7/25/2019 1505 Lts Paper 1 Aiot Dlp http://slidepdf.com/reader/full/1505-lts-paper-1-aiot-dlp 1/40 READ THE INSTRUCTIONS CAREFULLY / œi ; b u u n ' d ; u l i < GENERAL / l e ; : 1. This sealed booklet is your Question Paper. Do not break the seal till you are instructed to do so. ; g ek s g jcU / k i q f L r d k i z ' u i = g S A b ld h e q g j r c r d u r k s M + s tc r d b ld k f u n s Z ' k u f n ; k t k ; s A 2. Use the Optical Response sheet (ORS) provided separately for answering the questions. i z ' u k s a d k m Ÿ k j n s u s d s f y , v y x l s n h x ; h v k W I V h d y f jL i k a l' k h V (v k s - v k j- , l -) (ORS) d k m i ; k s x d j s a A 3. Blank spaces are provided within this booklet for rough work. d P p s d k ; Z d s f y , b li q f L r d k e s a [ k k y h LF k k u f n ; s x ; s g S a A 4. Write your name and form number in the space provided on the back cover of this booklet. , d i q f L r d k d s f i N y s i ` " B i j f n , x , LF k k u e s a v i u k u k e rF k k Q k W eZ u E cj f y f [ k ,A 5. After breaking the seal of the booklet, verify that the booklet contains 40 pages and all the 20 questions in each subject and along with the options are legible. b li q f L r d k d h e q g j r k s M + u s d s ck n œ i ; k t k ° p y s f d b le s a 40 i ` " B g S a v k S j v k S j i z R ; s d f o" k ;d s lH k h 20 i z ' u v k S j m u d s m Ÿ k j f od Y i B h d l s i < + s t k ld r s g S A QUESTION PAPER FORMAT AND MARKING SCHEME / i ' ui = d i :i v v d u ; tu : 6. The question paper has three parts : Physics, Chemistry and Mathematics. Each part has three sections. b li z ' u i = e s a r h u H k k x g S a % H k k S f r d f oK k u] jl k ; u f oK k u v k S j xf . k rA g j H k k x e s a r h u [ k . M g S a A 7. Carefully read the instructions given at the beginning of each section. i z R ; s d [ k . M d s i z k jE H k e s a f n ; s g q , f u n s Z ' k k s a d k s /; k u l s i < + s A 8. Section-I contains 10 multiple choice questions with one or more than one correct option. Marking scheme : +4 for correct answer, 0 if not attempted and –2 in all other cases. [ . M -I e s a 10 cg q f od Y i h ;i z ' u g S A f tu d s , d ; , d l v d f od Y i lg h g S a A v d ; tu : +4 lg h m Ÿ k j d s f y ,] 0 i z ; k lu g h a d ju s i j rF k k –2 v U ;lH k h v oL F k k v k s a e s a A 9. Section-II contains 2 ‘match the following’ type questions and you will have to match entries in Column-I with the entries in Column-II. Marking scheme : for each entry in column-I . +2 for correct answer, 0 if not attempted and –1 in all other cases. [ k . M -II e s a 2 ‘ l q e s f y r ’ i z k :i d s i z ' u g S a f tle s a v k i d y e -I d h i z f o" V ; k s a d k s d y e -II d h i z f of " V ; k s a l s l q e s f y r d j s a x s A v d ; tu : d k W y e -I d h i z R ; s d i z f of " V d s f y , +2 lg h m Ÿ k j d s f y ,] 0 i z ; k lu g h a d ju s i j rF k k –1 v U ; lH k h v oL F k k v k s a e s a A 10. There is no questions in SECTION-III / [ k . M –III e s a , d H k h i z ' u u g h a g S 11. Section-IV contains 8 questions. The answer to each question is a single digit integer ranging from 0 to 9 (both inclusive) Marking scheme : +4 for correct answer and 0 in all other cases. [ k . M -IV e s a 8 i z ' u g S a A i z R ; s d i z ' u d k 0 l s 9 r d ( n k s u k s a ' k k f ey ) d s ch p d k , d y v a d h ; i w . k k ± d g S A v d ; tu : +4 lg h m Ÿ k j d s f y ,rF k k 0 v U ;lH k h v oL F k k v k s a e s a A PAPER – 1 Test Type : ALL INDIA OPEN TEST(MAJOR) Test Pattern : JEE-Advanced TEST # 12 TEST DATE : 15 - 05 - 2016 TARGET : JEE (ADVANCED) 2016 LEADER TEST SERIES / JOINT PACKAGE COURSE Paper Code : 0000CT103115008 DISTANCE LEARNING PROGRAMME (Academic Session : 2015 - 2016) Time : 3 Hours Maximum Marks : 264 Please see the last page of this booklet for rest of the instructions / œi ; ' u n ' d y , b l i r d d v r e i B d i D O N O T B R E A K T H E S E A L S W I T H O U T B E I N G I N S T R U C T E D T O D O S O B Y T H E I N V I G I L A T O R / u { d d v u n ' d c u e g u r M
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READ THE INSTRUCTIONS CAREFULLY / œi; b u un ' d ; u l i<
GENERAL / l e ;:
1. This sealed booklet is your Question Paper. Do not break the seal till you are instructed to do so.
; g e k s g j c U / k i q f L r d k i z ' u i = g S A b ld h e q g j r c r d u r k s M + s tc r d b ld k f u n s Z ' k u f n ; k tk ; s A2. Use the Optical Response sheet (ORS) provided separately for answering the questions.
i z ' u k s a d k m Ÿ k j n s u s d s f y , v y x ls n h x ; h v k W I V h d y f j L i k a l ' k h V (v k s - v k j- , l-)(ORS) d k m i ; k s x d j s a A
3. Blank spaces are provided within this booklet for rough work.
d P p s d k ; Z d s f y , b l i q f L r d k e s a [ k k y h L F k k u f n ; s x ; s g S a A
4. Write your name and form number in the space provided on the back cover of this booklet.
, d i q f L r d k d s f i N y s i ` " B i j f n , x , L F k k u e s a v i u k u k e rF k k Q k W e Z u E c j f y f [ k ,A
5. After breaking the seal of the booklet, verify that the booklet contains 40 pages and all the 20 questions in each
subject and along with the options are legible.
b l i q f L r d k d h e q g j r k s M + u s d s c k n œ i ; k tk ° p y s f d b le s a40 i ` " B g S a v k S j v k S j i z R ; s d f o " k ; d s lH k h 20 i z ' u v k S j m u d s m Ÿ k j f o d Y i
B h d ls i < + s tk ld r s g S A
QUESTION PAPER FORMAT AND MARKING SCHEME / i 'ui= d i :i v v du ; tu:
6. The question paper has three parts : Physics, Chemistry and Mathematics. Each part has three sections.
b l i z ' u i = e s a r h u H k k x g S a % H k k S f r d f o K k u] j lk ; u f o K k u v k S j x f . k rA g j H k k x e s a r h u [ k . M g S a A
7. Carefully read the instructions given at the beginning of each section.
i z R ; s d [ k . M d s i z k j E H k e s a f n ; s g q , f u n s Z ' k k s a d k s / ; k u ls i < + s A
8. Section-I contains 10 multiple choice questions with one or more than one correct option.
Marking scheme : +4 for correct answer, 0 if not attempted and –2 in all other cases.
