28 5FGF D]lãT K[P Test Booklet Code 1 : PHYSICS ......2. The Answer Sheet is kept inside this Test...

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VF 5]l:TSFDF\ 28 5FGF D]lãT K[P

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BM,JFGM lGN["X D/[ tIFZ[ p¿Z 5+G[ ACFZ SF-L wIFG5}J"S lJUTM EZL

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Z;FI6 XF:+GF\ 5|tI[S EFUDF\ 𝟑𝟎 5|̀ GM K[ VG[ T[ ;DFG U]6 WZFJ[ K[P

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VFJX[P p¿Z5+DF\ SM.56 5|̀ GGM p¿Z G VF5TF D[/J[,F S],

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OST E}ZL q SF/L AM, 5M.g8 5[G GM p5IMU SZJMP 5[lg;,GM p5IMU

;J"YF lGlQFâ K[P

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PAPER – 1 : PHYSICS, MATHEMATICS & CHEMISTRY

5ZL1FF 5]l:TSF v 1 o EF{lTS XF:+4 Ul6T VG[ Z;FI6 XF:+

A

[ Rough Page ]

Physics

3 | P a g e [ Rough Space ]

1. GLR[GFDF\YL S. HM0 VFNX" 5lZDF6M WZFJTL

GYLP (a) SM6LI J[UDFG VG[ 5,FgSGM VR/F\S (b) A/GM VF3FT VG[ J[UDFG (c) H0tJGL RFSDF+F VG[ A/GL RFSDF+F (d) SFI" VG[ 8MS"

1. Out of the following pairs, which one does not have identical dimensions?

(a) Angular momentum and Planck’s constant

(b) Impulse and momentum (c) Moment of inertia and moment of a

force (d) Work and torque

2. V[S :Ê}U[H J0[ V[S TFZGM jIF; DF5TF\ D[.G

:S[,G]\ JF\RG0 𝑚𝑚 VG[ JT]"/FSFZ :S[,G]\ DF5G

52 SF5F D/[ K[P D[.G :S[,GM 1 𝑚𝑚 V[

JT]"/FSFZ :S[,GF100 SF5F AZFAZ K[P TM TFZGM

jIF; = PPPPPPPPPP 𝑐𝑚 (a) 0.052 cm (b) 0.026 cm (c) 0.005 cm (d) 0.52 cm

2. A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm; Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is .....

(a) 0.052 cm (b) 0.026 cm (c) 0.005 cm (d) 0.52 cm

3. SM. V[S S6 𝑥 = 0 ;DI[ 𝑡 = 0

VFU/YLUlTGL X~VFT SZL WG𝑥 lNXF TZO 𝑣

J[UYL VFU/ JW[ K[P 𝑣 = 𝛼 𝑥 TM S6G]\

:YFGF\TZ ;DI ;FY[ PPPPPPP 5|DF6[ K[P (a) 𝑡3 (b) 𝑡2 (c) T (d) 𝑡1/2

3. A particle located at x = 0 at time t = 0, starts moving along the positive x –direction with a velocity v that varies at

v = α x. The displacement of the particle varies with time as :

(a) 𝑡3 (b) 𝑡2 (c) T (d) 𝑡1/2

4. V[S S6GM X~VFTGM J[U 3𝑖 + 4𝑗 VG[ 5|J[U

0.4𝑖 + 0.3𝑗 K[P TM 10 𝑠 5KL T[GL h05 XMWMm

(a) 10V[SD (b) 7 2V[SD (c) 7V[SD (d) 8.5V[SD

4. A particle has an initial velocity 3i + 4j and an acceleration of 0.4𝑖 + 0.3𝑗 Its speed after 10 s is .........

(a) 10 units (b) 7 2 units (c) 7 units (d) 8.5 units

Physics


5. GLR[GL VFS'lTDF\ 0.4 𝑘𝑔 N/GF 5NFY"GL V[S

5FlZDFl6S UlT DF8[ :YFGF\TZ 𝑋 → ;DI (𝑡)

VF,[B NXF"jIM K[P A/GF VF3FTG]\ D}<I PPPPPP

YFIP (a) 0.2 Ns (b) 0.4 Ns (c) 0.8 Ns (d) 1.6 Ns

5. The figure shows the position – time (x – t) graph of one – dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is ...........

(a) 0.2 Ns (b) 0.4 Ns (c) 0.8 Ns (d) 1.6 Ns

6. V[S 0.2 𝑘𝑔 GF\ N0FG[ lXZM,\A lNXFDF\ p5Z TZO

CFYGF\ A/ J0[ O[SJFDF\ VFJ[ K[P A/ ,UFJTL

JBT[ CFY 0.2 𝑚 B;[ K[ VG[ AM, 2 𝑚

é\RF.V[ 5CM\R[ K[ TM A/G]\ D}<I XMWMP

s𝑔 = 10𝑚/𝑠2 ,Mf

(a) 22 N (b) 4 N (c) 16 N (d) 20 N

6. A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves 0.2 m while applying the force and the ball goes upto 2 m height further, find the magnitude of the force.

[Consider = 𝑔 = 10 𝑚/𝑠2] (a) 22 N (b) 4 N (c) 16 N (d) 20 N

7. HIFZ[ ZAZ A[\0G[ 𝑥 V\TZ[ B[\RJFDF\ VFJ[ tIFZ[

pt5gG YT]\ 5]Go:YF5S A/ 𝐹 = 𝑎𝑥 + 𝑏𝑥2 K[P

𝑎 VG[ 𝑏 VR/F\SM K[P VF ZAZ A[\0G[ T[GL D]/

l:YlTDF\YL B[\RLG[ T[GL ,\AF.DF\ 𝐿 H[8,M JWFZM

SZJF SZJ\] 50T]\ SFI" PPPPPPPPP YFIP

(a) 𝑎𝐿2 + 𝑏𝐿3 (b) 1

2 𝑎𝐿2 + 𝑏𝐿3

(c) 𝑎𝐿2

2+

𝑏𝐿3

3 (d)

1

2

𝑎𝐿2

2+

𝑏𝐿3

3

7. When a rubber band is stretched by a distance 𝑥, it exerts a restoring force of magnitude 𝐹 = 𝑎𝑥 + 𝑏𝑥2 , where 𝑎 and 𝑏 are constants. The work done in stretching the unstretched rubber – band by 𝐿 is ..........

