæÌé °·¤ ¥´ÌÑ·ð¤ç‹ÎýÌ ƒæÙèØ ÁæÜ·¤ ×ð´ ç·ý¤SÅUçÜÌ ãæðÌæ ãñ çÁâ·ð¤ ·¤æðÚU ·¤è Ü´Õæ§ü 4.29Å ãñÐ âæðçÇUØ× ÂÚU×æ‡æé ·¤è ç˜æ’Øæ ֻܻ ãñ Ñ

approximately :

84.

(1)

0.93Å

(1)

0.93Å

(2)

1.86Å

(2)

1.86Å

(3)

3.22Å

(3)

3.22Å

(4)

5.72Å

(4)

5.72Å

300 K for the reaction 2A ì B 1 C is

ÂÚU ¥çÖç·ý¤Øæ 2A ì B 1 C ·¤è ×æÙ·¤ 绎$ Á ª¤Áæü 2494.2 J ãñ Ð çΰ »° â×Ø ×ð ´

2494.2 J. At a given time, the composition

¥çÖç·ý ¤ Øæ

The standard Gibbs energy change at

of the reaction mixture is [A] 5

84.

1 , [B]52 2

1 . The reaction proceeds in 2 the : [R58.314 J/K/mol, e52.718]

300 K

çןæ‡æ ·¤æ â´ ƒ æÅUÙ

[B]52 ¥æñÚU [C] 5

1 2

[A] 5

ãñÐ ¥çÖç·ý¤Øæ ¥»ýçâÌ ãæðÌè

and [C] 5

ãñ Ñ

[R58.314 J/K/mol, e52.718]

(1)

reverse direction because Q < Kc

(1)

çßÂÚUèÌ çÎàææ ×𴠀Øæð´ç·¤ Q < Kc

(2)

forward direction because Q > Kc

(2)

¥»ý çÎàææ ×𴠀Øæð´ç·¤ Q > Kc

(3)

reverse direction because Q > Kc

(3)

çßÂÚUèÌ çÎàææ ×𴠀Øæð´ç·¤ Q > Kc

(4)

forward direction because Q < Kc

(4)

¥»ý çÎàææ ×𴠀Øæð´ç·¤ Q < Kc

C/Page 36

SPACE FOR ROUGH WORK /

1 , 2

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

85.

Which

compound

would

give

85.

5 - keto - 2 - methyl hexanal upon

¥æð $ Á æð Ù æð ç Üçââ ·¤ÚUÙð ÂÚU ·¤æñ Ù âæ Øæñ ç »·¤ 5 - ·¤èÅUæð - 2 - ×ðçÍÜ ãð€âæÙñÜ ÎðÌæ ãñ?

ozonolysis ?

86.

(1)

(1)

(2)

(2)

(3)

(3)

(4)

(4)

Which of the following compounds is not

86.

çِÙçÜç¹Ì ×ð´ âð ·¤æñÙ âæ Øæñç»·¤ ÂýçÌ¥Ü Ùãè´ ãñ?

an antacid ? (1)

Ranitidine

(1)

ÚñUçÙçÅUÇUèÙ

(2)

Aluminium hydroxide

(2)

°ðÜéç×çÙØ× ãæ§ÇþUæ€âæ§ÇU

(3)

Cimetidine

(3)

çâ×ðçÅUÇUèÙ

(4)

Phenelzine

(4)

çȤÙçËÁÙ

C/Page 37

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

87.

In the following sequence of reactions : KMnO

SOCl

87.

H /Pd BaSO 4

çΰ »° ¥çÖç·ý¤Øæ ¥Ùé·ý¤× ×ð´ ©ˆÂæÎ KMnO

4 2 2 Toluene → A  → B  → C,

SOCl

C ãñ

Ñ

H /Pd BaSO 4

4 2 2 Toluene → A  → B  →C

the product C is :

88.

(1)

C6H5CHO

(1)

C6H5CHO

(2)

C6H5COOH

(2)

C6H5COOH

(3)

C6H5CH3

(3)

C6H5CH3

(4)

C6H5CH2OH

(4)

C6H5CH2OH

Which of the vitamins given below is water

88.

çِÙçÜç¹Ì çßÅUæç×Ùæð´ ×ð´ ÁÜ ×ð´ çßÜðØ ãæðÙð ßæÜæ ãñ Ñ (1) çßÅUæç×Ù K (2) çßÅUæç×Ù C (3) çßÅUæç×Ù D (4) çßÅUæç×Ù E

89.

KMnO4 ·ð¤

soluble ?