[ .M-I e s a10 c g q f o d Y i h ; i z ' u g S A f tu d s,d ; ,d l v d
f o d Y i lg h g S a A
v d ; tu: +4 lg h m Ÿ k j d s f y ,]0 i z ; k l u g h a d j u s i j rF k k –2 v U ; lH k h v o L F k k v k s a e s a A
9. Section-II contains 2 ‘match the following’ type questions and you will have to match entries in Column-I with the
entries in Column-II.
Marking scheme : for each entry in column-I. +2 for correct answer, 0 if not attempted and –1 in all other cases.
[ k . M -II e s a2 ‘ lq e s f y r ’ i z k :i d s i z ' u g S a f tle s a v k id ye-I d h i z f o " V ; k s a d k s
d ye-II d h i z f o f " V ; k s a ls lq e s f y r d j s a x s A
v d ; tu: d k W y e -I d h i z R ; s d i z f o f " V d s f y , +2 lg h m Ÿ k j d s f y ,]0 i z ; k l u g h a d j u s i j rF k k –1 v U ; lH k h v o L F k k v k s a e s a A
10. There is no questions in SECTION-III / [ k . M –III e s a , d H k h i z ' u u g h a g S
11. Section-IV contains 8 questions. The answer to each question is a single digit integer ranging from
0 to 9 (both inclusive)
Marking scheme : +4 for correct answer and 0 in all other cases.
[ k . M -IV e s a8 i z ' u g S a A i z R ; s d i z ' u d k0 ls 9 r d ( n k s u k s a ' k k f e y ) d s c h p d k , d y v a d h ; i w . k k ± d g S A
v d ; tu: +4 lg h m Ÿ k j d s f y , rF k k0 v U ; lH k h v o L F k k v k s a e s a A
PAPER – 1
Test Type : ALL INDIA OPEN TEST (MAJOR) Test Pattern : JEE-Advanced
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
SOME USEFUL CONSTANTS A tomic No. H = 1, B = 5, C = 6, N = 7, O = 8, F = 9, Al = 13, P = 15, S = 16, Cl = 17, Br = 35,
Xe = 54, Ce = 58,
A tomic masses : H = 1, Li = 7, B = 11, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24,
Al = 27, P = 31, S = 32, Cl = 35.5, Ca=40, Fe = 56, Br = 80, I = 127,
Xe = 131, Ba=137, Ce = 140,
LTS-2/40 0000CT103115008
Note : In case of any correction in the test paper, please mail to [email protected] within 2 days along with Paper Code
& Your Form No.( u V
; f n b l i z ' u i = e s a d k s b ZCorrection g k s r k s œ i ; kPaper Code , o a v k i d s Form No. , o a i w . k ZTest Details d s lk F k 2 f n u d s v U n j [email protected] i j mail d j s a A)
Space for Rough Work / dP p d ; d y, L u
Boltzmann constant k = 1.38 × 10 –23 JK –1
Coulomb's law constant
1
= ×1
4
Universal gravitational constant G = 6.67259 × 10 –11 N–m2 kg –2
Speed of light in vacuum c = 3 × 108 ms –1
Stefan–Boltzmann constant
= 5.67 × 10 –8 Wm –2 –K –4
Wien's displacement law constant b = 2.89 × 10 –3 m–K
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
P H Y S I C S
LTS-3/400000CT103115008
PART-1 : PHYSICS
H x
-1 :H rd oK u
SECTION–I : (Maximum Marks : 40)
[ .M–I : ( v dre v d: 40)
This section contains TEN questions.
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these
four option(s) is (are) correct.
For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS
Marking scheme :
+4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened
0 If none of the bubbles is darkened
–2 In all other cases
b l [ k . M e s anl i z ' u g S a i z R ; s d i z ' u e s a p k j f o d Y i(A), (B), (C) rF k k (D) g S a A b u p k j f o d Y i k s a e s a ls,d ; ,d l v d f o d Y i lg h g S a A i z R ; s d i z ' u e s a ] lH k h lg h f o d Y i ( f o d Y i k s a ) d s v u q :i c q y c q y s ( c q y c q y k s a ) d k s v k s -v k j- , l- e s v a d u ; k s tu k :
+4 ; f n f lQ Z lH k h lg h f o d Y i ( f o d Y i k s a ) d s v u q :i c q y c q y s ( c q y c q y k s a ) d k s d k y k f d ; k tk ; 0 ; f n d k s b Z H k h c q y c q y k d k y k u f d ; k g k s
–2 v U ; lH k h v o L F k k v k s a e s a1. Two identical blocks are resting on supports as shown. Two identical bullets travelling with the same
speed hit the blocks & get embedded in them in very short t ime. The blocks leave the contact immediately
after bullet strikes them. In case (i) bullet's velocity is toward centre of mass and in case (ii) bullet's
velocity is off centre. The kinetic energies after collision are K 1 & K
2 and maximum height reached by
the centre of mass are h1 & h
2respectively. Then :
n k s , d tS ls C y k W d f p = k u q lk j v k / k k j k s a i j f o j k e k o L F k k e s a g S A n k s , d tS lh x k s f y ; k ° le k u p k
V d j k r h g S rF k k c g q r v Y i le ; e s a b u e s a / k a l tk r h g S A x k s f y ; k s a d s V d j k u s d s B h d i ' p k r ~ C y k W
(i) e s a x k s y h d k o s x Ê O ; e k u d s s U Ê d h v k s j g S rF k k i z d j . k(ii) e s a x k s y h d k o s x d s U Ê ls i j s g S A V D d j d s c k n x
ÿ e ' k % K 1 rF k k K
2 rF k k Ê O ; e k u d s U Ê k j k i z k I r v f / k d r e ≈ ° p k b Z ÿ e ' k %h
1 o h
2 g S r k s % &
Case (i) Case (ii)
(A) K 1 < K
2(B) K
1 = K
2(C) h
1 > h
2(D) h
1= h
2
BEWARE OF NEGATIVE MARKING
HAVE CONTROL HAVE PATIENCE HAVE CONFIDENCE 100% SUCCESS
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
LTS-4/40 0000CT103115008
Space for Rough Work /dP p d ; d y, L u
2. A barometer is made of glass. It contains mercury (density 13.6 × 103 kg/m3, surface tension
0.085 N/m, angle of contact 143°). The barometer scale has a least count of 1mm. If the radius of
barometer tube is 0.5 mm, and height of mercury column recorded is 762 mm, what can be true
atmospheric pressure (in mm of mercury column) :-
d k ° p ls c u s c S j k s e h V j e s a ? k u R o13.6 × 103 kg/m3, i ` " B r u k o0.085 N/m o lE i d Z d k s . k143° o k y k i k j k H k j k g q v k g S b ld s i S e k u s d k v Y i r e k a d1mm g S A ; f n c S j k s e h V j u y h d h f = T ; k0.5 mm o i k j n ~ L r E H k d h n tZ ≈ ° p k b Z762 mm g k s r k s
o k L r f o d o k ; q e . M y h ; n k c ( i k j n ~ L r E H k i jmm e s a ) g k s ld r k g S % &
(A) 760 mm (B) 761 mm (C) 763 mm (D) 765 mm
3. For a certain transverse standing wave on a long string, an antinode is formed at x = 0 and next to it, a
node is formed at x = 0.10 m. The displacement y(t) of the string particle at x = 0 is shown in figure.
(A) Transverse displacement of the particle at x = 0.05m and t = 0.05 s is – 2 2 cm.
(B) Transverse displacement of the particle at x = 0.04 m and t = 0.025 s is – 2 2 cm.
(C) Speed of the travelling waves that interfere to produce this standing wave is 2 m/s.