(a) 𝑎𝐿2 + 𝑏𝐿3 (b) 1

2 𝑎𝐿2 + 𝑏𝐿3

(c) 𝑎𝐿2

2+

𝑏𝐿3

3 (d)

1

2

𝑎𝐿2

2+

𝑏𝐿3

3

8. R l+HIF WZFJTL 5FT/L JT]"/FSFZ TSTLG[ 𝜎

H[8,L ;DFG 5'Q9 3GTF J0[ lJn]TEFlZT SZJFDF\

VFJ[ K[P (𝜎 > 0) TSTL T[GF S[gãGL ;F5[1F[

VR/ SM6LI h05 𝜔 YL E|D6 SZ[ K[P TM TSTLGL

R]\ASLI RFSDF+F S[8,L CX[ m (a) 2𝜋𝑅4𝜎𝜔 (b) 𝜋𝑅4𝜎𝜔

(c) 𝜋𝑅4

2𝜎𝜔 (d)

𝜋𝑅4

4. 𝜎𝜔

8. A thin circular disk of radius R is uniformly charged with density 𝜎 > 0 per unit area. The disk rotates about its axis with a uniform angular speed 𝜔. The magnetic moment of the disk is :

(a) 2𝜋𝑅4𝜎𝜔 (b) 𝜋𝑅4𝜎𝜔

(c) 𝜋𝑅4

2𝜎𝜔 (d)

𝜋𝑅4

4. 𝜎𝜔

Physics


9. ′𝑎′ AFH]GL VG[ ′𝑚′ N/GL V[S RMZ; TSTL

lJRFZM VF TSTLGF ;DT,G[ ,\A TYF T[GF V[S

B}6FDF\YL 5;FZ YTL V1FG[ VG],1FLG[ TSTLGL

H0tJGL RFSDF+FPPPPPPPP

(a) 2

3𝑚𝑎2 (b)

5

6𝑚𝑎2

(c) 1

12𝑚𝑎2 (d)

7

12𝑚𝑎2

9. Consider 𝑎 uniform square plate of side 𝑎 and mass 𝑚. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is ..........

(a) 2

3𝑚𝑎2 (b)

5

6𝑚𝑎2

(c) 1

12𝑚𝑎2 (d)

7

12𝑚𝑎2

10. V[S lä5FlZDF6LS V6]4 ãjIDFG𝑚1 VG[ 𝑚2 YL

AgIM K[ H[ 𝛾 H[8,F\ V\TZ[ K[P HM VF56[ ACMZGF

SM6LI J[UDFG SJMg8F.h[XGGF lGID VG];FZ

T[GL RlÊI éÔ" U6LV[P TM T[GL éÔ" PPPPP YFIP

s𝑛 = WG 5}6F"S ;\bIFf

(a) 𝑚1+𝑚2

2𝑛2ℏ2

2𝑚12𝑚2

2𝑟2 (b)

𝑛2ℏ2

2 𝑚1+𝑚2 𝑟2

(c) 2𝑛2ℏ2

𝑚1+𝑚2 𝑟2 (d)

𝑚1+𝑚2 𝑛2ℏ2

2𝑚1𝑚2𝑟2

10. A diatomic molecule is made of two masses m1 and m2 which are separated by a distance𝑟, If we calculate its rotational energy by applying Bohr’s rule of angular momentum quantisation, its energy will be given by (𝑛 is an integer)

(a) 𝑚1+𝑚2

2𝑛2ℏ2

2𝑚12𝑚2

2𝑟2 (b)

𝑛2ℏ2

2 𝑚1+𝑚2 𝑟2

(c) 2𝑛2ℏ2

𝑚1+𝑚2 𝑟2 (d)

𝑚1+𝑚2 𝑛2ℏ2

2𝑚1𝑚2𝑟2

11. 𝑚VG[ 4𝑚 N/GF A[ S6M JrR[G]\ V\TZ 𝑟 K[P

U]Z]tJ1F[+ X}gI CMI T[JL HuIFV[ A\G[ S6MG[ HM0TL

Z[BF 5ZGF\ lA\N]V[ U]Z]tJ l:YlTDFG = PPPPPPP

(a) −4𝐺𝑚

𝑟 (b) −

6𝐺𝑚

𝑟

(c) −9𝐺𝑚

𝑟 (d) X}gI

11. Two bodies of masses 𝑚 and 4 𝑚 are placed at a distance 𝑟. The gravitational potential at a point on the line joining them where the gravitational field is zero, is ...........

(a) −4𝐺𝑚

𝑟 (b) −

6𝐺𝑚

𝑟

(c) −9𝐺𝑚

𝑟 (d) Zero

12. V[S V\TlZ1FIFGG]\ ãjIDFG 1000 lSU|F K[4 VF

V\TlZ1FIFGG[ 5'yJLGL ;5F8LYL D]ST :5[;DF\

KM0JFDF\ VFjIM K[P VCL\IF ′𝑔′ VG[ ′𝑅′ GL lS\DT

VG]ÊD[ 10 𝑚/𝑠2 VG[ 6400 𝑘𝑚 K[P VF SFI"

DF8[ éÔ" PPPPPPPPP K[P (a) 6.4 × 1011 𝐽 (b) 6.4 × 108 𝐽 (c) 6.4 × 109 𝐽 (d) 6.4 × 1010 𝐽

12. The mass of spaceship is 1000 𝑘𝑔. It is to be launched from the earth’s surface out into free space. The value of 𝑔 and 𝑅 (radius of earth) are 10 𝑚/𝑠2 and 6400 𝑘𝑚 respectively. The required energy for this work will be ............

(a) 6.4 × 1011 𝐽 (b) 6.4 × 108 𝐽 (c) 6.4 × 109 𝐽 (d) 6.4 × 1010 𝐽

Physics


13. ;FA]GF 5F6LGF ãFJ6G]\ 5'Q9TF6 0.03 𝑁𝑚−1

K[P ;FA]GF VF 5F6L J0[ AGTF 5Z5M8FGL l+HIF

3𝑐𝑚 YL JWFZL 5𝑐𝑚 SZJF DF8[ S[8,]\ SFI" SZJ]\

50[ m (a) 0.2𝜋 𝑚𝐽 (b) 2𝜋 𝑚𝐽 (c) 0.4𝜋 𝑚𝐽 (d) 4𝜋 𝑚𝐽

13. Work done in increasing the size of a soap bubble from radius of 3 𝑐𝑚 to 5 𝑐𝑚 is nearly (surface tension of soap solution = 0.03 𝑁𝑚−1)

(a) 0.2𝜋 𝑚𝐽 (b) 2𝜋 𝑚𝐽 (c) 0.4𝜋 𝑚𝐽 (d) 4𝜋 𝑚𝐽

14. 7𝑚𝑚S\5lJ:TFZDF\YL ;Z/ VFJT" UlT SZTF V[S

S6GM DC¿D J[U 4.4𝑚/𝑠 K[ TM NM,GGM

VFJT"SF/ PPPPPPPPP YX[P (a) 100 𝑠 (b) 0.01 𝑠 (c) 10 𝑠 (d) 0.1 𝑠

14. The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 𝑚𝑚. is 4.4 𝑚/𝑠. The period of oscillation is ........

(a) 100 𝑠 (b) 0.01 𝑠 (c) 10 𝑠 (d) 0.1 𝑠

15. V[S DM8Z ;F.S, l:YZ l:YlTDF\YL 2 𝑚/𝑠2 GF

5|J[UYL ;]Z[B 5Y 5Z UlT SZ[ K[P DM8Z ;F.S,GL

UlTGF X~VFTGF :YFG 5Z V[S l:YZ .,[S8=LS

;F.ZG ZFBL K[P HM DM8Z ;F.S,GF 0=F.JZG[

T[GL l:YZ l:YlTGF 94% H[8,M VJFH ;\E/FI

TM DM8Z ;F.S,[ SF5[,]\ V\TZ PPPPPPPP sVJFHGL h05 = 330 𝑚𝑠−1

f (a) 49 𝑚 (b) 98 𝑚 (c) 147 𝑚 (d) 196 𝑚

15. A motor cycle starts from rest and acceleratesalong a straight path at 2 𝑚𝑠−2. At the starting point of the motor cycle, there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest?

