2019-SOLUTIONS-JEE ENTRANCE...

Vidyamandir Classes

VMC | Paper-1 1 Joint Entrance Exam-2019 | Advanced

SOLUTIONS 2019-Joint Entrance Examination - Advanced | Paper-1

PART-I PHYSICS

SECTION-1

1.(4) (1) The potential is reduced by dq

dv kR

Also, 0 kQ

vR

2

20

( 4 )

(4 )

dv dq R

v Q R 0 dv v

(1) is wrong

(2) The field is reduced by 02

vkdq dvdE

R RR

(2) is wrong

(3) Initial field at centre is zero, so field increases by 02

vkdq dvdE

R RR

(3) is wrong

(4) Potential at centre 0 0(1 ) v dv v

Potential at 0 0 02 (1 2 )2 ( / 2)

R kdqv v dv v

R

Ratio1

1 2

(4) is correct

2.(2) A particle at distance r will experience gravitational force by the sphere of radius r (or mass say M)

2 2

2

2GM mv v K rm M r

r Gm m Gmr

2

2KdM dr

Gm

22

24

Kr dr dr

Gm

2 22

K

r m G

3.(4) 1 2( )0

tkN N e

1 2( )0 0[1 t

Ca Ar KN N N N N e

Given : 1 2

1 2

( )

( )

199 99

t

Ca Art

K

N N e

N e

1 2( ) 1

100 te

Vidyamandir Classes


1 2( ) 100 2 10 t n n

10 1010

2(2 3) 4610 9.2 10

5(4 5 0 5) 10

t Years

4.(2) 1/40( ) (1 ) T t T t

4

0

0

( )

T t Tt

BT

Differentiating w.r.t. time

304 4

0

1 ( )4[ ( ) ] 1

dT t

T t TdtT

… (i)

Also dQ CdT dT P

Pdt dt dt C

(C – heat capacity)

Putting in (i) :

3

04 4

0

4 [ ( ) ]P T t TC

T

SECTION-2 1.(134) L mVR

As L and m are dimension less and [R] = L

1[ ] V L

Kinetic energy, 2 21[ ]

2 K mv K L

(3) is correct

Dimension of work is also 2L

2 3[ ] [ ] F L L F L

Power, 3 1 4[ ] [ ][ ] P FV P F v L L L

(2) is wrong

Linear momentum p mv

1[ ] [ ][ ] p m v L (4) is correct

2.(234) For 2h R and ,r R the sphere will completely be inside the cylinder.

enclosedQ Q

0

Q

(3) is correct

For 3

5

Rr and

4

2 5

h R

2 2 2

2 29 86

2 25

h R Rr R

For 3

5

Rr and ,

5

Rh the sphere will completely be outside the cylinder.

Vidyamandir Classes


0 0 enclosedQ (4) is correct

For 2h R and 3

5

Rr

3

sin5

r

R

Area of curved surface of sphere enclosed by cylinder

22[2 (1 cos ) ] S R

2 44 1

5

S R

2 54

enclosedQ Q

Q SR

05

Q

(2) is correct

Similarly, for 4

2 ,5

R

h R r

4

sin5

2 2 32[2 (1 cos ) ] 4 1

5

S R R

2

2

54enclosed

Q QQ S

R

0

2

5

Q

(1) is wrong

3.(123) In case I, capillary rise in 1T is 3

2 cos0 2(0.075)(1) 757.5

10001000(10)(0.2 10 )

h mgr

cm

(3) is correct

In case II, capillary rise in 2T is 2 cos60

3.75

hgr

cm

(1) is correct

In case I, if joint is 5 cm above water, water will not rise in 2T as the surface tension force

( 2 cos60 ) r can balance the weight of only 3.75 cm water column. Water will rise till 5 cm

and its curvature will adjust at some angle between 0 and 60° to balance the weight of 5 cm water column

(4) is wrong Due to different volume of meniscus, the correct will be different for both cases. (2) is correct.

