This booklet contains 40 printed pages. §â ÂéçSÌ·¤æ ×ð´ ×éçÎýÌ ÂëcÆ 40 ãñ´Ð
PAPER - 1
ÂýàÙÂéçSÌ·¤æ -
LMN
: MATHEMATICS, PHYSICS & CHEMISTRY 1 : »çæÌ, ÖæñçÌ·¤ çßææÙ ÌÍæ ÚUâæØÙ çßææÙ
Do not open this Test Booklet until you are asked to do so.
§â ÂÚèÿææ ÂéçSÌ·¤æ ·¤æð ÌÕ Ì·¤ Ù ¹æðÜð´ ÁÕ Ì·¤ ·¤ãæ Ù Áæ°Ð
Read carefully the Instructions on the Back Cover of this Test Booklet.
§â ÂÚèÿææ ÂéçSÌ·¤æ ·ð¤ çÂÀÜð ¥æßÚæ ÂÚ çΰ »° çÙÎðüàææð´ ·¤æð ØæÙ âð Âɸð´Ð Important Instructions :
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 Side2 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 Side2 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 àæÎæð´ ×ð´
Examination Centre Number :
ÂÚèÿææ ·ð¤Îý ÙÕÚU Ñ
Name of Examination Centre (in Capital letters) :
ÂÚUèÿææ ·ð¤Îý ·¤æ Ùæ× (ÕǸð ¥ÿæÚUæð´ ×ð´ ) Ñ Candidates Signature :
ÂÚèÿææÍèü ·ð¤ ãSÌæÿæÚ Ñ
Test Booklet Code
ÂÚèÿææ ÂéçSÌ·¤æ â´·ð¤Ì
C
×ãßÂêæü çÙÎðüàæ Ñ 1. ÂÚUèÿææ ÂéçSÌ·¤æ ·ð¤ §â ÂëcÆU ÂÚU ¥æßàØ·¤ çßßÚUæ ÙèÜð / ·¤æÜð ÕæòÜ ß槴ÅU ÂðÙ âð Ì·¤æÜ ÖÚð´Ð ÂðçâÜ ·¤æ ÂýØæð» çÕË·é¤Ü ßçÁüÌ ãñÐ 2. ©æÚU Âæ §â ÂÚUèÿææ ÂéçSÌ·¤æ ·ð¤ ¥ÎÚU ÚU¹æ ãñÐ ÁÕ ¥æ·¤æð ÂÚUèÿææ ÂéçSÌ·¤æ ¹æðÜÙð ·¤æð ·¤ãæ Áæ°, Ìæð ©æÚU Âæ çÙ·¤æÜ ·¤ÚU âæßÏæÙèÂêß·ü ¤ çßßÚUæ ÖÚðU´Ð 3. ÂÚUèÿææ ·¤è ¥ßçÏ 3 æ´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¤ ÂýØð·¤ Öæ» ×ð´ »çæÌ, ÖæñçÌ·¤ çßææÙ °ß´ ÚUâæØÙ çßææÙ ·ð¤ 30 ÂýàÙ ãñ´ ¥æñÚU âÖè ÂýàÙæ𴠷𤠥´·¤ â×æÙ ãñ´Ð ÂýØð·¤ ÂýàÙ ·ð¤ âãè ©æÚU ·ð¤ çÜ° 4 (¿æÚU) ¥´·¤ çÙÏæüçÚUÌ ç·¤Øð »Øð ãñ´Ð 6. ¥ØçÍüØæð´ ·¤æð ÂýØð·¤ âãè ©æÚU ·ð¤ çÜ° ©ÂÚUæðÌ çÙÎðüàæÙ â´Øæ 5 ·ð¤ çÙÎðüàææÙéâæÚU ¥´·¤ çÎØð ÁæØð´»ðÐ ÂýØð·¤ ÂýàÙ ·ð¤ »ÜÌ ©æÚU ·ð¤ çÜØð ¼ ßæ´ Öæ» ·¤æÅU çÜØæ ÁæØð»æÐ ØçÎ ©æÚU Âæ ×ð´ ç·¤âè ÂýàÙ ·¤æ ©æÚU Ùãè´ çÎØæ »Øæ ãæð Ìæð ·é¤Ü Âýæ#æ´·¤ âð ·¤æð§ü ·¤ÅUæñÌè Ùãè´ ·¤è ÁæØð»èÐ 7. ÂýØð·¤ ÂýàÙ ·¤æ ·ð¤ßÜ °·¤ ãè âãè ©æÚU ãñÐ °·¤ âð ¥çÏ·¤ ©æÚU ÎðÙð ÂÚU ©âð »ÜÌ ©æÚU ×æÙæ ÁæØð»æ ¥æñÚU ©ÂÚUæðÌ çÙÎðüàæ 6 ·ð¤ ¥ÙéâæÚU ¥´·¤ ·¤æÅU çÜØð ÁæØð´»ðÐ 8. ©æÚU Âæ ·ð¤ ÂëcÆU-1 °ß´ ÂëcÆU-2 ÂÚU ßæ´çÀUÌ çßßÚUæ °ß´ ©æÚU ¥´ç·¤Ì ·¤ÚUÙð ãðÌé ·ð¤ßÜ ÙèÜð/·¤æÜð ÕæòÜ ß槴ÅU ÂðÙ ·¤æ ãè ÂýØæð» ·¤Úð´UÐ ÂðçâÜ ·¤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¤ §ÜðÅþUæòçÙ·¤ ©Â·¤ÚUææð´ 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 ÂýØð·¤ ÂëcÆU ÂÚU Ùè¿ð ·¤è ¥æðÚU ¥æñÚU ÂéçSÌ·¤æ ·ð¤ ¥´Ì ×ð´ °·¤ ÂëcÆU ÂÚU (ÂëcÆU 39) Îè »§ü ãñÐ 11. ÂÚUèÿææ â×æÌ ãæðÙð ÂÚU, ÂÚUèÿææÍèü ·¤ÿæ/ãæòÜ ÀUæðǸÙð âð Âêßü ©æÚU Âæ ·¤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, ©æÚU Âæ ·ð¤ ÂëcÆU-2 ÂÚU ÀUÂð â´·ð¤Ì âð ç×ÜÌæ ãñ ¥æñÚU Øã Öè âéçÙçà¿Ì ·¤ÚU Üð´ ç·¤ ÂÚUèÿææ ÂéçSÌ·¤æ, ©æÚU Âæ ÂÚU ·ý¤× â´Øæ ç×ÜÌè ãñÐ ¥»ÚU Øã çÖóæ ãæð Ìæð ÂÚUèÿææÍèü ÎêâÚUè ÂÚUèÿææ ÂéçSÌ·¤æ ¥æñÚU ©æÚU Âæ ÜðÙð ·ð¤ çÜ° çÙÚUèÿæ·¤ ·¤æð ÌéÚUÌ ¥ß»Ì ·¤ÚUæ°¡Ð 13. ©æÚU Âæ ·¤æð Ù ×æðǸ𴠰ߴ Ù ãè ©â ÂÚU ¥Ø çÙàææ٠ܻ氡Ð