(D) The transverse velocity of the string particle at x =1
15 m and t = 0.1 s is 20 cm/s
y(cm)0.05 0.1 0.15 0.2
t(s)
4
–4
f d lh y E c h j L lh i j , d v u q i z L F k v i z x k e h r j a x d s f y ; s , d i z L i U nx = 0 i j rF k k b ld s c k n , d f u L i U nx = 0.10 m
i j c u r k g S Ax = 0 i j j L lh d s d . k d k f o L F k k i uy(t) f p = e s a n ' k k Z ; k x ; k g S % &(A) x = 0.05m rF k k t = 0.05 s i j d . k d k v u q i z L F k f o L F k k i u – 2 2 cm g S A
(B) x = 0.04 m rF k k t = 0.025 s i j d . k d k v u q i z L F k f o L F k k i u – 2 2 cm g S A
(C) b lv i z x k e h r j a x d k s m R i U u d j u s d s f y ; s O ; f r d f j r g k s u s o k y h i z x k e h r j a x k s a d h p k y2 m/s g S A
(D) x =1
15 m rF k k t = 0.1 s i j j L lh d s d . k d k v u q i z L F k o s x20 cm/s g S A
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
LTS-6/40 0000CT103115008
Space for Rough Work /dP p d ; d y, L u
5. A parallel beam of light is incident on a lens of focal length 10 cm. A parallel slab of refractive index
1.5 and thickness 3 cm is placed on the other side of the lens. The Nature of the final image from the
lens slab combination is: (Assume rays to be paraxial) :-
(A) At Distance of 11 cm and Image is virtual if x = 12 cm.
(B) At Distance of 11 cm and Image is real if x = 14 cm.(C) At the Distance of 11 cm and Image is Virtual if x = 16 cm
(D) At Distance of 11 cm and Image is real if x = 5 cm.
x
Q k s d l n w j h10 cm o k y s y s a l i j , d le k U r j i z d k ' k i a q tv k i f r r g k s r k g S A y s a l d s n w lj h v k s j1.5 v i o r Z u k a d rF k k3 cm
e k s V k b Z o k y h , d le k U r j i f Í d k j [ k n h tk r h g S A y s a l& i f Í d k f u d k ; ls v a f r e i z f r f c E c ( f d j . k k s a d k s
(A) v k H k k lh g k s x k rF k k11 cm d h n w j h i j g k s x k ; f nx = 12 cm g k s A(B) o k L r f o d g k s x k rF k k11 cm d h n w j h i j g k s x k ; f nx = 14 cm g k s A
(C) v k H k k lh g k s x k rF k k11 cm d h n w j h i j g k s x k ; f nx = 16 cm g k s A
(D) o k L r f o d g k s x k rF k k11 cm d h n w j h i j g k s x k ; f nx = 5 cm g k s A
6. A bead is connected at one end of an inextensible massless string whose other end is fixed to a fixed
vertical cylinder. Cylinder does not rotate. The bead can move on a horizontal smooth surface. The
bead is given a velocity v0 perpendicular to the string. The bead moves on a curve and consequently
collides on the cylinder after sometime. Then, before it collides:
(A)Work done by string on the bead is positive(B) The speed of the bead remains v
0.
(C) The tension in the string remains constant.
(D) Kinetic energy of bead increases gradually.
R
V0
f d lh d . k d k s v f o r k U ; Ê O ; e k u g h u j L lh d s , d f lj s i j tk s M + k tk r k g S f tld k n w lj k f lj k , d f L F k j ≈ / o k Z / k
g q v k g S A c s y u ? k w . k Z u u g h d j r k g S A ; g d . k k S f r t f p d u h lr g i j x f r d j ld r k g S A d . k d k s j L lh d sv0 o s x f n ; k
tk r k g S A d . k o ÿ i j x f r d j r k g q v k d q N le ; i ' p k r ~ c s y u i j V d j k r k g S A r c V d j k u s ls i g y s % &
(A) j L lh k j k d . k i j f d ; k x ; k d k ; Z / k u k R e d g S A(B) d . k d h p k yv0 c u h j g r h g S A
(C) j L lh e s a r u k o f u ; r c u k j g r k g S A (D) d . k d h x f r t ≈ tk Z / k h j s & / k h j s c < + r h g S A
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
LTS-8/40 0000CT103115008
Space for Rough Work /dP p d ; d y, L u
8. A small bead of mass m is threaded on a smooth circular ring of radius a in xy plane as shown. The
bead experiences a force whose potential energy is given by2 2
2 2
x yV C
a b
b > a . The bead is at
x = a at rest as shown. Neglect gravity. Choose the CORRECT statement(s):-
(A) At initial position, normal force =2c
a(B) At initial position, there is no acceleration.
(C) If the bead was at y = a at rest , it's normal force is 2
2ca
b(D) If the bead was at y = a at rest, there is no acceleration.
x
y
Ê O ; e k um d k , d N k s V k d . k f p = k u q lk jxy r y e s aa f = T ; k d h f p d u h o ` Ÿ k k d k j o y ; i j c a / k k g S A d . k i j , d c y y
g S f tld h f L F k f r t ≈ tk Z2 2
2 2
x yV C
a b
b > a k j k n h tk r h g S A d . k f p = k u q lk jx = a i j f o j k e k o L F k k e s a g S A x q
d k s u x . ; e k u s a Alg dF k u@ dF k u k s a d k s p q f u ; s % &
(A) Á k j f E H k d f L F k f r i j v f H k y E c c y2c
a g S A
(B) i z k j f E H k d f L F k f r i j d k s b Z R o j . k u g h a y x r k g S A
(C) ; f n d . k y = a i j f o j k e k o L F k k e s a g S r k s b ld k v f H k y E c c y2
2ca
b g S A
(D) ; f n d . k y = a i j f o j k e k o L F k k e s a g S r k s d k s b Z R o j . k u g h y x r k g S A
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
LTS-10/40 0000CT103115008
10. In a toy gun, we have a horizontal hollow smooth pipe. Two blocks of different masses are fitted in it.
The spring can be compressed by a certain distance and then released. It was seen that (case-1) when
m1 is fixed & m
2was released, it comes out with a speed of 4 m/s. (case-2) when m
2 was fixed & m
1
was released, it comes out with a speed of 2m/s. In all cases, initial compression of spring was same &
finally it remains at natural length (spring is not connected to either blocks).
(A) If both blocks are released simultaneously, v1 =
2
5 m/s and 2
8v
5 m/s.
(B) If both blocks are released simultaneously, 1
20v
4 m/s and
2v 20 m/s.
(C) m2 took lesser time to come out in case-1 than m
1 in case-2.