4.(134) The x-comp of dl is parallel to velocity so, emf is induced only due to its y-component

0 0 01

yd Bv dy B v dy

L

2

0 0

0

1

yB v dy

L

1

0 0 0 01 1

1( 1) 1

LB v L B v L

L

As the integration is independent of the shape of wire so we can replace by a straight wire with same initial and final y-coordinates,

Vidyamandir Classes


(1) is correct

For 0 00, 2 B v L

(2) is wrong

For 0 04

2,3

B v L

(3) is correct

As L (4) is correct

5.(124) When 1 2n n n

1 1 1 2( 1)

( 1)n

nf R R R

… (i)

When 1 2,n n n n n

1 2

1 1 1 1 1 1 1( 1) ( 1)n n n

f f f f R R

1 (2 2)

n n

f f R … (ii)

( ) ( )i ii

2( 1) 2 2

12 2 2 2 2 2

f f n f n n

f n n f n n n n

As ( 1)n n

1

12( 1)2 1

df n n

f n nn

As the ratio of independent of sign of radius of curvature,

(1) is correct

f

f and

n

n

are opposite in sign (as 1)n

(2) is correct

Also 1 1 1

2 2 1 12

nn n

f n

f n

(3) is wrong

For 31.5, 10 , 20n n t cm

3(10 )

(20) 0.022(1.5 1)

f cm (4) is correct

6.(3, 4) Just after 1S is closed, capacitors behave as zero resistance wires (as they are initially uncharged)

5

25100 30 70

I A mA

(3) is correct

After 1S is closed for a long time current will be zero. Assuming total charge circulation to be q in

anticlockwise direction, and applying KVL,

Vidyamandir Classes


5 010 80 80

q q q

40q C

Voltage across 140

4 volts10

C

(4) is correct

Also 1

4 voltsP Q CV V V

(1) is wrong

Now immediately after 2S is also closed, charges remain same

1

404

10CV V

2

0CV

3

400.5

80CV V

4

400.5

80CV V

Applying KVL in two loops 4 30 10 70( ) 0x x y

100 70 6x y . . . . (i)

4 0.5 5 30 0.5 100 70( ) 0y y x y

200 70 0y x . . . . . (ii)

Solving (i) and (ii), 0.0769x A

7.(2, 4) 3 6100 10 2 10 VR 350 10 50VR k

(3) is wrong

16 32 10 10 1 10 AR 320 10 0.02AR

(2) is correct

Reading of (A) :

V

AV

IR R

RR R

Reading of (V) : V

V

R RV I

R R

Measured value of (50000) (1000)

980.4(51000)

V

V

R RVR

I R R

(4) is correct

If the ideal cell replaced by a cell of internal resistance 5 , reading of ammeter (I) and voltmeter

V

V

R RV I

R R

will change, but V

I remains same.

(1) is wrong.

Vidyamandir Classes


8.(3, 4) Process 1 2 and 3 4 are isobaric (as )V T

Process 2 3 and 4 1 are isochoric (as V is constant)

(1) is wrong 1 2 0( )P PQ nC T nC T

03 4 2P P

TQ nC T nC

1 2

3 4

2Q

Q

(2) is wrong 1 2 0( )W P V nR T nR T

2 3 0W

3 4 0W

Total work, 0 0

2 2

nRT RTW

(3) is correct 1 2 0( )P PQ nC T nC T

2 3 0( )V VQ nC T nC T

1 2

2 3

5

3P

V

Q C

Q C

(4) is correct

SECTION-3 1.(8.12 or 8.13)

1330 10

(120)330

f

2330 10cos53

(120)330 30cos37

f

330 6(120)

330 24

2 1bf f f 336 340

(120) 8.128306 330

2.(0.75) ˆ ˆ( 2 )F yi xj N

ˆ ˆ ˆ ˆ. ( 2 ) .( )dw F dr yi xj dxi dyj

2ydx xdy For AB : dy = 0, y = 1

1

0

ABw dx

For BC : dx = 0, x = 1

0.5

1

2 2 ( 0.5)BCw dy

Vidyamandir Classes


For CD : dy = 0, y = 0.5 0.5

1

(0.5) (0.5 ) ( 0.5) 0.25CDw dx

For DE : dx = 0, x = 0.5 0

0.5

2 (0.5) ( 0.5) 0.5DEw dy

For EF : dy = 0, y = 0 0FEw

For FA : dx = 0, x = 0 0FAw

Total work ( ) ( 0.25 ) ( 0.5 ) 0 0 0.75 0.75( 1) 0.75

3.(50.00) Time taken to cross the structure ( sinV is the velocity along the length)