Name of the Candidate (in Capital letters ) : Roll Number
No. :
1. Invigilators Signature :
çÙÚèÿæ·¤ ·ð¤ ãSÌæÿæÚ Ñ
2. Invigilators Signature :
çÙÚèÿæ·¤ ·ð¤ ãSÌæÿæÚ Ñ
Öæ» A »çæÌ
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×æ â´Øæ z °·¤×æÂæ´·¤è ·¤ãÜæÌè ãñ ØçÎ ?z?51 ãñÐ ×æÙæ z1 ÌÍæ z2 °ðâè âç×æ â´Øæ°¡ ãñ´
(1)
circle of radius
(2)
straight line parallel to x-axis.
(2)
çæØæ ßæÜð ßëæ 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 çæØæ
2.
(1)
2
·ð¤ â×æ´ÌÚU °·¤ ÚðU¹æ ÂÚUÐ ßæÜð ßëæ ÂÚUÐ
at (1, 1) :
ß·ý ¤ x 2 12xy23y 250 ·ð ¤ çÕ´ Î é ¥çÖÜÕ 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
æðæè 13 1 2 3 13 1 2 3 1 3 3 13 1 1 1 .... 1 113 11 31 5
Âýæ× 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
ææÌ
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·¤ÚUæ AAT59I, ·¤æð â´ÌécÅU ·¤ÚUÌæ ãñ, Áãæ¡ I, 333 ·¤æ Ìâ×·¤ ¥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 çßçÖÙ ßæSÌçß·¤ â´ Øæ¥æð ´ l ÌÍæ n (l, n > 1) ·¤æ â×æ´ÌÚU ×æØ (A.M.) m ãñ ¥æñÚU l ÌÍæ n ·ð¤ Õè¿ ÌèÙ »éææðæÚU ×æØ (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·¤ÚUæ
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 ÂêææZ·¤æð´ ·¤è â´Øæ 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),
çæÖéÁ, çÁâ·ð¤ àæèáü (0, 0), (0, 41) ÌÍæ (41, 0) ãñ´, ·ð¤ ¥æ´ÌçÚU·¤ Öæ» ×ð´ çSÍÌ ©Ù çÕ´Îé¥æð´ ·¤è â´Øæ çÁÙ·ð¤ ÎæðÙæð´ çÙÎðüàææ´·¤ ÂêææZ·¤ 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 çmææÌ â×è·¤ÚUæ 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¤ ÂýçÌÀðUÎ 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
ÿæðæ ·¤æ ÿæðæÈ¤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
Âýðÿæææð´ ßæÜð ¥æ¡·¤Ç¸æð´ ·¤æ ×æØ 16 ãñÐ ØçÎ °·¤ Âýðÿææ çÁâ·¤æ ×æÙ 16 ãñ, ·¤æð ãÅUæ ·¤ÚU, 3 ÙØð Âýðÿææ çÁÙ·ð¤ ×æÙ 3, 4 ÌÍæ 5 ãñ´, ¥æ¡·¤Ç¸æð´ ×ð´ ç×Üæ çÎØð ÁæÌð ãñ´, Ìæð ÙØð ¥æ¡·¤Ç¸æð´ ·¤æ ×æØ 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
Îèæüßëæ
·ð¤ ÙæçÖÜÕæð´ ·ð¤ çâÚUæð´ ÂÚU
¹è´¿è »§ü SÂàæü ÚðU¹æ¥æð´ mæÚUæ çÙç×üÌ ¿ÌéÖéüÁ ·¤æ ÿæðæÈ¤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·¤ÚUæ 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 :
ßëææð´
x21y216x118y12650