(D) m2 took more time to come out in case-1 than m
1 in case-2.
m1 m2
, d f [ k y k S u s e s a , d k S f r t [ k k s [ k y k f p d u k i k b i f y ; k tk r k g S A b le s a v y x& v y x Ê O ; e k u o k y s n k s
tk r s g S A f L i z a x d k s d q N n w j h r d lE i h f M + r d j f o j k e k o L F k k ls N k s M + f n ; k tk r k g S A ; g n s [ k k-1 e s a tcm1
f L F k j g S rF k km2 d k s f o j k e k o L F k k ls N k s M + k tk r k g S r k s ; g4 m/s d h p k y ls c k g j v k r k g S A i z d j . k -2 e s a tcm
2 f L F k j g S rF k k
m1 d k s f o j k e k o L F k k ls N k s M + k tk r k g S r k s ; g2m/s p k y ls c k g j v k r k g S A lH k h i z d j . k k s a e s a f L i a z a x d k i z k j f E H
F k k rF k k v a r e s a ; g v i u h e w y y E c k b Z e s a j g r h g S A ( f L i z a x f d lh H k h C y k W d ls tq M + h g q b Z
(A) ; f n n k s u k s a C y k W d k s d k s , d lk F k f o j k e k o L F k k ls N k s M + k tk ; s r k sv1 =
2
5 m/s o 2
8v
5 m/s g k s x k A
(B) ; f n n k s u k s a C y k W d k s a d k s , d lk F k f o j k e k o L F k k ls N k s M + k tk ; s r k s1
20v
4 m/s o
2v 20 m/s g k s x k A
(C) i z d j . k -1 e s am2 ] i z d j . k -2 e s am
1 d h r q y u k e s a c k g j f u d y u s e s a d e le ; y s x k A
(D) i z d j . k -1 e s am2 ] i z d j . k -2 e s am
1 d h r q y u k e s a c k g j f u d y u s e s a v f / k d le ; y s x k A
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
P H Y S I C S
LTS-11/400000CT103115008
SECTION–II : (Maximum Marks : 16)
[ .M
–II : ( v dre v d
: 16)
This section contains TWO questions.
Each question contains two columns, Column-I and Column-II.
Column-I has four entries (A), (B), (C) and (D) Column-II has five entries (P), (Q), (R), (S) and (T)
Match the entries in Column-I with the entries in column-II.
One or more entries in Column-I may match with one or more entries in Column-II.
The ORS contains a 4 × 5 matrix whose layout will be similar to the one shown below :
(A) (P) (Q) (R) (S) (T)
(B) (P) (Q) (R) (S) (T)
(C) (P) (Q) (R) (S) (T)
(D) (P) (Q) (R) (S) (T)
For each entry in column-I, darken the bubbles of all the matching entries. For example, if entry
(A) in Column-I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS.
Similarly, for entries (B), (C) and (D).
Marking scheme :
For each entry in Column-I
+2 If only the bubble(s) corresponding to all the correct match(es) is (are) darkened
0 If none of the bubbles is darkened
–1 In all other cases
b l [ k . M e s an i z ' u g S a i z R ; s d i z ' u e s a n k s d k W y e g S a ]d ye-I rF k kd ye-II
d ye-I e s ap i z f o " V ; k °(A), (B), (C) rF k k (D) g S a d ye-II e s ai p i z f o f " V ; k °(P), (Q), (R), (S) rF k k (T) g S a d ye-I d h i z f o f " V ; k s a d kd ye-II d h i z f o f " V ; k s a ls lq e s f y r d j s a d ye-I d h , d ; k , d ls v f / k d i z f o f " V ; k ° ]d ye-II d h , d ; k , d ls v f / k d i z f o f " V ; k s a ls lq e s f y r g k s ld r h v k s -v k j- , l- e s a s u h p s n ' k k Z ; h x ; h tS lh4 × 5 v k O ; w g n h x ; h g S:
(A) (P) (Q) (R) (S) (T)
(B) (P) (Q) (R) (S) (T)
(C) (P) (Q) (R) (S) (T)
(D) (P) (Q) (R) (S) (T)
d ye
-I d h i z R ; s d i z f o f " V d s f y , lH k h l q e s f y r i z f o f " V ; k s a d s c q y c q y k s a d k s d k y k d j s a Ad ye-I d h i z f o f " V(A) i z f o f " V ; k s a(Q), (R) rF k k (T) ls lq e s f y r g k s ] r k s b u r h u k s a c q y c q y k s a d k s v k s -v k
d j s a A b lh i z d k j i z f o f " V ; k s a(B), (C) rF k k (D) d s f y ; s H k h d j s a v a d u ; k s tu k :
d ye-I d h i z R ; s d i z f o f " V d s f y , +2 ; f n f lQ Z lH k h f o d Y i ( f o d Y i k s a ) d s v u q :i c q y c q y s ( c q y c q y k s a ) d k s d k y k f d ; k tk ;
0 ; f n d k s b Z H k h c q y c q y k d k y k u f d ; k g k s –1 v U ; lH k h v o L F k k v k s a e s a
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
LTS-12/40 0000CT103115008
Space for Rough Work /dP p d ; d y, L u
1. A double slit interference pattern is produced on a screen as shown in the figure, using monochromatic
light of wavelength 500nm. Point P is the location of the central bright fringe, that is produced when
light waves arrive in phase without any path difference. A choice of three strips A, B and C of transparent
materials with different thicknesses and refractive indices is available, as shown in the table, these are
placed over one or both of the slits, singularly or in conjunction, causing the interference pattern to be
shifted across the screen from the original pattern. In the column-I, how the strips have been placed, ismentioned whereas in the column-II, order of the fringe at point P on the screen that will be produced
due to the placement of the strip (s), is shown. Correctly match both the column.
Column-I Column-II
(A) Only strip B is placed over slit-I (P) First Bright
(B) Strip A is placed over slit-I and strip C is (Q) Fourth Dark
placed over slit-II
(C) Strip A is placed over the slit-I and strip (R) Fifth Dark
B and strip C are placed over the slit-II
in conjunction.
(D) Strip A and strip C are placed over slit-I (in (S) Central Brightconjuction) and strip B is placed over slit-II. (T) First dark
Slit I
Slit II
P
Screen
Film A B C
Thickness5 1.5 0.25
in m
Re fractive index 1.5 2.5 2
, d f f L y V O ; f r d j . k i z f r :i d k s f p = k u q lk j i n s Z i j500nm r j a x n S / ; Z d s , d o . k h Z ; i z d k ' k k j k m R i U u f d ; k k f c U n qP d s U Ê h ; p e d h y h f ›U t d h f L F k f r g S tk s d y k e s a i z d k ' k r j a x k s a d s f c u k iF k k U r j i g q ° p u s i j
e k s V k b Z rF k k v i o r Z u k a d , o a i k j n ' k h Z i n k F k k s Z o k y h r h u i f Í d k v k s aA, B o C d k s u h p s i z n f ' k Z r r k f y d k e s a n ' k k Z ; k x ; kv d s y s ; k , d& n w lj s d s ≈ i j f d lh , d vF k o k n k s u k s a f L y V k s a i j j [ k u s i j i n s Z i j O ; f r d j . k i z f r :i] e w y i z f r
g k s ld r k g S A d k W y e -I e s a n ' k k Z ; k x ; k g S f d b u i f Í d k v k s a d k s f d l i z d k j j [ k k tk r k g S tc f d d k W y e -II e s a b u i f Í d k v k s a d k s j [ k u s d s d k j . k i n s Z i j f c U n qP i j m R i U u f ›U tk s a d k ÿ e n ' k k Z ; k x ; k g S A d k W y e lq e s y u d h f t; s s A
d ye-I d ye-II
(A) d s o y i f Í d k B d k s f L y V -I i j j [ k k tk r k g S (P) i z F k e p e d h y h (B) i f Í d k A d k s f L y V -I i j rF k k i f Í d kC d k s (Q) p r q F k Z v n h I r
f L y V -II i j j [ k k tk r k g S A(C) i f Í d k A d k s f L y V -I i j rF k k i f Í d kB o C (R) i k ° p o h v n h I r
d k s , d d s ≈ i j , d f L y V -II i j j [ k u s i j (D) i f Í d k A o C d k s , d d s ≈ i j , d f L y V -I i j (S) d s U Ê h ; p e d h y h
rF k k i f Í d kB d k s f L y V -II i j j [ k u s i j (T) i z F k e v n h I r
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
P H Y S I C S
LTS-13/400000CT103115008
Space for Rough Work /dP p d ; d y, L u
2. A square loop of conducting wire is placed near a long straight current carrying wire as shown. Match
the statements in column-I with the corresponding results in column-II.