sin

Lt

V

For max ,sint should be minimum

So, should be minimum angle for TIR

1.44

sin sin1.5C C

max 11.44

1.5

Lt

V

Also, 8

8

1

3 102 10

1.5

CV

n

8 9max 8

9.6 1.55 10 50 10

2 10 1.44t s s

4.(1.00) For very large N, is very small. Let it be dx

d N

x m m d

N x

Capacitance of elemental capacitor

0 01mK A AxdC K

d dx

Such capacitors are connected in series

0 00

1 12

dd dx d

nC dC K A d x K A

0 12

K AC

d n

5.(2.00) 1 2sin 60 sin30T T

2 13T T 1 2cos60 cos30T T mg

11 1 1

33 100 2 100 50

2 2

TT T T N

2 13 50 3T T N

T

AY

1 1 2

2 2 1

1 3(2) 2

13

T Yc

s T Y

Vidyamandir Classes


6.(270.00) 5( ) (80 30) 5 (110 80)s L C , where C is heat capacity of calorimeter

250 5 30s L C

80( ) (50 30) (80 50)s C

1600 30s c 250 5 1600s L s 5 1350 270L

L ss

PART-II CHEMISTRY

SECTION-1

1.(4) 2 6 4HC C , CH CH and p - MeO C H acts as electron withdrawing group while

3 2CH CH acts as electron releasing group. Presence of electron withdrawing group increases

acidic strength while presence of electron releasing group decreases acidic strength.

2.(4) 32 3 2 3Cr (salt) B O Cr(BO )

Green beads of chromium metaborate will be formed.

3.(2) Calamine 3ZnCO Malachite 3 2CuCO Cu(OH)

Magnetite 3 4Fe O Cryolite 3 6Na AlF

4.(3) Molar conductivity decreases with concentration till CMC & further decreases rapidly beyond

CMC.

SECTION-2

1.(3, 4) Here 2Q SnCl

2SnCl Cl 3(X)Sn Cl 3(sp hybrid, pyramidal)

2 3 3 2(Y)

SnCl Me N Me N SnCl (Coordination compound)

2 2 4(Z)

SnCl 2CuCl SnCl 2CuCl

2.(3, 4) Standard formation of enthalpy is the enthalpy involved in the reaction when one mole of a

substance is formed from its constituent elements in their standard elemental state.

8 2 2

2 3

1S (s) O (g) SO (g)

8 formation reactions3

O (g) O (g)2

Vidyamandir Classes


3.(1, 2, 3) 2 2 2 4 2(W)

1MnO 2KOH O K MnO H O

2

(W) 6Mn state, paramagnetic, green coloured and tetrahedral shape of the anion 24MnO

Structure bonds between (d)(p)

O Mn

Electrolyric4Oxidation

W KMnO (X)

(X) 7Mn , diamagnetic, purple coloured and tetrahedral shape of the anion 14MnO

Structure

(d)(p)

O Mn

4.(3, 4) (3) 2 3 3 3NO , NH , POCl , CH Cl (polar molecule)

(4) 2 6 5 2 5SO , C H Cl, H Se, BrF (polar molecule)

5.(1, 2, 4) rms3RT

M rms

1

M

av3

kT2

independent of molar mass

rms T

rms is doubled when temperature is increased four times

6.(2, 3)

7.(1, 3, 4) Sucrose 2(leavo)(dextro)

H O glucose + fructose

Glucose [O] gluconic acid

Monosaccharides are simplest carbohydrates and can't be hydrolysed

Cyclic hemiacetal pyranose (six membered) forms of glucose are called as anomers.

8.(1, 2, 4) 31 2 4XX X X238 234 234 234 23092 90 91 90U Th Pa Z Th

1X : particle 2X : particle

3X : particle 4X : particle

Z : 23492 Z (isotope of uranium)

Vidyamandir Classes


SECTION-3

1.(8.92) 2 2Fe (aq) S (aq) FeS(s) 17CK 1.6 10

0.03 M 0.1 M 0.03 x 0.1 x

Since CK 1 x 0.03

2[S ] 0.1 0.03 0.07M

2 217

1[Fe ][S ]

1.6 10

2 17 17 171[Fe ] 10 8.928 10 y 10

1.6 0.07

y 8.93 (Round off)

or y 8.92 (After Truncation)

2.(6.75) x y zr k[A] [B] [C]

5 x y z6 10 k(0.2) (0.1) (0.1) ........ (i)

5 x y z6 10 k(0.2) (0.2) (0.1) ........ (ii)

4 x y z1.2 10 k(0.2) (0.1) (0.2) ........ (iii)