ÚðU¹æ¥æð´ ·¤è â´Øæ 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×é¿Ø, çÁÙ·ð¤ çÜ° ÚñUç¹·¤ â×è·¤ÚUæ 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 °·¤ ¥ÌéÀU ãÜ ãñ, (1) ×ð´ Îæð âð ¥çÏ·¤ ¥ßØß ãñ´Ð (2) °·¤ çÚUÌ 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 Õâæð´ ×ð´ ÚU¹è ÁæÌè ãñ´, Ìæð §Ù×ð´ âð °·¤ Õâð ×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´
ææÌæ𴠷𤠻éææ´·¤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 ÂêææZ·¤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)
çæØæ ·¤æ ßëæ ãñÐ x-¥ÿæ ·ð¤ â×æ´ÌÚU ÚðU¹æ ãñÐ y-¥ÿæ ·ð¤ â×æ´ÌÚU ÚðU¹æ ãñÐ 2 çæØæ ·¤æ ßëæ 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 ·¤æðæ ·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×é¿Øæð´ ·¤è â´Øæ, çÁÙ×ð´ ÂýØð·¤ ×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 àæêØðÌÚU °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 ·¤æðæ u ãñ, Ìæð sin u ·¤æ °·¤
(1)
C/Page 11
1 → → → b c a 3
ÚUȤ ·¤æØü ·ð¤ çÜ° Á»ã
Öæ» B ÖæñçÌ·¤ çßææÙ
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 (àæêØ) 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 çæØæ R ÌÍæ àæ´·é¤ ·¤è ª¡¤¿æ§ü h ãæð Ìæð z0 ·¤æ ×æÙ çÙÙæ´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¤ ÂçÚUææ×) ·ð¤ âæÍ âé×ðÜÙ (×ñ¿) ·¤èçÁØð ¥æñÚU çÙÙæ´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) âÕ
(B)
Photo-electric experiment.
(ii)
Discrete energy levels of atom
(B)
§âËÅË 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 §âËÅË Í ÌøËË §âÐ̱ øËÎ Õ ÌÄÌÄþ± ¦Ëá S±¿U ÁÕþªãUË×¾ Í ±¿U §âÐ̱ §¿U¼ËøËÎ Í Ç¿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 æǸè âð ÙæÂæ »Øæ ãñÐ Ìæð, g ·ð¤ çÙÏæüÚUæ ×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 ©âÁü·¤ ÇUæØæðÇU) 0.1 ßæÅU ÂÚU, °·¤â×æÙ Âý·¤æàæ ©âçÁüÌ ·¤ÚUÌæ ãñÐ ÇUæØæðÇU âð 1 m ÎêÚUè ÂÚU, §â Âý·¤æàæ ·ð¤ çßléÌ ÿæðæ ·¤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´ÏæçÚUæ 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 ÜÕð ÌæÚUæð´ ×ð´ ÂýØð·¤ âð I ÏæÚUæ ÂýßæçãÌ ãæð ÚUãè ãñÐ §ãð´ L ÜÕæ§ü ·ð¤ çßléÌÚUæðÏè Ïæ»æð´ âð ÜÅU·¤æØæ »Øæ ãñÐ §Ù Ïæ»æð´ ×ð´ ÂýØð·¤ ·ð¤ mæÚUæ ª¤ßæüÏÚU çÎàææ âð u ·¤æðæ ÕÙæÙð ·¤è çSÍçÌ ×ð´, Øð ÎæðÙæð´ ÌæÚU âæØæßSÍæ ×ð´ ÚUãÌð ãñ´Ð ØçÎ §Ù ÌæÚUæð´ ·¤è ÂýçÌ §·¤æ§ü ÜÕæ§ü ÎýÃØ×æÙ l ãñ ÌÍæ g »éL¤ßèØ ßÚUæ 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 â´æÅ÷UÅU (ÅU·¤ÚU) ÂêæüÌÑ ¥ÂýØæSÍ 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 Üæò·¤ (»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 æáüæ »éææ´·¤ ·¤æ ×æÙ, A ÌÍæ B ·ð¤ Õè¿ 0.1 ÌÍæ B ¥æñÚU ÎèßæÚU ·ð¤ Õè¿ 0.15 ãñ Ìæð, ÎèßæÚU mæÚUæ Üæò·¤ 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 ÕÎ (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 ¥çÖçßØæâæð´ (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 ¿éÕ·¤èØ ÿæðæ, ÏÙæ×·¤ z çÎàææ ×ð´ çßl×æÙ ãñ Ìæð, ÎàææüØð »Øð 緤⠥çÖçßØæâ ×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 çæØæ R ãñ ¥æñÚU §â·¤æ Ìæ T ãñÐ §â·ð¤ ÖèÌÚU ·ë¤çcæ·¤æ çßç·¤ÚUææð´ ·¤æð ȤæðÅUæòÙæð´ ·¤è °·¤ °ðâè ¥æÎàæü »ñâ ×æÙæ Áæ â·¤Ìæ ãñ çÁâ·¤è ÂýçÌ §·¤æ§ü ¥æØÌÙ ¥æÌçÚU·¤ 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 §ÜðÅþUæòÙ, ãæ§ÇþUæðÁÙ Áñâð ÂÚU×ææé /¥æØÙ ·¤è ©æðçÁÌ ¥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 ÚUæçæ ×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·¤ÚUæ-´éÁ ÿæñçÌÁ çÎàææ ×ð´ Áæ ÚUãæ ãæð Ìæð, ã槻ðâ ·ð¤ çâhæÌ âð Øã ÂçÚUææ× Âý æ Ì ãæð Ì æ ãñ ç·¤, ¿ÜÌð ãé ° Âý·¤æàæ-ç·¤ÚUæ ´éÁ Ñ
(1)
bends upwards
(1)
ª¤ÂÚU ·¤è ¥æðÚU Ûæé·¤ ÁæØð»æÐ
(2)
becomes narrower
(2)
â´·é¤ç¿Ì (â´·¤èæü) 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 çæØæ
R
ãñÐ
§ââð çæØæ ·¤æ °·¤ »æðÜèØ Öæ», ¥æÚðU¹ ×ð´ ÎàææüØð 2 »Øð ¥ÙéâæÚU ·¤æÅU çÜØæ ÁæÌæ ãñÐ r5:(¥ÙÌ) ÂÚU »éL¤ßèØ çßÖß ·ð¤ ×æÙ V ·¤æð àæêØ (V50) ×æÙÌð ãé°, §â Âý·¤æÚU ÕÙð ·¤æðÅUÚU (·ñ¤çßÅUè) ·ð¤ ·ð¤Îý ÂÚU, »éL¤ßèØ çßÖß ·¤æ ×æÙ ãæð»æ Ñ (G5 »éL¤ßèØ 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 ·¤æðæ A ãñÐ §â ÂÚU °·¤ßæèü Âý·¤æàæ ¥æÂçÌÌ ãæðÌæ ãñÐ ØçÎ, çÂý× ·ð¤ ÂÎæÍü ·¤æ ¥ÂßÌüÙæ´·¤ m ãñ Ìæð, çÂý× ·ð¤ AB Ȥܷ¤ ÂÚU, u ·¤æðæ ¥æÂçÌÌ Âý·¤æàæ ·¤è ç·¤ÚUæ, 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 ÂÍÚUæð´ ·¤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, çÙÙæ´ç·¤Ì ×ð´ âð ·¤æñÙâæ »ýæȤ (¥æÜð¹) ÂãÜð ÂÍÚU ·ð¤ âæÂðÿæ ÎêâÚðU ÂÍÚU ·¤è çSÍçÌ ·ð¤ â×Ø çß¿ÚUæ (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·¤, ÂÍÚU 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 çÙÙæ´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 ßçÙ ·¤è ¥æßëçæ 1000 Hz ãñÐ ØçÎ ßçÙ ·¤è ßæØé ×ð´ ¿æÜ 320 ms21 ãæð Ìæð, ÂÅUçÚUØæð´ ·ð¤ çÙ·¤ÅU ¹Ç¸ð ÃØçÌ ·ð¤ Âæâ âð ÅþðUÙ ·ð¤ »éÁÚUÙð ÂÚU, ©â ÃØçÌ mæÚUæ âéÙè »§ü âèÅUè ·¤è ßçÙ ·¤è ¥æßëçæ ×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´ÏæçÚUæ ·¤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 çÙÙæ´ç·¤Ì ×ð´ âð ·¤æñÙ âæ »ýæȤ âãè ãñ? (ÜæòÅU ·ð¤ßÜ ÃØßSÍæ ÜæòÅU 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·ü¤ ×ð´ ÚU¹·¤ÚU çÙÙ Îæð Âý·¤æÚU âð »×ü ç·¤Øæ ÁæÌæ ãñ, (i) ¥Ùé·ý¤ç×·¤ M¤Â âð 2 ª¤c×·¤æð´ ·ð¤ â·ü¤ ×ð´ §â Âý·¤æÚU ÚU¹·¤ÚU ç·¤ ÂýØð·¤ ª¤c×·¤ â×æÙ ×æææ ×ð´ ª¤c×æ ÎðÌæ ãñ, (ii) ¥Ùé·ý¤ç×·¤ M¤Â âð 8 ª¤c×·¤æð´ ·ð¤ â·ü¤ ×ð´ §â Âý·¤æÚU ÚU¹·¤ÚU ç·¤ ÂýØð·¤ ª¤c×·¤ â×æÙ ×æææ ×ð´ ª¤c×æ ÎðÌæ ãñ, ÎæðÙæð´ çSÍçÌØæð´ ×ð´ ç´ÇU ·¤æ ÂýæÚ´UçÖ·¤ Ìæ 1008C ÌÍæ ¥çÌ× 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·¤ ÕÎ ÚU¹æ »Øæ ãñÐ §â·ð¤ Âà¿æÌ÷ â×Ø t50 ÂÚU, K1 ·¤æð ¹æðÜ ·¤ÚU âæÍ ãè âæÍ, K2 ·¤æð ÕÎ ç·¤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 çæØæØð ´ , ·ý ¤ ×àæÑ R1, R2, R3 ÌÍæ R4 ãñ´Ð Ìæð,