Column-I Column-II
(A) If the magnitude of current I is increased (P) Induced current in the loop will be
clockwise(B) If the magnitude of current I is decreased (Q) Induced current in the loop will
be anticlockwise
(C) If the loop is moved away from the wire (R) wire will attract the loop
(D) If the loop is moved towards the wire (S) wire will repel the loop
(T) Torque about centre of mass of loop
is zero due to magnetie force
p k y d r k j ls c u s , d o x k Z d k j y w i d k s f p = k u q lk j , d y E c s lh / k s / k k j k o k g h r k j d s u tn h d j [ k k tk r k
d h f t; s A
d ye-I d ye-II
(A) ; f n / k k j kI d s i f j e k . k d k s c < + k ; k tk ; s r k s (P) y w i e s a i z s f j r / k k j k n f k . k k o r h Z g k s x h
(B) ; f n / k k j kI d s i f j e k . k d k s ? k V k ; k tk ; s r k s (Q) y w i e s a i z s f j r / k k j k o k e k o r h Z g k s x h A
(C) ; f n y w i d k s r k j ls n w j y s tk ; k tk ; s (R) r k j y w i d k s v k d f " k Z r d j s x k A(D) ; f n y w i d k s r k j d h v k s j y s tk ; k tk ; s (S) r k j y w i d k s i z f r d f " k Z r d j s x k A
(T) p q E c d h ; c y d s d k j . k y w i d s Ê O ; e k u
d s U Ê d s lk i s k c y k ? k w . k Z ' k w U ; g k s
SECTION–III : Integer Value Correct Type
[ .M–III : i . d e u lg i d
No question will be asked in section III / [ .M III e d b i 'u ug g A
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
P H Y S I C S
LTS-15/400000CT103115008
Space for Rough Work /dP p d ; d y, L u
3. Figure shows a conducting disc rotating about its axis in a perpendicular uniform and constant magnetic
field B. A resistor of resistance R is connected between the centre and the rim. The radius of the disc
is 5.0 cm, angular speed = 40 rad/s, B = 0.1 T and R = 1 . The current through the resistor in
milliampere is.
f p = e s a , d p k y d p d r h f d lh y E c o r ~ le :i f u ; r p q E c d h ; k s =B e s a b ld h v k d s lk i s k ? k w . k Z u d j j g h g S A f j e d s e/ ; , d i z f r j k s / kR tk s M + f n ; k tk r k g S A p d r h d h f = T ; k5.0 cm ] d k s . k h ; p k y = 40 rad/s, B = 0.1 T
o R = 1 g S A i z f r j k s / k e s a i z o k f g r / k k j k f e y h , f E i ; j e s a K k r d h f t; s A
× ×
R
×
×
×
×××××
×
×
×
×
4. A continuous flow geyser has water flowing in it at a continuous rate. It comes in at a rate of
0.08 litres/sec and leaves at a rate of 0.081 litres/sec. The temperature coefficient of thermal expansion
of water is 2 × 10 –3/°C. The specific heat capacity of water is 4000 J/kg°C. If the inlet temperature is
7°C at which the density of water is 103 kg/m3, what is the power consumed by geyser (in kW) ?
, d lr r ~ i z o k g x h tj e s a ty , d f u ; r n j ls i z o k f g r g k s j g k g S A ty b le s a0.08 y h V j@ ls d . M n j ls i z o s s ' k d j r k g S r
0.081 y h V j@ ls d . M n j ls c k g j f u d y r k g S A ty d k r k i h ; i z lk j . k r k i x q . k k a d2 × 10 –3/°C g k s r k g S A ty d h f o f ' k " V
≈ " e k / k k f j r k4000 J/kg°C g k s r h g S A ; f n i z o s ' k h r k i e k u7°C g k s f tl i j ty d k ? k u R o103
kg/m3
g k s r k s x h tj k j k O ; f ; r ' k f D r (kW e s a ) D ; k g k s x h \
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
LTS-16/40 0000CT103115008
Space for Rough Work /dP p d ; d y, L u
5. Two positive and two negative point charges (|Q| = 0.01 µC) are placed at the corners of a square
insulator frame of side 15 m and the side of the frame are hinged together. The frame is deformed into
a rhombus as shown. The new potential at the centre is given by volt. Fill in OMR sheet.
, d 15m H k q tk o k y s o x k Z d k j d q p k y d ›s e d s ' k h " k k s ± i j n k s / k u k R e d rF k k n k s Ω . k k R e d f c U n q v k(|Q| = 0.01 µC) j [ k s
tk r s g S a rF k k ›s e d h H k q tk d k s f p = k u q lk j , d lk F k d h y d h r d j n s r s s g S A b l ›s e d k s f p = k u q lk j , d
e s a c n y f n ; k tk r k g S A v c d s U Ê i j u ; s f oH k o d k e k u o k s Y V g k s r k s d k e k u K k r d j s a A
+Q –Q
–Q +Q
Q –Q
–Q +Q
74º
6. While expanding a mixture of gas did work P1V
1 – P
2V
2on the piston. Here P
1 and V
1 are initial
pressures and volumes and P2 and V
2 are final pressures and volumes. Find molar heat capacity of the
gas in this process. Take for mixture as 1.5. Express your answer in terms of xR where R is universal
gas constant. Fill x in OMR sheet.
, d x S lh ; f eJ . k i z lj . k d s n k S j k u f i L V u i jP1V
1 – P
2V
2 d k ; Z d j r k g S ] ; g k °P
1 o V
1 ÿ e ' k % i z k j f E H k d n k c o v k ; r u rF k k
P2 o V
2 ÿ e ' k % v a f r e n k c o v k ; r u g S A f eJ . k d s f y ; s = 1.5 y h f t; s A b l i z ÿ e e s a x S l d h e k s y j ≈ " e k / k k f j r k ; f
xR g k s r k sx d k e k u K k r d h f t; s AR lk o Z f = d x S l f u ; r k a d g S A
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
P H Y S I C S
LTS-17/400000CT103115008
Space for Rough Work /dP p d ; d y, L u
7. The body of mass m = 0.5 kg is held on a vertical wall by a force F of 15 N as shown in the figure is
applied on the body at an angle = 53º to the vertical (Figure). The coefficient of friction between the
body and the wall is µ = 0.5. Determine acceleration of the body in m/s2.
Ê O ; e k um = 0.5 kg o k y s f i . M d k s f p = k u q lk j , d ≈ / o k Z / k j n h o k j d s lg k j s15 N d k c yF y x k d j j k s d d j j [ k k x ; k
g S A c y d k s ≈ / o k Z / k j ls = 53º d k s . k i j y x k ; k tk r k g S A ; f n f i . M o n h o k j d s e/ ; ? k " k Z . k x q . k k a dµ = 0.5 g k s r k s f i . M
d k R o j . k(m/s2 e s a) K k r d h f t; s A
F
8. An electron of mass m when accelerated through a potential difference V, has de Broglie wavelength
. The de-Broglie wavelength associated with a particle of mass m/4 and charge e accelerated through
the same potential difference is n. Then find the value of n.
m n z O ; e k u d k , d b y s D V ™ k W u tcV f oH k o k U r j ls R o f j r g k s r k g S r k s b ld h M h c z z k W X y h r j a x n S / ; Z g S A le k u f oH k o k U r j ls R o f j
n z O ; e k um/4 rF k k v k o s ' ke o k y s , d d . k ls lE c a º M h & c z k W X y h r j a x n S / ; Zn g S r k sn d k e k u K k r d h f t,A
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
C H E M I S T R Y
LTS-19/400000CT103115008
Space for Rough Work /dP p d ; d y, L u
2. If heat of formation of PCl3(g) and PH
3(g) are 140 and 8 kJ /mole respectively and heat of atomisation
of phosphorous[P4(s)], chlorine and hydrogen are 320, 120 and 216 kJ/mole respectively then.