5 x y z9 10 k(0.3) (0.1) (0.1) ........ (iv) From (i) & (ii) y 0

From (i) & (iii) z 1

From (i) & (iv) x 1

r k[A][C]

From equation (i)

56 10 k(0.2)(0.1)

5

32

6 10k 3 10

2 10

3r 3 10 [A][C]

For 3 3 3[A] 0.15mol dm , [B] 0.25mol dm & [C] 0.15mol dm

3r 3 10 0.15 0.15

5r 6.75 10

y 6.75

3.(4)

Vidyamandir Classes


4.(4)

5.(1.03) 650 640 0.5 78i

640 M 39

f fT i K m

650 640 M 39 0.5 10005.12

640 0.5 78 M 39

10 10005.12 1.025 1.03

640 78

6.(19) 4 2 2 6 2XeF O F XeF O

Vidyamandir Classes


PART-III MATHEMATICS

SECTION-1

1.(3) 1 11

2 1

y

x

1 2 y x 1 x y

1 y x

0 0

0 0

4 4 2

2 ( ) ( ) 2

z z x

z z i x iy x iy i 4 2 4 2 4 2 1

2 2 2 ( 1) 2 (2 )

x x x

iiy i i y i x i

2.(3) 1 M I M

2 0 M M I ( ) rT M 4 4 1sin cos , 1

2

4 4 2 2| | ( (1 )(1 )) M S C S C 4 4 2 2 2 2( 2), S C S C S C t

2 1( 2) 0,

4

t t t

* 1

2

* * *37 29

16 16

3.(3) Line with slope 1

mpassing through (3, –2)

3 2 n my m

( 1) (3 2 ) x m mx m

2

3 3 3

51

m

xm

215 15 3 3 m m

23 15 18 2 m m

2 5 6 0 m m 2,3m

4.(4)

2 8

2

1 2

87 x dx dx

x

78 4 7

3 n 14

16 23

n sq. units

Vidyamandir Classes


SECTION-2 1.(2, 4) 1B = Event of selection of bag 1B (5 Red, 5 green)

13

( )10

P B

2B = Event of selection of Bag 2B (3 Red, 5 Green)

13

( )10

P B

3 B Event of selection of Bag 2B (5 Red, 3 Green)

34

( )10

P B

R Event of selection of Red Ball

G Event of selection of a Green Ball.

1 1 2 2 3 3( ) ( / ) ( ) ( / ) ( ) ( / ) ( ) P G P G B P B P G B P B P G B P B

5 3 5 3 3 4 39

10 10 8 10 8 10 80

3 3 33

( ) ( / ) ( )( / )

( ) ( )

P B G P G B P BP B G

P G P G

12 12 480 39 1339

80

33

( / )8

P G B

2.(1, 3, 4) 1 2(1 , 2 , 2 ), (2 , , 2 ) L L

D.Rs of 1 2L L (1 2 , 2 2 2 )

1 21ˆˆ( 2 2 ) 0 9 1 09

L L i j k

1 22ˆˆ ˆ(2 2 ) 0 9 29

L L i j k

1 28 2 2 4 2 4

, , , , ,9 9 9 9 9 9

N N

DRs of 1 2N N (2, 2, 1)

3.(2, 3) 6 cos 4 sin 12 sin 2 A

1 max 12, sin 2 14

R A

2 23 2

,2 2

a b

1 1

2,

2 2

n nn n

a b

Eccentricity 2

2

4 51 1

9 3 n

nn

be n

a

2 36, 3.... R R1 1

1224

11

2

N

n nn n

R R

Latus rectum

2

29

98

22 8

2 23

2

b

a

8 1

3 24 6

Vidyamandir Classes


4.(2, 3) ( ) dy

Y y X xdx

0,

pdy

Y y xdx

2

2 2 1

pdy

PY x xdx

21

'

dy x

ydx x

2' 1 0 xy x

21

, sin

xdy dx c x

x

cos dx d

2cos

sin

y d c | cos cos | cos n ec c

2

21 11

x

y n xx

5.(2, 3, 4) 2 1 0 x x

1 5

2

x

1 5 1 5, , ( )

2 2

5, 1, 1 2 1 21 0 0 n n n 2 1 21 0 0 n n n 1 1 2 2( ) ( ) ( ) 0 n n n n n n 1 2 1 20 n n n n n na a a a a a or 2 1 n n na a a