(1)
(1)
(2) (3) (4) 54.
R çæØæ
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 ÜÕð ÕðÜÙæ·¤æÚU ·¤æðàæ ·ð¤ ª¤ÂÚUè Öæ» ×ð´ ÏÙæ×·¤ ÂëcÆU ¥æßðàæ s ÌÍæ çÙ¿Üð Öæ» ×ð´ «¤ææ×·¤ ÂëcÆU ¥æßðàæ 2s ãñ´Ð §â ÕðÜÙ (çâçÜÇUÚU) ·ð¤ ¿æÚUæð´ ¥æðÚU çßléÌ ÿæðæ-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 Ùðæ ·¤è ÂéÌÜè ·¤è çæØæ 0.25 cm, ¥æñÚU SÂcÅU âéçßÏæ ÁÙ·¤ Îð¹Ùð ·¤è ÎêÚUè 25 cm ãæð Ìæð, 500 nm ÌÚ´U»ÎñØü ·ð¤ Âý·¤æàæ ×ð´, Îæð ßSÌé¥æð´ ·ð¤ Õè¿ ç·¤ÌÙè ØêÙÌ× ÎêÚUè Ì·¤ ×æÙß Ùðæ ©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 :
¥æßëçæ ·ð¤ ç·¤âè â´·ð¤Ì (çâÙÜ) ·¤æ 2 MHz ¥æßëçæ ·¤è ßæã·¤ ÌÚ´U» ÂÚU ¥æØæ× ×æòÇéUÜÙ ç·¤Øæ »Øæ ãñÐ Ìæð, ÂçÚUææ×è çâÙÜ (â´·ð¤Ì) ·¤è ¥æßëçæ 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´, ÂýØð·¤ âð I ÏæÚUæ °·¤ ãè çÎàææ ×ð´ ÂýßæçãÌ ãæð ÚUãè ãñÐ ØçÎ, ÕæãÚUè ÂçÚUÙæçÜ·¤æ ·ð¤ ·¤æÚUæ, ÖèÌÚUè ÂçÚUÙæçÜ·¤æ ÂÚU ¿éÕ·¤èØ ÕÜ →
F1
be
ÌÍæ ÖèÌÚUè ÂçÚUÙæçÜ·¤æ ·ð¤ ·¤æÚUæ, ÕæãÚUè ÂçÚUÙæçÜ·¤æ
ÂÚU ¿éÕ·¤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 Youngs 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 (çæØ) 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 ÿæðæÈ¤Ü A ãñÐ §ââð ÕÙæØð »Øð °·¤ ÜæðÜ·¤ ·¤æ ¥æßÌü·¤æÜ T ãñÐ §â ÜæðÜ·¤ ·ð¤ »æðÜ·¤ âð °·¤ ¥çÌçÚUÌ M ÎýÃØ×æÙ ÁæðǸ ÎðÙð âð ÜæðÜ·¤ ·¤æ ¥æßÌü·¤æÜ ÂçÚUßçÌüÌ ãæð·¤ÚU TM ãæð ÁæÌæ ãñÐ ØçÎ §â ÌæÚU ·ð¤ ÂÎæÍü ·¤æ Ø´» »éææ´·¤ Y ãæð Ìæð (g5»éL¤ßèØ
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
ßÚUæ) 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 çæØæ R ãñÐ §â×ð´ âð ¥çÏ·¤Ì× â´Öß ¥æØÌÙ ·¤æ °·¤ ØêÕ (æÙ) ·¤æÅU çÜØæ ÁæÌæ ãñÐ §â ØêÕ ·¤æ ÁÇ¸ß ¥ææêæü ç·¤ÌÙæ ãæð»æ, ØçÎ, §â·¤è æêæüÙ-¥ÿæ, §â·ð¤ ·ð¤Îý âð ãæð·¤ÚU »é$ÁÚUÌè ãñ ÌÍæ §â·ð¤ ç·¤âè °·¤ Ȥܷ¤ ·ð¤ ÜÕßÌ÷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 §ÜðÅþUæòÙæð´ ·¤è ¥Âßæã ¿æÜ 2.531024 ms21 ãæðÌè ãñÐ ØçÎ §â ÌæÚU ×ð´ §ÜðÅþUæòÙ æÙß 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 çßææÙ
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 ×ð´ 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 °·¤ æ´ÅðU ·ð¤ Âà¿æÌ÷ ©âð ÀUæÙæ »Øæ ¥æñÚU çÙSØ´Î ·¤è ÂýÕÜÌæ 0.042 N Âæ§ü »§üÐ ¥çÏàææðçáÌ °çâçÅU·¤ ¥Ü ·¤è ×æææ (·¤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 ?