(speed of sound = 330 𝑚𝑠−1) (a) 49 𝑚 (b) 98 𝑚 (c) 147 𝑚 (d) 196 𝑚

16. V[S SFGM"8 V[lgHGGL SFI"1FDTF 40% K[4

500𝐾 TF5DFG 5Z ZC[, V[S éÔ" :+MTYL pQDF

,. ZCI]\ K[4 V[J]\ DFGJFDF\ VFJ[ K[ S[ V[lgHGGL

SFI"1FDTF 60% CMI4 tIFZ[ lGQÊD6 éÔ" DF8[

éÔ" :+MTG]\ GJ]\ TF5DFG S[8,]\ CX[ m (a) 120 𝐾 (b) 1200 𝐾 (c) 750 𝐾 (d) 600 𝐾

16. A Carnot engine, whose efficiency is 40% takes in heat from a source maintained at a temperature of 500 𝐾. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be .....

(a) 120 𝐾 (b) 1200 𝐾

(c) 750 𝐾 (d) 600 𝐾

Physics


17. V[S SFGM"8 V[lgHGGF SFI"SFZL 5NFY" TZLS[

läv5ZDFl^JS (Rigid Rotator) VFNX" JFI]GM

p5IMU SZJFDF\ VFJ[ K[P HM ;DMQDL lJ:TZ6

NZlDIFG JFI]G]\ SN 𝑉 YL JWLG[ 32𝑉 YFI TM

SFGM"8 V[lgHGGL SFI"1FDTFPP (a) 0.25

(b) 0.5 (c) 0.75

(d) 0.99

17. A diatomic ideal gas is used in a car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32 V, the efficiency of the engine is ..........

(a) 0.25 (b) 0.5 (c) 0.75 (d) 0.99

18. V[S pQDF VJFCS 5F+DF\ 𝑀 V6]EFZ JF/M

VFNX" JFI] EZ[,M K[P VF JFI]GL lJlXQ8

pQDFVMGM U]6M¿Z𝛾 K[P VF 5F+ 𝑣 J[UYL UlT

SZ[ K[ VG[ VRFGS T[G[ l:YZ l:YlTDF\ ,FJJFDF\

VFJ[ K[P VF 5|lÊIFG[ SFZ6[ TF5DFGDF\ PPPPPPP

S[<JLG (𝐾) H[8,M JWFZM YX[PsJFTFJZ6DF\

pQDFGM SM. jII YTM GYL V[D WFZMf

(a) (𝛾−1)

2𝛾𝑅∙ 𝑀𝑣2𝐾

(b) 𝛾−𝑀𝑣2

2𝑅𝐾

(c) 𝛾−1

2𝑅𝑀𝑣2. 𝐾

(d) 𝛾−1

2 𝛾+1 𝑅∙ 𝑀𝑣2𝐾

18. A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heat 𝛾. It is moving with speed 𝑣 and it suddenly brought to rest. Assuming no heat is lost to the surroundings, its

temperature increases by ............

(a) (𝛾−1)

2𝛾𝑅∙𝑀𝑣2𝐾

(b) 𝛾−𝑀𝑣2

2𝑅𝐾

(c) 𝛾−1

2𝑅𝑀𝑣2. 𝐾

(d) 𝛾−1

2 𝛾+1 𝑅∙𝑀𝑣2𝐾

19. I\UGF 0A, l:,8 5|IMUDF\ A\G[ l:,8 ;];dAâ

pNUD TZLS[ JT[" K[P A\G[ l:,8DF\YL GLS/TF\

TZ\UGM S\5lJ:TFZ 𝐴 VG[ TZ\U,\AF. 𝜆 K[P ALÔ

V[S 5|IMUDF\ A\G[ l:,8 V;];dAâ pNUD TZLS[

JT[" K[P sS\5lJ:TFZ VG[ TZ\U,\AF. ;DFG K[f

50NFGF S[gã 5ZGL TLJ|TF 𝐼1 CMI s5|YD 5|IMU

DF8[f TYF ALÔ 5|IMU DF8[ TLJ|TF 𝐼2 CMI TM

U]6MTZ 𝐼1

𝐼2= PPPPPPPPP

(a) 4 (b) 2 (c) 1 (d) 0.5

19. In a Young’s double slit experiment, the two slits act as coherent sources of waves of equal amplitude A and Wave length 𝜆 . In another experiment with the same arrangement the two slits are made to act as incoherent sources of waves of same amplitude and wavelength. If the intensity at the middle point of the screen in the first case is 𝐼1 and in the second case is 𝐼2

, then the ratio 𝐼1

𝐼2 is :

(a) 4 (b) 2 (c) 1 (d) 0.5

Physics


20. 20𝑐𝑚 GL S[gã,\AF. JF/F AlCUM"/ VZL;FG[

SFZGF c;F.0vjI]vDLZZc TZLS[ OL8 SIM" K[P VF

SFZYL 2.8𝑚 5FK/ ZC[,L ALÒ SFZ T[GM

15𝑚/𝑠 GL ;F5[1F h05YL VMJZ8[S SZ[ K[P TM

5|YD SFZGM c;F.0vjI]vDLZZc DF\ N[BFTL ALÒ

SFZGF\ 5|lTlA\AGL h05 PPPPPPPP

(a) 1

15 𝑚/𝑠 (b) 10 𝑚/𝑠

(c) 15 𝑚/𝑠 (d) 1

10 𝑚/𝑠

20. A car is fitted with a convex side – view mirror of focal length 20 cm. A second car 2.8 m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is .......