(A) Bond energy of P–Cl is 63 kJ/mole
(B) Bond energy of P–H is 210 kJ/mole
(C) Heat of formation of isolated gaseous hydrogen atom is 108 kJ/mole
(D) Heat of formation of isolated gaseous chlorine atom is 60 kJ/mole
; f n PCl3(g) rF k kPH
3(g) d s f u e k Z . k d h ≈ " e k ÿ e ' k %140 rF k k8 kJ / e k s y g S rF k k Q k W L Q k s j l [P
4(s)] ] D y k s j h u rF k k
g k b M ™ k s tu d h i j e k f . o ; d j . k d h ≈ " e k ÿ e ' k %320, 120 rF k k216 kJ/ e k s y g S r k s
(A) P–Cl d h c a / k ≈ tk Z63 kJ/ e k s y g S
(B) P–H d h c a / k ≈ tk Z210 kJ/ e k s y g S
(C) f o y f x r x S lh ; g k b M ™ k s tu i j e k . k q d h f u e k Z . k d h ≈ " e k108 kJ/ e k s y g S
(D) f o y f x r x S lh ; D y k s j h u i j e k . k q d h f u e k Z . k d h ≈ " e k60 kJ/ e k s y g S3. 100 L aqueous solution of KBr is electrolysed by using current of 9.65 ampere for 10 sec. using
Pt electrodes. Which of the following species will be produced due to electrolysis ?
KBr d s 100 L ty h ; f o y ; u d k s Pt b y s D V ™ k s M d k m i ; k s x d j d s10 sec. d s f y ; s 9.65 , s f E i ; j d h / k k j k d s i z ; k s x
k j k o S |q r v i ? k f V r f d ; k tk r k g S A o S |q r v i ? k V u d s d k j . k f u E u e s a ls d k S u lh L i h ' k h t m R i k f n
(A) H2
(B) O2 (C) Br 2 (D) KOH
4. Which of the following molecule(s) is/are non planar -
f u E u e s a ls d k S u ls v . k q v le r y h ; g S a-
(A) BF3
(B) SF6
(C) IF5
(D) PCl5
5. Which of the following option is/are CORRECT for solution of liquid NH3 with alkali metal -
(A) It is paramagnetic (B) It is blue in colour
(C) It is good conductor of electricity (D) It is nonconductor of electricity
f u E u e s a ls d k S u ls f o d Y i] k k j / k k r q d s n z o NH3 d s lk F k f o y ; u d s f y , lg h g S @ g a S \
(A) ; g v u q p q E c d h ; g S (B) ; g u h y s j a x d k g S
(C) ; g f o |q r d k lq p k y d g S (D) ; g f o |q r d k d q p k y d g S
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
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Space for Rough Work /dP p d ; d y, L u
9. C = CH C3
H H
CH3 OsO / NaHSO4 3 (A)
(B)(i) CF C3 –
(ii) Aq. KOH
O OH
O
Select correct statement(s) for above reaction sequence :
(A) A is pair of enantiomer and A and B are distereomers
(B) B is pair of enantiomer and A and B are distereomers
(C) A represents meso compound
(D) B represents meso compound
C = CH C3
H H
CH3 OsO / NaHSO4 3 (A)
(B)
(i) CF C3 –
(ii) Aq. KOH
OO
H
O
m i j k s D r v f H k f ÿ ; k ÿ e d s f y ; s lg h dF k u k s a d k p ; u d h f t; s &
(A) A i z f r f c E c :i le k o ; o h d k ; q X e g S rF k kA , o a B f o o f j e le k o ; o h g S
(B) B i z f r f c E c :i le k o ; o h d k ; q X e g S rF k kA , o a B f o o f j e le k o ; o h g S(C) A e h lk s ; k S f x d d k s i z n f ' k Z r d j r k g S
(D) B e h lk s ; k S f x d d k s i z n f ' k Z r d j r k g S
10. Which of the following compound(s) will form stable (isolable) hydrate on addition of H2O ?
f u E u e s a ls d k S u ls ; k S f x dH2O d k ; k s x d j k u s i j L F k k ; h ( i ` F k D d j . k h ;) g k b M ™ s V c u k ; s a x s a &
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
LTS-22/40 0000CT103115008
SECTION–II : (Maximum Marks : 16)
[ .M–II : ( v dre v d: 16)
This section contains TWO questions.
Each question contains two columns, Column-I and Column-II.
Column-I has four entries (A), (B), (C) and (D) Column-II has five entries (P), (Q), (R), (S) and (T)
Match the entries in Column-I with the entries in column-II.
One or more entries in Column-I may match with one or more entries in Column-II.
The ORS contains a 4 × 5 matrix whose layout will be similar to the one shown below :
(A) (P) (Q) (R) (S) (T)
(B) (P) (Q) (R) (S) (T)
(C) (P) (Q) (R) (S) (T)
(D) (P) (Q) (R) (S) (T)
For each entry in column-I, darken the bubbles of all the matching entries. For example, if entry(A) in Column-I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS.
Similarly, for entries (B), (C) and (D).
Marking scheme :
For each entry in Column-I
+2 If only the bubble(s) corresponding to all the correct match(es) is (are) darkened
0 If none of the bubbles is darkened
–1 In all other cases
b l [ k . M e s an i z ' u g S a
i z R ; s d i z ' u e s a n k s d k W y e g S a ]d ye
-I rF k kd ye
-II d ye-I e s ap i z f o " V ; k °(A), (B), (C) rF k k (D) g S a
d ye-II e s ai p i z f o f " V ; k °(P), (Q), (R), (S) rF k k (T) g S a
d ye
-I d h i z f o f " V ; k s a d kd ye
-II d h i z f o f " V ; k s a ls lq e s f y r d j s a
d ye-I d h , d ; k , d ls v f / k d i z f o f " V ; k ° ]d ye-II d h , d ; k , d ls v f / k d i z f o f " V ; k s a ls lq e s f y r g k s ld r h
v k s -v k j- , l- e s a s u h p s n ' k k Z ; h x ; h tS lh4 × 5 v k O ; w g n h x ; h g S:
(A) (P) (Q) (R) (S) (T)
(B) (P) (Q) (R) (S) (T)
(C) (P) (Q) (R) (S) (T)
(D) (P) (Q) (R) (S) (T)
d ye-I d h i z R ; s d i z f o f " V d s f y , lH k h l q e s f y r i z f o f " V ; k s a d s c q y c q y k s a d k s d k y k d j s a A
d ye-I d h i z f o f " V(A) i z f o f " V ; k s a(Q), (R) rF k k (T) ls lq e s f y r g k s ] r k s b u r h u k s a c q y c q y k s a d k s v k s -v k
d j s a A b lh i z d k j i z f o f " V ; k s a(B), (C) rF k k (D) d s f y ; s H k h d j s a
v a d u ; k s tu k : d ye-I d h i z R ; s d i z f o f " V d s f y , +2 ; f n f lQ Z lH k h f o d Y i ( f o d Y i k s a ) d s v u q :i c q y c q y s ( c q y c q y k s a ) d k s d k y k f d ; k tk ;
0 ; f n d k s b Z H k h c q y c q y k d k y k u f d ; k g k s –1 v U ; lH k h v o L F k k v k s a e s a
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
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3. Among the following find out total number of reagent(s), which give white precipitate with aqueous solu-
tion of Zn+2.