çÙÙçÜç¹Ì ×ð´ âð ãæ§üÇþUæðÁÙ ·¤è â´Öß ©æðçÁÌ ¥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.
çÙÙçÜç¹Ì ×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)
çÜÅUæÜ
(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
°·¤ ßæçæØ ÚðUç$ÁÙ ·¤æ ¥æçß·¤ âêæ C8H7SO3Na ãñ (¥æçß·¤ ÖæÚU = 206) §â ÚðUç$ÁÙ ·¤è Ca21 ¥æØÙ ·¤è ¥çÏ·¤Ì× ¥´Ì»ýüãæ ÿæ×Ìæ (×æðÜ ÂýçÌ »ýæ× ÚðUç$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×æçß·¤ 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 ¥æòâèÁÙ ßæÌæßÚUæ ·ð¤ ×éØ æÅU·¤ ãñ´ ÂÚUÌé Øã ç·ý¤Øæ ·¤ÚU·ð¤ Ùæ§ÅþUæðÁÙ ·ð¤ ¥æòâæ§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 ¥æòâèÁÙ ·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·¤ÚUæ ãñÐ
(3)
¥çÖ·¤ÍÙ ¥æñÚU Ì·ü¤ ÎæðÙæð´ âãè ãñ´ ÂÚUÌé Ì·ü¤ ¥çÖ·¤ÍÙ ·¤æ âãè SÂcÅUè·¤ÚUæ Ùãè´ ãñÐ
(4)
¥çÖ·¤ÍÙ »ÜÌ ãñ ÂÚUÌé 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.
çÙÙçÜç¹Ì ¥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·¤ ×éÌ ª¤Áæü 86.6 kJ/mol ãñÐ 298 K ÂÚU NO2(g) ·¤è ×æÙ·¤ ×éÌ 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 ?
çÙÙçÜç¹Ì ×ð´ âð ·¤æñÙ âð ÿææÚUèØ ×ëÎæ ÏæÌé âËÈð¤ÅU ·¤è ÁÜØæðÁÙ °ðÍæËÂè ©â·ð¤ ÁæÜ·¤ °ðÍæËÂè 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 â´Øæ 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´àÜðáæ ·ð¤ çÜ° âÕâð ÕðãÌÚUèÙ çßçÏ ãñ Ñ
(1)
Swarts reaction
(1)
SßæÅüUâ ¥çÖç·ý¤Øæ
(2)
Free radical fluorination
(2)
×éÌ ×êÜ·¤ ÜæðçÚUÙðàæÙ
(3)
Sandmeyers reaction
(3)
âñÇU×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·¤ ¥ØæðØ ç·ý¤Øæ Áæð ¥æé¥æð´ ·ð¤ Õè¿ ·¤è ÎêÚUè ·ð¤ ÂýçÌÜæð× æÙ ÂÚU çÙÖüÚU ãñ, ãñ Ñ
between the molecules is : (1)
hydrogen bond
(1)
ãæ§üÇþUæðÁÙ Õ´Ï·¤
(2)
ion - ion interaction
(2)
¥æØÙ - ¥æØÙ ¥ØæðØ
(3)
ion - dipole interaction
(3)
¥æØÙ - çmÏýéß ¥ØæðØ
(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·¤áüæ ·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 ¥ÂæÅ÷UØ ·¤æ ·¤æ× ·¤ÚUÌæ
ãñÐ §â Âý·ý¤× ×ð´ CO ÌÍæ CO2 ·¤æ ©ÂæÎÙ ãæðÌæ ãñÐ CaF2 ·¤æð Al2O3 ×ð´ ç×ÜæÙð ÂÚU ç×ææ ·¤æ »ÜÙæ´·¤ ·¤× ãæðÌæ ãñ ¥æñÚU ©â×ð´ ¿æÜ·¤Ìæ ¥æÌè ãñÐ ·ñ¤ÍæðÇU ÂÚU Al31 ¥Â¿çØÌ ãæð ·¤ÚU Al ÕÙæÌæ ãñÐ
75.