(a) 1

15 𝑚/𝑠 (b) 10 𝑚/𝑠

(c) 15 𝑚/𝑠 (d) 1

10 𝑚/𝑠

21. V[S AlCUM"/ ,[g;DF\ 5C[,F\ JFN/L Z\UGF 5|SFXGM

p5IMU SZJFDF\ VFJ[ K[P tIFZAFN JFN/LGF AN,[

ZFTF Z\UGF 5|SFXGM p5IMU SZJFDF\ VFJ[ TM T[GL

S[gã,\AF. = PPPPPPPPPP (a) VR/ ZC[X[ (b) JWX[ (c) 38X[ (d) 5|SFXGF Z\U 5Z VFWFlZT GYL

21. When monochromatic red light is used instead of blue light in a convex lens, its focal length will : (a) remain same (b) increase (c) decrease (d) does not depend on colour of light

22. GLR[GL VFS'lTDF\ U[<J[GMDL8ZGF X}gI VFJT"G

;FY[ DL8Z A|LH NXF"J[, K[P TM V7FT VJZMW 𝑅

G]\ D]<I S[8,]\ CX[ m (a) 55Ω

(b) 13.75Ω (c) 220Ω

(d) 110Ω

22. Shown in the figure adjacent is a meter – bridge set up with null deflection in the galvanometer. The value of the unknown

resistor R is ....... (a) 55Ω (b) 13.75Ω (c) 220Ω (d) 110Ω

23. V[S ;DF\TZ %,[8 S[5[;L8ZGL A[ %,[8M JrR[

CJFG]\DFwID CMI tIFZ[ S[5[l;8g; 9𝑝𝐹 K[P A\G[

%,[8 JrR[G]\ V\TZ ′𝑑′ K[P CJ[ VF A\G[ %,[8 JrR[ A[

0FI.,[S8=LS ãjIM EZJFDF\ VFJ[ K[P V[S

0FI.,[S8=LS ãjIMGM 0FI.,[S8=LS VR/F\S

𝐾1 = 3 VG[ V\TZ𝑑

3 K[P HIFZ[ ALÔ ãjIMGM

0FI.,[S8=LS VR/F\S 𝐾2 = 6 VG[ V\TZ 2𝑑

3 K[P

TM VF S[5[l;8ZG]\ S[5[l;8g; CJ[ S[8,]\ YX[ m (a) 40.5 𝑝𝐹 (b) 20.25 𝑝𝐹 (c) 1.8 𝑝𝐹 (d) 45 𝑝𝐹

23. A parallel plate capacitor with air between the plates has a capacitance of 9 𝑝𝐹. The separation between its plates is 𝑑. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectrics. constant K1 = 3

and thickness 𝑑

3 while the other one has

dielectric constant K2 = 6 and thickness 2𝑑

3. Capacitance of the capacitor is now

(a) 40.5 𝑝𝐹 (b) 20.25 𝑝𝐹 (c) 1.8 𝑝𝐹 (d) 45 𝑝𝐹

Physics


24. V[S WG lJn]TEFZ +𝑞 V[ 𝐸 = 3𝑖 + 4𝑗 + 𝑘

TYF 𝐵 = 𝑖 + 𝑗 − 3𝑘 JF/F lJn]TR]\ASLI

1F[+DF\ 𝑉 = 3𝑖 + 4𝑗 + 𝑘 H[8,F J[UYL UlT SZ[

K[P VF lJn]TEFZG[ ,UTF\ A/GF 𝑦 38SG]\ D}<I ? (a) 2 𝑞 (b) 11 𝑞 (c) 5 𝑞 (d) 3 𝑞

24. An electric charge +q moves with velocity

𝑉 = 3𝑖 + 4𝑗 + 𝑘 , in an electromagnetic

field given by : 𝐸 = 3𝑖 + 4𝑗 + 𝑘 and

𝐵 = 𝑖 + 𝑗 − 3𝑘 . The y - component of the force experienced by + q is ............

(a) 2 𝑞 (b) 11 𝑞 (c) 5 𝑞 (d) 3 𝑞

25. z[6L VG]GFN 𝐿𝐶𝑅 5lZ5YDF\4 𝑅 VF;5F;GM

lJn]Tl:YlTDFGGM TOFJT 100 𝑣𝑜𝑙𝑡𝑠 VG[

𝑅 = 1𝐾Ω TYF 𝐶 = 2𝜇𝐹 K[P HM VG]GFN

VFJ'lT 𝜔 = 200 𝑟𝑎𝑑/𝑠 CMI TM VG]GFN

JBTGL .g0S8Z VF;5F;G]\ JM<8[H = PPPPPPPP (a) 4 × 10−3 𝑉 (b) 2.5 × 10−2 𝑉 (c) 40 𝑉 (d) 250 𝑉

25. In a series resonant 𝐿𝐶𝑅 circuit, the voltage across 𝑅 is 100 𝑉 and 𝑅 = 1 𝑘 Ω with 𝐶 = 2𝜇 𝐹. The resonant frequency 𝜔 is 200 𝑟𝑎𝑑/𝑠. At resonance, the voltage across 𝐿 is .............

(a) 4 × 10−3 𝑉 (b) 2.5 × 10−2 𝑉 (c) 40 𝑉 (d) 250 𝑉

26. GLR[GFDF\YL SI]\ lJWFG ;tI GYL m DM0I],[XG GLR[GF DF8[ H~ZL K[P (a) l;,[S8LJL8L JWFZJF DF8[ (b) DFlCTLGF l;uG,GF 8=Fg;DLXG VG[ lZ;[%XG

JrR[GM ;DIUF/M 38F0JF DF8[ (c) V[lg8GFGL ;F.h VMKL SZJF DF8[ (d) O|[SXG, A[g0JLY 38F0JF DF8[

26. Which of the following four alternatives is not correct? We need modulation: (a) to increase the selectivity. (b) to reduce the time lag between

transmission and reception of the information signal

(c) to reduce the size of antenna (d) to reduce the fractional band width.

27. SMDG A[h V[ld5,OFIZDF\ .G5]8 l;uG, JM<8[H

VG[ VFp85]8 l;uG, JM<8[H JrR[ PPPPPPPP S/F

TOFJT CMI K[P

(a) 𝜋

4 (b) 𝜋

(c) 0 (d) 𝜋

2

27. In a common base amplifier, the phase difference between the input signal voltage and output voltage is ........

(a) 4 × 10−3 𝑉 (b) 2.5 × 10−2 𝑉 (c) 40 𝑉 (d) 250 𝑉

28. GLR[GFDF\YL S. ;\ÊF\lTNZlDIFG DC¿D

VFJ'lTJF/F OM8MG pt;lH"T YFI m sCF.0=MHG

5ZDF6] DF8[f (a) 𝑛 = 2YL 𝑛 = 6 (b) 𝑛 = 6YL 𝑛 = 2 (c) 𝑛 = 2YL 𝑛 = 1 (d) 𝑛 = 1YL 𝑛 = 2

28. Which of the following transitions in hydrogen atoms emit photons of highest frequency?

(a) 𝑛 = 2to𝑛 = 6 (b) 𝑛 = 6to𝑛 = 2 (c) 𝑛 = 2to𝑛 = 1 (d) 𝑛 = 1to𝑛 = 2

Physics


29. VMlS;HGGF ;D:YFlGS 𝑂817

G]\ 𝑚0 K[P 5|M8MG

VG[ gI]8=MGGF\ N/ VG]ÊD[ 𝑚𝑝 VG[ 𝑚𝑛 K[P TM

VF ;D:YFlGSGL A\WGéÔ" S[8,L CX[ m

(a) 𝑚0 − 8𝑚𝑝 𝑐2

(b) 𝑚0 − 8𝑚𝑝 − 9𝑚𝑛 𝑐2

(c) 𝑚0𝑐2

(d) 𝑚0 − 17𝑚𝑛 𝑐2

29. If 𝑀0 is the mass of an oxygen isotope

𝑂817 , 𝑀𝑝 and 𝑀𝑛 are the masses of a proton

and a neutron respectively, the nuclear binding energy of the isotope is ............. (a) 𝑚0 − 8𝑚𝑝 𝑐