1 1 n n nb a a1 1 1 1 1 2 1 2( 1) ( 1)

n n n n n n

1 1( 2) ( 2)

n n1 15 5 5 5

2 2

5

n n

n nnb

1 1 1

1

10 1010 5

n n

nn

n n n

a 1 1 5 1 5 1 40 5 10

356 895 19 5 19 5 5

1 1 1

1

5

n n nr r

rr r r

a

1 1 1 1 1 11 1

1 1 1 15 5

n n n n

Vidyamandir Classes


1 1

15 5

n n n n

1 1 n na a 2 1 na

1 1 1

1 5 1 5 48 12

10 10 10 10 356 8910 19 5 19 5

n n

nn n n

bn

6.(1, 2, 4) 3 12 2

sin sinR

P Q

3 1sin , sin

2 2P Q

60 or 120 ; 30 or 150 P Q

60 , 30 , 90P Q R (Right triangle)

60 , 150 180P Q P Q (Not valid)

120 , 30 30P Q R (Valid)

120 , 150P Q (Not valid)

120 , 30 1P Q R q r

Slope of 1 / 4 1

3 3 / 4 3 3

RS

Equation: 3

3 32

x y

1 1

6 6k OE

27 1 28 7

16 16 4 2RS

Area

0 0 1

1 1 30 1

2 6 48

3 11

4 4

SOE

1 1 33 3(2 3)2 2 2

5 23 2 31

2

r

7.(1, 2, 3) 2adj. (adj. ) | |M M a = 2, b = 1

0 2 4 0 1 2

2 4 6 2 1 2 3 | | 2

6 2 2 3 1 1

M

2 1 1 2

2 3 2 2 2 3 2 2 4 3 3 3 3 1 2 3 2 2

Vidyamandir Classes


1 1 2 1 1 1 1 1 3

1 1 1 2(adj. ) adj. 2(adj. )

| |M M M M M

M

22 4 4adj. adj. | | ( 2) 16M M M

8.(1, 2, 3)

4 3 2

4

2

5 20 30 20 30

5( 1) 20 1

' 2 11 3

2 8 73

ln ( 2) 1

x x x xx

xx

f xx

x xx

x

3 220 60 60 20 02 0 1

" 4 8 1 31 3

2

x x x x

xf x x

xx

''(1 ) 4 0, ''(1 ) 2 0f f is continuous inf R ( )f ( )f is ontof

SECTION-3

1.(10.00) 2

1

2rAC

BC r

2 2 2AC BC AC AB

Vidyamandir Classes


2 4 AC AB AD16 18 23

4 1010

2.(0.75)

1 1

( , ,0) , ,02 2

ˆˆ

1 1 10

2 2 21 1 1

6 6 3

i j k

1 1 1 1 1 1 3ˆˆ 32 6 6 6 2 6 12

i j k

2 3 3(6 ) 36 0.75

144 4

3.(157.00) (1,3) {1,4,7,10,....}AP

(2,5) {2,7,12,17,....}AP

(3,7) {3,10,17,24,....}AP

(1,3) (2,5) (7,15) {7,22,37,52,...} AP AP AP

(2,5) (3,7) (17,35) {17,52,...}A AP AP

(1,3) (2,5) (3,7) (52,105) 157 AP AP AP AP a d

4.(4.00) /4 sin

sin/4

2 12

(1 )(2 cos2 )

x

x

eI dx

e x

/4 /4

2 20 0

2 2

2 cos 1 2sin

dx dxI

x x

/4 2

20

2 sec

1 3tan

x dx

x

1

20

2

1 3

dt

t

11

0

2 3tan

3 1/ 3

t

2 3

3 3

2 3

9I

2 4.327 27 4

81 I

5.(3.00) 22 2 2( )( ) a b c a b c a b c 2 3 2 a b c ab bc ca

2 2 21 1(( ) ( ) ( ) ) (1 1 4) 3

2 2 a b b c c a

Vidyamandir Classes


6.(0.50) 2 E seven1, two zeros

92 2

9.8( ) 36

2 m E C

1 21 2

( ) 18 1( / )

36 36 2

n E EP E E

Two zero’s in same row/column

1 0 0

1 1 1 0

1 1 1

3 6 18

Two zeros not in same row/column

1 1 0

1 0 1 1

1 1 1

2019-SOLUTIONS-JEE ENTRANCE...

Documents

Transcript of 2019-SOLUTIONS-JEE ENTRANCE...