çÙÙçÜç¹Ì ×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 - ØêÅUèÙ (3) 3 - Èð¤çÙÜ - 1 - ØêÅUèÙ (4) 2 - Èð¤çÙÜ - 1 - ØêÅUèÙ
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·¤ çæØæØð´ (Å ×ð´)
1.40 1.71 1.40 1.36
â´ÎÖü ×ð´, çÙÙçÜç¹Ì ·¤ÍÙæð´ ×ð´ âð »ÜÌ ·¤ÍÙ ¿éçÙ° Ñ (1) §âð ÏêÜ âð ÎêÚU ÚU¹Ùæ ¿æçã° (2) Øã ·ð¤ßÜ ¥æòâè·¤æÚU·¤ ãñ (3) Âý·¤æàæ ×ð´ §â·¤æ ¥ÂæÅUÙ ãæðÌæ ãñ (4) §âð ÜæçSÅU·¤ 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¤Øæ ª¤Áæü ×ð´ ßëçh ãæðÌè ãñÐ
(4)
Üæð¿ÎæÚU ÅU·¤ÚUæß ·ð¤ ·¤æÚUæ ¥çÖ·¤æÚU·¤æð´ ·¤è çÎàææ ×ð´ âæØ ·¤æ SÍæÙæ´ÌÚUæ 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 »° ©ÂýðÚU·¤æð´ ·¤æð âãè Âý·ý¤× ·ð¤ âæÍ âé×ðçÜÌ ·¤Úð´U Ñ ©ÂýðÚU·¤
Process
Âý·ý¤×
(A)
TiCl3
(i)
Wacker process
(A)
TiCl3
(i)
ßæò·¤ÚU Âý·ý¤×
(B)
PdCl2
(ii)
Ziegler - Natta
(B)
PdCl2
(ii)
âèÜÚ-Ù^æ ÕãéÜ·¤è·¤ÚUæU
(C)
CuCl2
(iii)
Contact process
(C)
CuCl2
(iii)
â´SÂàæü Âý·ý¤×
(D)
V 2O 5
(iv)
Deacons 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.
çÙÙçÜç¹Ì ×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´ ©ÂæÎ 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¤çÎýÌ æÙèØ ÁæÜ·¤ ×ð´ ç·ý¤SÅUçÜÌ ãæðÌæ ãñ çÁâ·ð¤ ·¤æðÚU ·¤è Ü´Õæ§ü 4.29Å ãñÐ âæðçÇUØ× ÂÚU×ææé ·¤è çæØæ ֻܻ 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·¤ ç»$ 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
ç×ææ ·¤æ â´ 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 ×ð´ Øæð´ç·¤ Q < Kc
(2)
forward direction because Q > Kc
(2)
¥»ý çÎàææ ×ð´ Øæð´ç·¤ Q > Kc
(3)
reverse direction because Q > Kc
(3)
çßÂÚUèÌ çÎàææ ×ð´ Øæð´ç·¤ Q > Kc
(4)
forward direction because Q < Kc
(4)
¥»ý çÎàææ ×ð´ 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 ãðâæÙñÜ ÎðÌæ ãñ?
ozonolysis ?
86.
(1)
(1)
(2)
(2)
(3)
(3)
(4)
(4)
Which of the following compounds is not
86.
çÙÙçÜç¹Ì ×ð´ âð ·¤æñÙ âæ Øæñç»·¤ ÂýçÌ¥Ü Ùãè´ ãñ?
an antacid ? (1)
Ranitidine
(1)
ÚñUçÙçÅUÇUèÙ
(2)
Aluminium hydroxide
(2)
°ðÜéç×çÙØ× ãæ§ÇþUæâæ§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´ ©ÂæÎ 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.