2

(b) 𝑚0 − 8𝑚𝑝 − 9𝑚𝑛 𝑐2

(c) 𝑚0𝑐2

(d) 𝑚0 − 17𝑚𝑛 𝑐2

30. V[S WFT]GL ;5F8LG[ 400 𝑛𝑚 GL TZ\U,\AF.

JF/F 5|SFX J0[ 5|SFlXT SZJFDF\ VFJ[ K[P pt;lH"T

YTF OM8MGGL UlTéÔ" 1.68 𝑒𝑉 K[[P TM WFT]G]\

JS" O\SXG X]\ YFI m(ℎ𝑐 = 1240 𝑒𝑉 𝑛𝑚) (a) 3.09 𝑒𝑉 (b) 1.41 𝑒𝑉 (c) 1.51 𝑒𝑉 (d) 1.68 𝑒𝑉

30. The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 𝑒𝑉. The work function of the metal is ............. (ℎ𝑐 = 1240 𝑒𝑉 𝑛𝑚)

(a) 3.09 𝑒𝑉 (b) 1.41 𝑒𝑉 (c) 1.51 𝑒𝑉 (d) 1.68 𝑒𝑉

Chemistry


31. 1000 𝑔𝑚 5F6LDF\ 120 𝑔𝑚 I]ZLIF VMUF/LG[

AGFJ[,F ãFJ6GL 3GTF 1.15 𝑔𝑚/𝑚𝑙 K[P

ãFJ6GL DM,FlZ8L H6FJMP (a) 0.5 M (b) 1.78 M (c) 1.02 M (d) 2.05 M

31. The density of a solution prepared by dissolving 120 g of urea (mol. mass=60 u) in 1000 g of water is 1.15 g/mL. The molarity of this solution is ..........

(a) 0.5 M (b) 1.78 M (c) 1.02 M (d) 2.05 M

32. é\RF NAF6[ JF:TlJS JFI] DF8[ NAGLI VJIJ (a) 1+RT/Pb (b) 1

(c) 1+Pb/RT (d) 1 – pb/RT

32. The compressibility factor for a real gas at high pressure is ........

(a) 1+RT/Pb (b) 1 (c) 1+Pb/RT (d) 1 – pb/RT

33. GLR[GFDF\YL SI] lG~56 BM8]\ K[P

(a) ∆𝐺𝑠𝑦𝑠𝑡𝑒𝑚

∆𝐺𝑡𝑜𝑡𝑎𝑙= −𝑇

(b);DMQDL 5|lÊIFDF\

𝑊5|lTJTL" = −𝑛𝑅𝑇 ln 𝑉𝑓/𝑉𝑖

(c) 𝑙𝑛𝑘 =∆𝐻°−𝑇∆𝑆°

𝑅𝑇

(d) 𝐾 = 𝑒−∆𝐺°

𝑅𝑇

33. The incorrect expression among the following is ............

(a) ∆𝐺𝑠𝑦𝑠𝑡𝑒𝑚

∆𝐺𝑡𝑜𝑡𝑎𝑙= −𝑇

(b) In isothermal process,

𝑊𝑟𝑒𝑣𝑒𝑟𝑠𝑖𝑏𝑙𝑒 = −𝑛𝑅𝑇 𝐼𝑛 𝑉𝑓

𝑉𝑖

(c) 𝑙𝑛𝑘 =∆𝐻°−𝑇∆𝑆°

𝑅𝑇

(d) 𝐾 = 𝑒−∆𝐺°

𝑅𝑇

34. 𝑇 TF5DFG[ VF5[,L 5|lÊIF 𝑁2(𝑔) + 2𝑁𝑂(𝑔)

DF8[ ;\T],G VR/F\SG]\ D}<I 4 × 10−4 K[P TM

VF H TF5DFG[ 5|lÊIF 𝑁𝑂(𝑔) →1

2𝑁2(𝑔) +

1

2𝑂2(𝑔) DF8[ 𝐾𝑐 H6FJMP

(a) 0.02 (b) 2.5 × 102

(c) 4 × 10−4 (d) 50.0

34. The equilibrium constant (Kc) for the reaction, 𝑁2 𝑔 + 𝑂2 𝑔 → 2𝑁𝑂(𝑔) at temperature T is 4 × 10−4. The value of Kc for the reaction

𝑁𝑂 𝑔 →1

2𝑁2 𝑔 +

1

2𝑂2(𝑔) at the same

temperature is ........ (a) 0.02 (b) 2.5 × 102 (c) 4 × 10−4 (d) 50.0

35. HM CF.0=MHG VW"SMQF lZ0SXG 5M8[lgXI, k6

CMI TMP (a) p H2 = 1JFTF VG[ H+ = 2.0 M

(b) p H2 = 1JFTF VG[ H+ = 1.0 M

(c) p H2 = 2JFTF VG[ H+ = 2.0 M

(d) p H2 = 2JFTF VG[ H+ = 1.0 M

35. The reduction potential of hydrogen half-cell will be negative if ............. (a) P(H2)=1 atm and [H+]=2.0 M (b) P(H2)=1 atm and [H+]=1.0 M (c) P(H2)=2 atm and [H+]=1.0 M (d) P(H2)=2 atm and [H+]=2.0 M

Chemistry


36. TF5DFGDF\ 10° ;[P GM JWFZM SZTF\ ZF;FIl6S

5|lÊIFGM J[U AD6M YFI K[P HM TF5DFGDF\ 50° ;[P GM JWFZM SIM" CMI TM 5|lÊIF J[U S[8,M JW[ m

(a) 10 U6M (b) 24 U6M (c) 32U6M (d) 64 U6M

36. The rate of a chemical reaction doubles for every 10℃ rise of temperature. If the temperature is raised by 50℃ , the rate of the reaction increases by about

(a) 10 times (b) 24 times (c) 32 times (d) 64 times

37. 9\0F4 JFTFJZ6DF\ 9FZ6ZMWS TZLS[ .YL,LG

u,FISM, J5ZFI K[P 5F6LG] 9FZlA\N] VJGIG

SZJF 4 𝑘𝑔 5F6LDF\ S[8,M .YL,LG u,FISM,

pD[ZTF\ −6° ;[ 9FZlA\N] YFI m s5F6LGM 𝐾𝑓 = 1.86 𝐾 𝑘𝑔𝑚𝑜𝑙−1

.YL,LG

u,FISM, V6]EFZ = 62 U|FD DM,−1

f (a) 804.32 g (b) 204.30 g

(c) 400.00 g (d) 304.60 g

37. Ethylene glycol is used as an antifreeze in a cold climate. Mass of ethylene glycol which should be added to 4 kg of water to prevent it from freezing at −6℃ will be ............ (Kf for water = 1.86 K kg mol-1 and molar mass of ethylene glycol = 62 g mol-1)

(a) 804.32 g (b) 204.30 g (c) 400.00 g (d) 304.60 g

38. V[S O,S S[lgãT WG ZRGFDF\ 𝐴 5ZDF6]VM WGGF

B}6F 5Z VG[ 𝐵 5ZDF6]VM O,SGF S[gã 5Z CMI

K[P HM V[S O,SGF S[gã 5ZYL 𝐵 5ZDF6]

lJ:YFlGS'T YFI TM ;\IMHGG]\ ;}+ X]\ CX[ m (a) A2B (b) AB2

(c) A2B2 (d) A2B5

38. In a face centered cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If once atom of B is missing from one of the face centred points, the formula of the compound is .............