NH4OH, NaOH, (NH
4)
2S, K
4[Fe(CN)
6]
f u E u e s a ls , s ls v f H k d e Z d k s a d h d q y la [ ; k c r k b , s a tk sZn+2 d s ty h ; f o y ; u d s lk F k ' o s r v o k s i n s r s g a S A
NH4OH, NaOH, (NH
4)
2S, K
4[Fe(CN)
6]
4. Find the total number of species that do not exist.
H2, HeH – , He
2
+, Li2, O
2
2– , FeI3
f u E u e s a ls , s lh L i h ' k h t d h d q y la [ ; k c r k b ; s f tu d k v f L r R o u g h a g S A
H2, HeH – , He
2
+, Li2, O
2
2– , FeI3
5.
HOOC COOH
(A)
For the above compound how many statement(s) are true ?
(i) Total number of stereoisomers possible for (A) are 3
(ii) Total number of meso compounds possible for (A) is 1
(iii) Number of plane of symmetry in cis form of A are 2
(iv) cis form of above compound (A) is meso
(v) Number of enantiomeric pair possible for (A) is 1
HOOC COOH
(A)
m i j k s D r ; k S f x d d s f y ; s f d r u s dF k u lg h g S A
(i) (A) d s f y ; s f = f o e ~ le k o ; f o ; k s a d h lE H k k f o r d q y la [ ; k3 g S
(ii) (A) d s f y ; s e h lk s ; k S f x d k s a d h lE H k k f o r d q y la [ ; k1 g S
(iii) A d s f ll :i e s a le f e f r d s r y d h la [ ; k2 g S
(iv) m i j k s D r ; k S f x d(A) d k f l l :i e h l k s g S
(v) (A) d s f y ; s i z f r f c E c :i le k o ; o h ; q X e k s a d h lE H k k f o r la [ ; k1 g S
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
M A T H E M A T I C S
LTS-29/400000CT103115008
PART-3 : MATHEMATICS
H x
-3 :x . r
SECTION–I : (Maximum Marks : 40)
[ .M
–I : ( v dre v d
: 40)
This section contains TEN questions.
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these
four option(s) is (are) correct.
For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS
Marking scheme :
+4 If only the bubble(s) corresponding to all the correct option(s) is (are) darkened
0 If none of the bubbles is darkened
–2 In all other cases
b l [ k . M e s anl i z ' u g S a i z R ; s d i z ' u e s a p k j f o d Y i(A), (B), (C) rF k k (D) g S a A b u p k j f o d Y i k s a e s a ls,d ; ,d l v d f o d Y i lg h g S a A i z R ; s d i z ' u e s a ] lH k h lg h f o d Y i ( f o d Y i k s a ) d s v u q :i c q y c q y s ( c q y c q y k s a ) d k s v k s -v k j- , l- e s v a d u ; k s tu k :
+4 ; f n f lQ Z lH k h lg h f o d Y i ( f o d Y i k s a ) d s v u q :i c q y c q y s ( c q y c q y k s a ) d k s d k y k f d ; k tk ; 0 ; f n d k s b Z H k h c q y c q y k d k y k u f d ; k g k s
–2 v U ; lH k h v o L F k k v k s a e s a
1. Consider the plane P 2x – 2y + z = 9 and a point A(13,–11,15) not on the plane. Now which of the
following holds good ?
(A) foot of perpendicular from A on plane P is (1,1,9)
(B) image of point A in plane P is (–11,13,3)
(C) perpendicular distance of A from plane P is 18.
(D) The volume of tetrahedron formed by xy,yz,zx planes with plane P is 35/23.
e k u k le r yP 2x – 2y + z = 9 rF k k , d f c U n qA(13,–11,15) g S ] tk s le r y i j u g h a g S A v c f u E u e s a ls d k
lR ; g k s a x s \
(A) le r y P i j f c U n qA ls y E c d k i k n(1,1,9) g k s x k A
(B) le r y P e s a f c U n qA d k i z f r f c E c(–11,13,3) g k s x k A(C) le r y P ls f c U n q A d h y E c o r n w j h18 g k s x h A
(D) le r y P d s lk F kxy,yz,zx le r y k s a k j k f u f e Z r p r q " Q y d k v k ; r u35/23 g k s x k A
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
M A T H E M A T I C S
LTS-31/400000CT103115008
Space for Rough Work /dP p d ; d y, L u
e k u kA O ; q R ÿ e . k h ; o x Z v k O ; w g g S ] f tld k i z f r y k s e1
1 2 3
A 1 3 6
2 5 7
k j k f n ; k x ; k g S A v c f u E u e s a ls d k S u ls lR
(|A|, A d s lk j f . k d d k s n ' k k Z r k g S)-
(A) A o x Z le v k O ; w g g k s x k A (B) v u q j s [ k(adjA)11
2 g k s x k A
(C) v u q j s [ k (A adjA)3
2 g k s x k A (D) |A –1| = –2
5. Figure shows a parabola with vertex at origin and axis of symmetry along x-axis. S(1,0) is the focus of
parabola & A(t1) and B(t
2) are the extremeties of a focal chord making an angle of 30º with
positive x-axis. Which of the following holds good ?
(A) Latus rectum of parabola is 4 (B)2
1 1t 2 3t 1 (C) Length AB is 1 (D) 2
2 2t 2 3t 1
y
0
B(t )2
A(t )1
30º
S (1,0) x
f p = k u q lk j , d i j o y ; f tld k ' k h " k Z e w y f c U n q i j g S rF k kx- v k d h le f e r d s v u q f n ' k i j o y ; d h u k f H kS(1,0) g S rF k k
u k H k h ; th o k d s v f U r e f lj sA(t1) rF k kB(t
2) / k u k R e dx- v k d s lk F k30º d k d k s . k c u k r s g S A f u E u e s a ls d k S u ls lR
(A) i j o y ; d k u k f H k y E c 4 g k s x k A (B) 2
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
LTS-34/40 0000CT103115008
SECTION–II : (Maximum Marks : 16)
[ .M–II : ( v dre v d: 16)
This section contains TWO questions.
Each question contains two columns, Column-I and Column-II.
Column-I has four entries (A), (B), (C) and (D) Column-II has five entries (P), (Q), (R), (S) and (T)
Match the entries in Column-I with the entries in column-II.
One or more entries in Column-I may match with one or more entries in Column-II.
The ORS contains a 4 × 5 matrix whose layout will be similar to the one shown below :
(A) (P) (Q) (R) (S) (T)
(B) (P) (Q) (R) (S) (T)
(C) (P) (Q) (R) (S) (T)
(D) (P) (Q) (R) (S) (T)
For each entry in column-I, darken the bubbles of all the matching entries. For example, if entry
(A) in Column-I matches with entries (Q), (R) and (T), then darken these three bubbles in the ORS.
Similarly, for entries (B), (C) and (D).