89.

90.

(1)

Vitamin K

(2)

Vitamin C

(3)

Vitamin D

(4)

Vitamin E

The color of KMnO4 is due to : (1) s 2 s* transition

(1)

(2)

M ® L charge transfer transition

(2)

(3)

d 2 d transition

(3)

(4)

L ® M charge transfer transition

(4)

Two Faraday of electricity is passed

90.

through a solution of CuSO4. The mass of

copper deposited at the cathode is :

Ú´U» ·¤æ ·¤æÚU‡æ ãñ Ñ s 2 s* â´·ý¤×‡æ M ® L ¥æßðàæ SÍæÙæ´ÌÚU‡æ â´·ý¤×‡æ d 2 d â´·ý¤×‡æ L ® M ¥æßðàæ SÍæÙæ´ÌÚU‡æ â´·ý¤×‡æ

CuSO4 ·ð¤

°·¤ çßÜØÙ ×ð´, Îæð Èñ¤ÚUæÇðU çßléÌ ÂýßæçãÌ ·¤è »§üÐ ·ñ¤ÍæðÇU ÂÚU çÙÿæðçÂÌ Ìæ´Õð ·¤æ ÎýÃØ×æÙ ãñ : (Cu ·¤æ ÂÚU×æç‡ß·¤ ÎýÃØ×æÙ 563.5 amu)

(at. mass of Cu563.5 amu) (1)

127 g

(1)

127 g

(2)

0g

(2)

0g

(3)

63.5 g

(3)

63.5 g

(4)

2g

(4)

2g

-o0oC/Page 38

SPACE FOR ROUGH WORK /

-o0o-

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

SPACE FOR ROUGH WORK / ÚȤ ·¤æØü ·ð¤ çÜ° Á»ã

C/Page 39

SPACE FOR ROUGH WORK /

ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã

Read the following instructions carefully :