(a) A2B (b) AB2 (c) A2B2 (d) A2B5

39. V[S GF.8=MHG I]ST 29.5 𝑚𝑔 SFA"lGS 5NFY"G]\

XMWG H[<0FCGL 5wWlT 5|DF6[ SZTF\ pt5gG YTF\

V[DMlGIFG]\ 20 lDl, 0.1 𝑀 𝐻𝐶𝑙 ãFJ6DF\

XMQF6 SZJFDF\ VFJ[ K[P AFSLGF JWFZFGF V[l;0G]\

;\5}6" T8:YLSZ6 SZJF 15 lDl,

0.1 𝑀 𝑁𝑎𝑂𝐻 GL H~Z 50[ K[P TM ;\IMHGDF\

GF.8=MHGG]\ 8SFJFZ 5|DF6 S[8,] CX[P (a) 59.0 (b) 47.4

(c) 23.7 (d) 29.5

39. 29.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl’s method and the evolved ammonia was absorbed in 20 mL of 0.1 M HCI solution. The excess of the acid required 15 mL of 0.1 M NaOH solution for complete neutralization. The percentage of nitrogen in the compound is .........

(a) 59.0 (b) 47.4 (c) 23.7 (d) 29.5

Chemistry


40. GLR[GF A|MDF.0 5{SL 𝑆𝑁1 lJlWGM ;FRM ;lÊITF

ÊD SIM K[ m (a) ii > iii > (𝑖) (b) ii > i > (𝑖𝑖𝑖) (c) iii > ii > (𝑖) (d) i > ii > (𝑖𝑖𝑖)

40. Consider the following bromides The correct order of SN1 reactivity is

(a) ii > iii > (𝑖) (b) ii > i > (𝑖𝑖𝑖) (c) iii > ii > (𝑖) (d) i > ii > (𝑖𝑖𝑖)

41. C[%8[G VG[ VMS8[GG[ lDz SZTF VFNX" ãFJ6 AG[

K[P 373 𝐾 TF5DFG[ VF lDz6DF\ A\G[ 5|JFCL

sC[%8[G VG[ VMS8[Gf GF AFQ5NAF6 VG]ÊD[

105 𝑘𝑃𝑎 VG[ 45 𝑘𝑃𝑎 K[P 25.0 𝑔 C[%8[G

VG[ 35𝑔 VMS8[GG[ lDz SZJFYL AGTF ãFJ6G]\

AFQ5NAF6 PPPPPPPPP CX[P sC[%8[G = 100 U|FD DM ,

−1 VG[ VMS8[G

= 114 U|FD DM,−1

V6]EFZf (a) 72.0 kPa (b) 36.1 kPa

(c) 96.2 kPa (d) 144.5 kPa

41. On mixing, heptanes and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components (heptanes and octane) are 105 kPa and 45 kPa respectively. Vapour pressure of the solution obtained by mixing 25 g of heptanes and 35 g of octane will be (molar mass of haptane = 100 g mol-1, and of octane = 114 g mol-1).

(a) 72.0 𝑘𝑃𝑎 (b) 36.1 𝑘𝑃𝑎 (c) 96.2 𝑘𝑃𝑎 (d) 144.5 𝑘𝑃𝑎

42. GLR[GL 5|lÊIFGL D]bI lG5H

C6H5CH2CH OH CH CH3 2

;F\ãH2SO 4 ?

42. The main product of the following reaction is .......

C6H5CH2CH OH CH CH3 2

Conc. H2SO4 ?

43. GLR[GF 5{SL SIM VF<SMCM, 𝐻𝐶𝑙 VG[ 𝑍𝑛𝐶𝑙2

;FY[ ;F{YL h05YL 5|lÊIF VF5X[ m (a) 2 vaI]8[GM,

(b) 2 vlDYF., 5|M5[G v2v VM,

(c) 2 vlDYF., 5|M5[GM,

(d) 1vaI]8[GM,

43. From amongst the following alcohols, the one that would react fastest with conc. HCI and anhydrous ZnCl2, is

(a) 2 – butanol (b) 2 – methylpropan – 2 – ol (c) 2 – methylpropanol (d) 2 – butanol

Chemistry


44. GLR[GL pQDFUlTXFl:+I lJUTM 5ZYL

(∆𝑓𝐺° 𝐻 𝑎𝑞 + = 0)

𝐻2𝑂(𝑙) → 𝐻 𝑎𝑞 + + 𝑂𝐻𝑎𝑞

− ; ∆𝐻 = 57.32lSH}

𝐻2(𝑔) +1

2𝑂2(𝑔) → 𝐻2𝑂(𝑙); ∆𝐻 = −286.20lSH}

𝑂𝐻−VFIGGL 25° ;[ TF5DFG[ ;H"G V[gYFl<5G]\ D}<I X]\ CX[

m

(a) −22.88lSH} (b) −228.88lSH} (c) +228.88lSH} (d) −343.52lSH}

44. On the basis of the following thermo chemical

data: ∆𝑓𝐺° 𝐻 𝑎𝑞 + = 0

𝐻2𝑂 𝑙 → 𝐻 𝑎𝑞 + + 𝑂𝐻𝑎𝑞

− ; ∆𝐻 = 57.32 𝐾𝐽

𝐻2 𝑔 +1

2𝑂2 𝑔 → 𝐻2𝑂 𝑙 ; ∆𝐻 = −286.20 𝑘𝐽

The value of enthalpy of formation of 𝑂𝐻− ion at 25℃ is

(a) −22.88 KJ (b) −228.88 KJ (c) +228.88 KJ (d) −343.52 KJ

45. V[S 5ZDF6]DF\4 .,[S8=MG 600 DLq;[ GL h05 VG[

0.005% GL RMS;F.YLUlT SZ[ K[P .,[S8=MGGF

:YFGDF5GGL RMS;F. S[8,L CX[ m

(𝑕 = 6.6 × 10−34lSU|F DL

2;[

−14

.,[S8=MGG]\ N/ = 𝑒𝑚 = 9.1 × 10−31 lSU|F)

(a) 1.52 × 10−4DL (b) 5.01 × 10−3

DL (c) 1.92 × 10−3

DL (d) 3.84 × 10−3DL

45. In an atom, an electron is moving with a speed of 600 m/s with an accuracy of

0.005%. Certainly with which the position of the electron can be located is........