çÙÙçÜç¹Ì 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 ·¤æÚUæ ãñ Ñ s 2 s* â´·ý¤×æ M ® L ¥æßðàæ SÍæÙæ´ÌÚUæ â´·ý¤×æ d 2 d â´·ý¤×æ L ® M ¥æßðàæ SÍæÙæ´ÌÚUæ 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×æçß·¤ 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 :
çÙÙçÜç¹Ì çÙÎðüàæ ØæÙ âð Âɸð´ Ñ ÂÚUèÿææçÍüØæð´ ·¤æð ÂÚUèÿææ ÂéçSÌ·¤æ ¥æñÚU ©æÚU Âæ (ÂëD -1) ÂÚU ßæ´çÀUÌ çßßÚUæ ÙèÜð/·¤æÜð ÕæòÜ ß槴ÅU ÂðÙ âð ãè ÖÚUÙæ ãñÐ ©æÚU Âæ ·ð¤ ÂëD-2 ÂÚU çßßÚUæ çܹÙð/¥´ç·¤Ì ·¤ÚUÙð ·ð¤ çÜ° ·ð¤ßÜ ÙèÜð/·¤æÜð ÕæòÜ ß槴ÅU ÂðÙ ·¤æ ÂýØæð» ·¤Úð´UÐ 3. ÂÚUèÿææ ÂéçSÌ·¤æ/©æÚU Âæ ÂÚU çÙÏæüçÚUÌ SÍæÙ ·ð¤ ¥Üæßæ ÂÚUèÿææÍèü ¥ÂÙæ ¥ÙéR¤×æ´·¤ ¥Ø ·¤ãè´ Ùãè´ çܹð´Ð 4. ÂýØð·¤ ÂýàÙ ·ð¤ çÜØð çÎØð »Øð ¿æÚU çß·¤ËÂæð´ ×ð´ âð ·ð¤ßÜ °·¤ çß·¤Ë âãè ãñÐ 5. ÂýØð·¤ »ÜÌ ©æÚU ·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 ©æÚU Âæ ×ð´ ç·¤âè ÂýàÙ ·¤æ ·¤æð§ü ©æÚU Ùãè´ çÎØæ »Øæ ãñ, Ìæð ·é¤Ü Øæð» ×ð´ âð ·¤æð§ü ¥´·¤ Ùãè´ ·¤æÅðU Áæ°¡»ðÐ 6. ÂÚUèÿææ ÂéçSÌ·¤æ °ß´ ©æÚU Âæ ·¤æ ØæÙÂêßü·¤ ÂýØæð» ·¤Úð´U Øæð´ç·¤ ç·¤âè Öè ÂçÚUçSÍçÌ ×ð´ (·ð¤ßÜ ÂÚUèÿææ ÂéçSÌ·¤æ °ß´ ©æÚU Âæ ·ð¤ â´·ð¤Ì ×ð´ çÖóæÌæ ·¤è çSÍçÌ ·¤æð ÀUæðǸ·¤ÚU), ÎêâÚUè ÂÚUèÿææ ÂéçSÌ·¤æ ©ÂÜÏ Ùãè´ ·¤ÚUæØè Áæ°»èÐ 7. ©æÚU Âæ 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 ÂýØð·¤ ÂëD ÂÚU Ùè¿ð ·¤è ¥æðÚU ¥æñÚU ÂéçSÌ·¤æ ·ð¤ ¥´Ì ×ð´ °·¤ ÂëD ÂÚU (ÂëD 39) Îè »§ü ãñÐ 8. ÂÚèÿææ âÂóæ ãæðÙð ÂÚU, ÂÚUèÿææÍèü ·¤ÿæ/ãæòÜ ÀUæðǸÙð âð Âêßü ©æÚU Âæ ·¤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 ÂýØð·¤ 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 ©æÚU Âæ çΰ çÕÙæ °ß´ ©ÂçSÍçÌ Âæ ÂÚU ÎéÕæÚUæ ãSÌæÿæÚU ç·¤° çÕÙæ ·¤æð§ü ÂÚUèÿææÍèü ÂÚUèÿææ ãæòÜ Ùãè´ ÀUæðǸð´»ðÐ ØçÎ ç·¤âè ÂÚUèÿææÍèü Ùð ÎêâÚUè ÕæÚU ©ÂçSÍçÌ Âæ ÂÚU ãSÌæÿæÚU Ùãè´ ç·¤° Ìæð Øã ×æÙæ Áæ°»æ ç·¤ ©âÙð ©æÚU Âæ Ùãè´ ÜæñÅUæØæ ãñ çÁâð ¥Ùéç¿Ì âæÏÙ ÂýØæð» æðæè ×ð´ ×æÙæ Áæ°»æÐ ÂÚUèÿææÍèü ¥ÂÙð ÕæØð´ ãæÍ ·ð¤ ¥´»êÆðU ·¤æ çÙàææÙ ©ÂçSÍçÌ Âæ ×ð´ çΰ »° SÍæÙ ÂÚU ¥ßàØ Ü»æ°¡Ð 12. §ÜðÅþUæòçÙ·¤/ãSÌ¿æçÜÌ ÂçÚU·¤Ü·¤ °ß´ ×æðÕæ§Ü ȤæðÙ, ÂðÁÚU §ØæçÎ Áñâð ç·¤âè §ÜðÅþUæòçÙ·¤ ©Â·¤ÚUæ ·¤æ ÂýØæð» ßçÁüÌ ãñÐ 13. ÂÚUèÿææ ãæòÜ ×ð´ ¥æ¿ÚUæ ·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 ©æÚU Âæ ·¤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¤ §ÜðÅþUæòçÙ·¤ ©Â·¤ÚUææð´ 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 (Side1) with Blue/Black Ball Point Pen. 2. For writing/marking particulars on Side2 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, onefourth (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