çِÙçÜç¹Ì çÙÎðüàæ ŠØæÙ âð Âɸð´ Ñ ÂÚUèÿææçÍüØæð´ ·¤æð ÂÚUèÿææ ÂéçSÌ·¤æ ¥æñÚU ©žæÚU ˜æ (ÂëD -1) ÂÚU ßæ´çÀUÌ çßßÚU‡æ ÙèÜð/·¤æÜð ÕæòÜ Œß槴ÅU ÂðÙ âð ãè ÖÚUÙæ ãñÐ ©žæÚU Â˜æ ·ð¤ ÂëD-2 ÂÚU çßßÚU‡æ çܹÙð/¥´ç·¤Ì ·¤ÚUÙð ·ð¤ çÜ° ·ð¤ßÜ ÙèÜð/·¤æÜð ÕæòÜ Œß槴ÅU ÂðÙ ·¤æ ÂýØæð» ·¤Úð´UÐ 3. ÂÚUèÿææ ÂéçSÌ·¤æ/©žæÚU ˜æ ÂÚU çÙÏæüçÚUÌ SÍæÙ ·ð¤ ¥Üæßæ ÂÚUèÿææÍèü ¥ÂÙæ ¥ÙéR¤×æ´·¤ ¥‹Ø ·¤ãè´ Ùãè´ çܹð´Ð 4. ÂýˆØð·¤ ÂýàÙ ·ð¤ çÜØð çÎØð »Øð ¿æÚU çß·¤ËÂæð´ ×ð´ âð ·ð¤ßÜ °·¤ çß·¤Ë âãè ãñÐ 5. ÂýˆØð·¤ »ÜÌ ©žæÚU ·ð¤ çÜ° ©â ÂýàÙ ·ð¤ çÜ° çÙÏæüçÚUÌ ·é¤Ü ¥´·¤æð´ ×ð´ âð °·¤-¿æñÍæ§ü (¼) ¥´·¤ ·é¤Ü Øæð» ×ð´ âð ·¤æÅU çÜ° Áæ°¡»ðÐ ØçÎ ©žæÚU ˜æ ×ð´ ç·¤âè ÂýàÙ ·¤æ ·¤æð§ü ©žæÚU Ùãè´ çÎØæ »Øæ ãñ, Ìæð ·é¤Ü Øæð» ×ð´ âð ·¤æð§ü ¥´·¤ Ùãè´ ·¤æÅðU Áæ°¡»ðÐ 6. ÂÚUèÿææ ÂéçSÌ·¤æ °ß´ ©žæÚU Â˜æ ·¤æ ŠØæÙÂêßü·¤ ÂýØæð» ·¤Úð´U €Øæð´ç·¤ ç·¤âè Öè ÂçÚUçSÍçÌ ×ð´ (·ð¤ßÜ ÂÚUèÿææ ÂéçSÌ·¤æ °ß´ ©žæÚU Â˜æ ·ð¤ â´·ð¤Ì ×ð´ çÖóæÌæ ·¤è çSÍçÌ ·¤æð ÀUæðǸ·¤ÚU), ÎêâÚUè ÂÚUèÿææ ÂéçSÌ·¤æ ©ÂÜŽÏ Ùãè´ ·¤ÚUæØè Áæ°»èÐ 7. ©žæÚU ˜æ ÂÚU ·¤æð§ü Öè ÚUȤ ·¤æØü Øæ çܹæ§ü ·¤æ ·¤æ× ·¤ÚUÙð ·¤è ¥Ùé×çÌ Ùãè´ ãñÐ âÖè »‡æÙæ °ß´ çܹæ§ü ·¤æ ·¤æ×, ÂÚUèÿææ ÂéçSÌ·¤æ ×ð´ çÙÏæüçÚUÌ Á»ã Áæð ç·¤ ÒÚUȤ ·¤æØü ·ð¤ çÜ° Á»ãÓ mæÚUæ Ùæ×æ´ç·¤Ì ãñ, ÂÚU ãè ç·¤Øæ Áæ°»æÐ Øã Á»ã ÂýˆØð·¤ ÂëD ÂÚU Ùè¿ð ·¤è ¥æðÚU ¥æñÚU ÂéçSÌ·¤æ ·ð¤ ¥´Ì ×ð´ °·¤ ÂëD ÂÚU (ÂëD 39) Îè »§ü ãñÐ 8. ÂÚèÿææ âÂóæ ãæðÙð ÂÚU, ÂÚUèÿææÍèü ·¤ÿæ/ãæòÜ ÀUæðǸÙð âð Âêßü ©žæÚU Â˜æ ·¤ÿæ çÙÚUèÿæ·¤ ·¤æð ¥ßàØ âæñ´Â Îð´Ð ÂÚUèÿææÍèü ¥ÂÙð âæÍ §â ÂÚUèÿææ ÂéçSÌ·¤æ ·¤æð Üð Áæ â·¤Ìð ãñ´Ð 9. ×æ´»ð ÁæÙð ÂÚU ÂýˆØð·¤ ÂÚUèÿææÍèü çÙÚUèÿæ·¤ ·¤æð ¥ÂÙæ Âýßàð æ ·¤æÇü çι氡Р10. ¥Ïèÿæ·¤ Øæ çÙÚUèÿæ·¤ ·¤è çßàæðá ¥Ùé×çÌ ·ð¤ çÕÙæ ·¤æð§ü ÂÚUèÿææÍèü ¥ÂÙæ SÍæÙ Ù ÀUæðǸð´Ð 11. ·¤æØüÚUÌ çÙÚUèÿæ·¤ ·¤æð ¥ÂÙæ ©žæÚU ˜æ çΰ çÕÙæ °ß´ ©ÂçSÍçÌ Â˜æ ÂÚU ÎéÕæÚUæ ãSÌæÿæÚU ç·¤° çÕÙæ ·¤æð§ü ÂÚUèÿææÍèü ÂÚUèÿææ ãæòÜ Ùãè´ ÀUæðǸð´»ðÐ ØçÎ ç·¤âè ÂÚUèÿææÍèü Ùð ÎêâÚUè ÕæÚU ©ÂçSÍçÌ Â˜æ ÂÚU ãSÌæÿæÚU Ùãè´ ç·¤° Ìæð Øã ×æÙæ Áæ°»æ ç·¤ ©âÙ𠩞æÚU ˜æ Ùãè´ ÜæñÅUæØæ ãñ çÁâð ¥Ùéç¿Ì âæÏÙ ÂýØæ𻠟æð‡æè ×ð´ ×æÙæ Áæ°»æÐ ÂÚUèÿææÍèü ¥ÂÙð ÕæØð´ ãæÍ ·ð¤ ¥´»êÆðU ·¤æ çÙàææÙ ©ÂçSÍçÌ Â˜æ ×ð´ çΰ »° SÍæÙ ÂÚU ¥ßàØ Ü»æ°¡Ð 12. §Üð€ÅþUæòçÙ·¤/ãSÌ¿æçÜÌ ÂçÚU·¤Ü·¤ °ß´ ×æðÕæ§Ü ȤæðÙ, ÂðÁÚU §ˆØæçÎ Áñâð ç·¤âè §Üð€ÅþUæòçÙ·¤ ©Â·¤ÚU‡æ ·¤æ ÂýØæð» ßçÁüÌ ãñÐ 13. ÂÚUèÿææ ãæòÜ ×ð´ ¥æ¿ÚU‡æ ·ð¤ çÜ° ÂÚUèÿææÍèü Á.°.Õ./ÕæðÇüU ·ð¤ âÖè çÙØ×æð´ °ß´U çßçÙØ×æð´ mæÚUæ çÙØç×Ì ãæð´»ðÐ ¥Ùéç¿Ì âæÏÙ ÂýØæð» ·ð¤ âÖè ×æ×Üæð´ ·¤æ Èñ¤âÜæ Á.°.Õ./ÕæðÇüU ·ð¤ çÙØ×æð´ °ß´ çßçÙØ×æ𴠷𤠥ÙéâæÚU ãæð»æÐ 14. ç·¤âè Öè çSÍçÌ ×ð´ ÂÚUèÿææ ÂéçSÌ·¤æ ÌÍæ ©žæÚU Â˜æ ·¤æ ·¤æð§ü Öè Öæ» ¥Ü» Ùãè´ ç·¤Øæ Áæ°»æÐ 15. ÂÚUèÿææÍèü mæÚUæ ÂÚUèÿææ ·¤ÿæ/ãæòÜ ×ð´ Âýßðàæ ·¤æÇüU ·ð¤ ¥Üæßæ ç·¤âè Öè Âý·¤æÚU ·¤è ÂæÆ÷UØ âæ×»ýè, ×éçÎýÌ Øæ ãSÌçÜç¹Ì, ·¤æ»Á ·¤è Âç¿üØæ¡, ÂðÁÚU, ×æðÕæ§Ü ȤæðÙ Øæ ç·¤âè Öè Âý·¤æÚU ·ð¤ §Üð€ÅþUæòçÙ·¤ ©Â·¤ÚU‡ææð´ Øæ ç·¤âè ¥‹Ø Âý·¤æÚU ·¤è âæ×»ýè ·¤æð Üð ÁæÙð Øæ ©ÂØæð» ·¤ÚUÙð ·¤è ¥Ùé×çÌ Ùãè´ ãñÐ