(h = 6.6 × 10−34 𝑘𝑔 𝑚2𝑠−1,

𝑚𝑎𝑠𝑠 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛, 𝑒𝑚 = 9.1 × 10−31 𝑘𝑔) (a) 1.52 × 10−4𝑚 (b) 5.10 × 10−3𝑚

(c) 1.92 × 10−3𝑚 (d) 3.84 × 10−3𝑚

46. sOLhL;M5"XGf EF{lTS VlWXMQF6G[ VG],1FLG[

GLR[GF 5{SL SI]\ lJWFGV;tI K[ m (a) T[ JFg0ZJF<; A/MGF SFZ6[ pNEJ[ K[P (b) ;Z/TFYL 5|JFCLSZ6 5FDTF\ JFI]VMG]\ h05YL

VlWXMQF6 YFI K[P (c) JW] NAF6[ VlWXMQFS 5Z AC]VFl^JI :TZ ZRFI

K[P (d) VlWXMQF6 V[gYF<5L (∆𝐻

VlWXMQF6) G]\ D}<I VMK]\

VG[ WG CMI K[P

46. Which of the following statements is incorrect regarding physisorption? (a) It occurs because of van der Waals’ forces (b) More easily liquefiable gases are adsorbed

readily (c) Under high pressure, it results into multi –

molecular layer on adsorbent surface (d) Enthalpy of adsorbent (∆𝐻𝑎𝑑𝑠𝑜𝑟𝑝𝑡𝑖𝑜𝑛) is slow

and positive

47. GLR[ VF5[, S[lGhFZM 5|lÊIFDF\

2𝑃𝑕𝐶𝐻𝑂: 𝑂𝐻−

𝑃𝑕𝐶𝐻2𝑂𝐻 + 𝑃𝑕𝐶𝑂2−

;F{YL

WLDM 5|lÊIS SIM CX[P (a) : 𝑂𝐻−

5Z SFAM"lS;,LS ;D}CG]\ VFÊD6

(b) CF.0=F.0G]\ SFAM"lG, ;D}C 5Z :YFGF\TZ6 (c) SFAM"lS;, ;D}C 5ZYL 5|M8MGG]\ lJ:YF5G

(d) PhCH2OHG]\ 5|M8MG lJIMHG

47. In Cannizaro reaction given below

2𝑃𝑕𝐶𝐻𝑂:𝑂𝐻⊝

𝑃𝑕𝐶𝐻2𝑂𝐻 + 𝑃𝑕𝐶𝑂2⊝

the slowest step is

(a) The attack of :𝑂𝐻⊖at the carboxyl group (b) The transfer of hydride to the carbonyl

group (c) The abstraction of proton from the

carboxylic group (d) The deprotonation of PhCH2OH

Chemistry


48. E en 2 C2O4 NO2 DF\ ‘E’ GM ;JU" VF\S

VG[ VMlS;HG VF\S VG]ÊD[PPPPPPPP (en) = ઈથીીન ડાયએમાઈન

(a) 6 VG[ 2 (b) 4 VG[ 2 (c) 4 VG[ 3 (d) 6 VG[ 3

48. The coordination number and the oxidation state of the element ‘E’ in the comples [E(en)2(C2O4)]NO2 (where (en) is ethylene diamine) are , respectively (a) 6 and 2 (b) 4 and 2 (c) 4 and 3 (d) 6 and 3

49. ,[gY[GM.0; SZTF V[lS8GM.0; TtJMGF\

VMlS;0[XG VF\S JW] DM8L ;\bIFDF\ HMJF D/[ K[P

T[G]\ SFZ6 PPPPPPPPPP (a) 5𝑓 SZTF 4𝑓 S1FS JW] O[,FI[, K[P

(b) 5𝑓 VG[ 6𝑑 GF éÔ":TZGM TOFJT VMKM K[ 4𝑓

VG[ 5𝑑 S1FSMGF\ éÔ":TZGF TOFJT SZTFP (c) 5𝑓 VG[ 6𝑑 GF éÔ":TZGM TOFJT JW] K[ 4𝑓

VG[ 5𝑑 S1FSMGF éÔ":TZGF TOFJT SZTFP

(d) V[lS8GM.0; JWFZ[ ;ÊLI K[ ,[gY[GM.0; SZTFP

49. Larger number of oxidation states are exhibited by the actinoides than those by the lanthanoides , the main reason being (a) 4f orbitals diffused than the 5f orbitals (b) lesser energy difference between 5f and 6d

than between 4f and 5d orbitals (c) more energy difference between 5f and 6d

than between 4f and 5d orbitals (d) more reactive nature of the actinoids than

the lanthanoids

50. .,[P VG] 5|lÊIS 𝐸⊕ A[ghLG ZL\U 5Z VFÊD6 SZL

DwIJTL" ;\IMHG 𝜎 ;\SL6" AGFJ[ K[P GLR[GF DF\YL SIF\

𝜎 ;\SL6" 5F;[ gI]GTD éÔ" K[ m

50. The electrophile, 𝐸⊕ attacks the benzene ring to generate the intermediate 𝜎 −comlpex. Of the following, which 𝜎 −comlpex is of lowest energy?

51. H2SO4 GL CFHZLGF\ VMSh[l,S V[l;0GM ãFJ6G]\

VG]DF5G KMnO4 ;FY[ SZJFDF\ VFJ[ K[P 5Z\T]

HCl ;FY[ SZJFDF\ VFJ[ TM 5lZ6FD V;\TMQFSFZS

D/[ K[ SFZ6 S[ , HCl PPPPPPP (a) VMSh[l,S V[l;0 äFZF S,MZLGDF\ VMlS;0[XG 5FD[

K[P (b) VMSh[,LS V[l;0 DF\YL H+

D}ST SZ[ K[P (c) T[ 5ZD[U[G[8 DF\YL M+2

G] lZ0P SZ[ K[P (d) VMSh[l,S V[l;0G]\ VMlS;0[XG SZL CO2 VG[

H2O pt5gG SZ[ K[P

51. Amount of oxalic acid present in a solution can be determined by its titration with KMnO4 solution in the presence of H2SO4. The titration gives unsatisfactory result when carried out in the presence of HCI, because HCI. (a) Gets oxidized by oxalic acid to chlorine (b) Furnishes H+ ions in addition to those from

oxalic acid (c) Reduces permanganate to Mn2+ (d) Oxidizes oxalic acid to carbon dioxide and

water

Chemistry


52. 5|M8LGG]\ lälTIS A\WFZ6 V[ SMG[ ;\,uG K[ m (a) 𝛼 v C[,LS, A\WFZ6

(b) H,lJZFUL VF\TZlÊIF (c) 𝛼V[lDGM V[;L0GL X'\B,F

(d) RMSS; 5M,L5[%8F.0 VFWFZLT ;\ZRGF

52. The secondary structure of a protein refers to (a) 𝛼 −helical backbone (b) hydrophobic interaction (c) sequence of 𝛼 − amino acids (d) fixed configuration of the polypeptide

backcone

53. CH3CH2NH2 + CHCl3 + 3KOH → x + y + 2H2O 5|lÊIFDF\ (𝑥) VG[ (𝑦)

X]\ CX[ m (a) 𝐶2𝐻5𝐶𝑁VG[ 3𝐾𝐶𝑙 (b) 𝐶𝐻3𝐶𝐻2𝐶𝑂𝑁𝐻2VG[ 3𝐾𝐶𝑙 (c) 𝐶2𝐻5𝑁𝐶VG[ 𝐾2𝐶𝑂3

(d) 𝐶2𝐻5𝑁𝐶VG[ 3𝐾𝐶𝑙

53. In the chemical reaction, 𝐶𝐻3𝐶𝐻2𝑁𝐻2 + 𝐶𝐻𝐶𝐼3 + 3𝐾𝑂𝐻 → 𝐴 + 𝐵 +3𝐻2𝑂 , the compounds (A) and (B) are respectively (a) C2H5CN and 3KCI (b) CH3CH2CONH2 and 3KCI (c) C2H5NC and K2CO3 (d) C2H5NC and 3KCI