Marking scheme :
For each entry in Column-I
+2 If only the bubble(s) corresponding to all the correct match(es) is (are) darkened
0 If none of the bubbles is darkened
–1 In all other cases
b l [ k . M e s an i z ' u g S a i z R ; s d i z ' u e s a n k s d k W y e g S a ]d ye-I rF k kd ye-II
d ye
-I e s ap i z f o " V ; k °(A), (B), (C) rF k k (D) g S a d ye-II e s ai p i z f o f " V ; k °(P), (Q), (R), (S) rF k k (T) g S a d ye-I d h i z f o f " V ; k s a d kd ye-II d h i z f o f " V ; k s a ls lq e s f y r d j s a d ye-I d h , d ; k , d ls v f / k d i z f o f " V ; k ° ]d ye-II d h , d ; k , d ls v f / k d i z f o f " V ; k s a ls lq e s f y r g k s ld r h v k s -v k j- , l- e s a s u h p s n ' k k Z ; h x ; h tS lh4 × 5 v k O ; w g n h x ; h g S:
(A) (P) (Q) (R) (S) (T)
(B) (P) (Q) (R) (S) (T)
(C) (P) (Q) (R) (S) (T)
(D) (P) (Q) (R) (S) (T)
d ye-I d h i z R ; s d i z f o f " V d s f y , lH k h l q e s f y r i z f o f " V ; k s a d s c q y c q y k s a d k s d k y k d j s a Ad ye-I d h i z f o f " V(A) i z f o f " V ; k s a(Q), (R) rF k k (T) ls lq e s f y r g k s ] r k s b u r h u k s a c q y c q y k s a d k s v k s -v k
d j s a A b lh i z d k j i z f o f " V ; k s a(B), (C) rF k k (D) d s f y ; s H k h d j s a v a d u ; k s tu k :
d ye-I d h i z R ; s d i z f o f " V d s f y , +2 ; f n f lQ Z lH k h f o d Y i ( f o d Y i k s a ) d s v u q :i c q y c q y s ( c q y c q y k s a ) d k s d k y k f d ; k tk ;
0 ; f n d k s b Z H k h c q y c q y k d k y k u f d ; k g k s –1 v U ; lH k h v o L F k k v k s a e s a
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
M A T H E M A T I C S
LTS-35/400000CT103115008
Space for Rough Work /dP p d ; d y, L u
1. Consider an experiment of tossing a fair of coin six times. Let A and B be two events defined as
follows
A : Number of heads greater than number of tails.
B : The third toss results in head. Now match the columns.
Column-I Column-II
(A) If a
P A b
where a and b are relatively prime then 'a' is (P) an even number
(B) If p
P Bq
, where p and q are relatively prime then 'q' is (Q) an odd number
(C) IfA u
PB v
where u and v are relatively prime then 'u' is (R) a prime number
(D) IfB m
P
A n
where m and n are relatively prime then (S) a composite number
3(m + n) is (T) neither prime nor
composite number
e k u k , d i j h k . k e s a , d f u " i k i k r h f lD d s d k s N % c k j m N k y k tk r k g S A e k u k n k s ? k V u k ; s aA rF k kB b l i z d k j i f jH k k f " k r g S
A : f p r k s a d h l a [ ; k ] i V k s a d h la [ ; k l s v f / k d g S A
B : r h lj h m N k y i j i f j . k k e f p r v k r k g S A v c L r E H k k s a d k f e y k u d h f t,
d ye-I d ye-II
(A) ; f n a
P A
b
g S ] tg k °a rF k k b i j L i j vH k k T ; l[ ; k ; s a g S ] r k sa g k s x k (P) , d le la [ ; k
(B) ; f n p
P Bq
g S ] tg k ° p rF k kq i j L i j vH k k T ; l[ ; k ; s a g S ] r k sq g k s x k (Q) , d f o " k e la [ ; k
(C) ; f nA u
PB v
g S ] tg k °u rF k k v i j L i j vH k k T ; la [ ; k ; s a g S ] r k su g k s x k (R) , d vH k k T ; la [ ; k
(D) ; f nB m
PA n
g S ] tg k ° m rF k kn i j L i j vH k k T ; la [ ; k ; s a g S ] (S) , d la ; q D r la [ ; k
r k s3(m + n) g k s x k (T) u k r k s vH k k T ; u k g h
ALL INDIA OPEN TEST/JEE (Advanced)/15-05-2016/PAPER-1
OPTICAL RESPONSE SHEET / v V dy i l ' V:
12. The ORS is machine-gradable and will be collected by the invigilator at the end of the examination.
v k s - v k j- , l- e ' k h u& tk ° P ; g S rF k k ; g i j h k k d s le k i u i j f u j h k d d s k j k , d = d j f y ; k tk ; s x k A13. Do not tamper with or mutilate the ORS. / v k s - v k j- , l- d k s g s j& Q s j@ f o œ f r u d j s a A14. Write your name, form number and sign with pen in the space provided for this purpose on the original. Do not write
any of these details anywhere else. Darken the appropriate bubble under each digit of your form number.
v i u k u k e] Q k W e Z u E c j v k S j v k s - v k j- , l- e s a f n , x , [ k k u k s a e s a d y e ls H k j s a v k S j v i u s g L r k k j d j s a A b uv k S j u f y [ k s a A Q k W e Z u E c j d s g j v a d d s u h p s v u q :i c q y c q y s d k s d k y k d j s a A
DARKENING THE BUBBLES ON THE ORS / v v ,l i c yc y d d y d u d o:
15. Use a BLACK BALL POINT PEN to darken the bubbles in the upper sheet.
≈ i j h e w y i ` " B d s c q y c q y k s a d k sd y c y o b V dye ls d k y k d j s a A16. Darken the bubble COMPLETELY / c q y c q y s d k si . :i l d k y k d j s a A17. Darken the bubbles ONLY if you are sure of the answer / c q y c q y k s a d k sr d k y k d j s a tc v k i d k m Ÿ k j f u f ' p r g k s A
18. The correct way of darkening a bubble is as shown here :
c q y c q y s d k sd y d j u s d k m i ; q D r r j h d k ; g k ° n ' k k Z ; k x ; k g S:
19. There is NO way to erase or "un-darken" a darkened bubble
d k y s f d ; s g q ; s c q y c q y s d k s f e V k u s d k d k s b Z r j h d kug g S A20. The marking scheme given at the beginning of each section gives details of how darkened and not darkened
bubbles are evaluated.
g j [ k . M d s i z k j E H k e s a n h x ; h v a d u ; k s tu k e s ad y d; x; rF k kd y u d; x, c q y c q y k s a d k s e w Y ; k a f d r d j u s d k r j h d k f n x ; k g S A
21. Take g = 10 m/s2 unless otherwise stated.
g = 10 m/s2 i z ; q D r d j s a ] tc r d f d v U ; d k s b Z e k u u g h a f n ; k x ; k g k s A
I HAVE READ ALL THE INSTRUCTIONS
AND SHALL ABIDE BY THEM
e u l un ' d i< y; g v e m ud
vo'; i yu d: x d: x A
____________________________
Signature of the Candidate / i d g r
I have verified the identity, name and roll
number of the candidate, and that question
paper and ORS codes are the same.
e u i d i p; u e v Q e u c d i
y; d i 'u i= r v v ,l d M n u le u g A
____________________________
Signature of the invigilator / u d d g r
NAME OF THE CANDIDATE / i d u e.................................................................................
FORM NO / Q e u c..............................................