1. The candidates should fill in the required particulars 1. on the Test Booklet and Answer Sheet (Side–1) with Blue/Black Ball Point Pen. 2. For writing/marking particulars on Side–2 of the 2. Answer Sheet, use Blue/Black Ball Point Pen only.

3. The candidates should not write their Roll Numbers anywhere else (except in the specified space) on the Test Booklet/Answer Sheet. 4. Out of the four options given for each question, only one option is the correct answer. 5. For each incorrect response, one–fourth (¼) of the total marks allotted to the question would be deducted from the total score. No deduction from the total score, however, will be made if no response is indicated for an item in the Answer Sheet. 6. Handle the Test Booklet and Answer Sheet with care,

as under no circumstances (except for discrepancy in Test Booklet Code and Answer Sheet Code), another set will be provided.

7. The candidates are not allowed to do any rough work or writing work on the Answer Sheet. All calculations/ writing work are to be done in the space provided for this purpose in the Test Booklet itself, marked ‘Space for Rough Work’. This space is given at the bottom of each page and in one page (i.e. Page 39) at the end of the booklet. 8. On completion of the test, the candidates must hand over the Answer Sheet to the Invigilator on duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet with them. 9. Each candidate must show on demand his/her Admit Card to the Invigilator. 10. No candidate, without special permission of the Superintendent or Invigilator, should leave his/her seat. 11. The candidates should not leave the Examination Hall without handing over their Answer Sheet to the Invigilator on duty and sign the Attendance Sheet again. Cases where a candidate has not signed the Attendance Sheet second time will be deemed not to have handed over the Answer Sheet and dealt with as an unfair means case. The candidates are also required to put their left hand THUMB impression in the space provided in the Attendance Sheet. 12. Use of Electronic/Manual Calculator and any Electronic device like mobile phone, pager etc. is prohibited. 13. The candidates are governed by all Rules and Regulations of the JAB/Board with regard to their conduct in the Examination Hall. All cases of unfair means will be dealt with as per Rules and Regulations of the JAB/Board. 14. No part of the Test Booklet and Answer Sheet shall be detached under any circumstances. 15. Candidates are not allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, electronic device or any other material except the Admit Card inside the examination room/hall.

C/Page 40