54. GLR[ NXF"J[, 5|lÊIFDF\ D/TL V\lTD lG5HG]\

A\WFZ6 XMWMP

54. 𝑝 −cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the compound B. The letter on acidic hydrolysis gives chiral carboxylic acid. The structure of the carboxylic acid is .............

Chemistry


55. DNA VG[ RNA A\G[DF\ lJQFDRÊLI A[.h VG[

OM:O[8 V[:8Z A\WG PPPPPPP (a) XS"ZFGF\ V6]GF\ 𝐶5′ VG[ 𝐶1′ VG]ÊD[

(b) XS"ZFGF\ V6]GF\ 𝐶1′ VG[ 𝐶5′ VG]ÊD[ (c) XS"ZFGF\ V6]GF\ 𝐶2′ VG[ 𝐶5′ VG]ÊD[

(d) XS"ZFGF\ V6]GF\ 𝐶5′ VG[ 𝐶2′ VG]ÊD[

55. In both DNA and RNA heterocyclic base and phosphate ester linkages are at

(a) 𝐶5′ 𝑎𝑛𝑑 𝐶1

′ respectively of the sugar molecular

(b) 𝐶1′ 𝑎𝑛𝑑 𝐶5


(c) 𝐶2′ 𝑎𝑛𝑑 𝐶5


(d) 𝐶5′ 𝑎𝑛𝑑 𝐶2


56. V[S SFA"GLS ;\IMHGG]\ VFPN/ 60 K[P T[GF

C=20%, H=6.67% , N=46.67% K[ HIFZ[

AFSLGM VMlS;HG K[P T[G[ UZD SZTF WG VJ1F[5

;FY[ NH3 JFI] VF5[ K[P VF WG VJ1F[5

VF<S,F.G CuSO4 ;FY[ Ô\A,L Z\U VF5[ K[ TM

T[ ;\IMHG PPPPPPPPPPP (a) CH3CH2CONH2 (b) (NH2)2CO (c) CH3CONH2 (d) CH3NCO

56. An organic compound having molecular mass 60 is found to contain C=20%, H=6.67% and N=46.67% while rest is oxygen. On heating it gives NH3 along with a solid residue. The solid residue give violet colour with alkaline copper sulphate solution. The compound is ..........

(a) CH3CH2CONH2 (b) (NH2)2CO (c) CH3CONH2 (d) CH3NCO

57. GLR[GF 5{SL SIF VFIGMGM ;D}C

;D.,[S8=MlGI VFIGM NXF"J[ K[ m (a) 𝐾+, 𝐶𝑙−, 𝐶𝑎2+, 𝑆𝑐3+

(b) 𝐵𝑎2, 𝑆𝑟2+, 𝐾+, 𝑆2− (c) 𝑁3−, 𝑂2, 𝐹−, 𝑆2−

(d) 𝐿𝑖+, 𝑁𝑎+, 𝑀𝑔2+, 𝐶𝑎2+

57. Which one of the following sets of ions represents a collection of isoelectronic species?

(a) 𝐾+ , 𝐶𝑙− , 𝐶𝑎2+ , 𝑆𝐶3+

(b) 𝐵𝑎2+ , 𝑆𝑟2+ , 𝐾+ , 𝑆2−

(c) 𝑁3− , 𝑂2− , 𝐹+ , 𝑆2−

(d) 𝐿𝑖+ , 𝑁𝑎+ , 𝑀𝑔2+ , 𝐶𝑎2+

58. તત્વો B , P , S અન ેF ની પહેી આયનીકરણ

એન્થાલ્પી ને ચડતા ક્રમમાાં ગોઠવો. ( સૌપ્રથમ ઘુત્તમ )

(a) F < S < P < B (b)P < S < B < F (c) B < P < S < F (d)B < S < P < F

58. The increasing order of the first ionisation enthalpies of the elements B , P , S and F (lowest first) is

(a) F < S < P < B (b) P < S < B < F (c) B < P < S < F (d) B < S < P < F

Chemistry


59. GLR[GFDF\YL S. VF{QFW TFJ 38F0[ K[ m

(a) 5|XF\TSM (b) 5|lTÒJL (c) TF5XFDS (d) J[NGFXZ

59. Which of the following types of drugs reduces fever?

(a) Tranquilizer (b) Antibiotic (c) Antipyretic (d) Analgesic

60. DF+ .,[PGL l:5G G[ SFZ6[ pt5gG YTL R]\ASLI

RFSDF+FG]\ D}<I 2.84 𝐵. 𝑀. CMI TM

GLR[GFDF\YL X]\ ;FR] K[ m

(a) 𝑑5 s5|A/ l,U[g0GF\ 1F[+DF\f (b) 𝑑3 s5|A/ TYF lGA"/ l,U[g0GF\ 1F[+DF\f (c) 𝑑4 slGA"/ l,U[g0GF\ 1F[+DF\f (d) 𝑑4 s5|A/ l,U[g0 1F[+DF\f

60. The value of the ‘spin only’ magnetic moment for one of the following configurations is 2.84 BM. The correct one is (a) d5 (in strong ligand field) (b) d3 (in weak as well as in strong field) (c) d4 (in weak ligand field) (d) d4 (in strong ligand field)

Mathematics


61. 𝑤 એ1 ન ું કાલ્નનક (સુંકય) ધનભૂ છે. તો

(1 + 𝑤 − 𝑤2)7 =

(a) 128 𝑤 (b) −128𝑤

(c) 128𝑤2 (d) −128𝑤2

61. 𝑊 is a cube root of 1 ( complex ) , then (1 + 𝑤 −𝑤2)7 =

(a) 128 𝑤 (b) −128𝑤

(c) 128𝑤2 (d) −128𝑤2

62. 𝐴 = 𝑎 𝑏𝑏 𝑎

, 𝐴2 = 𝛼 𝛽𝛽 𝛼

તો

(a) 𝛼 = 𝑎2 + 𝑏2 , 𝛽 = 2𝑎𝑏

(b) 𝛼 = 𝑎2 + 𝑏2 , 𝛽 = 𝑎2 − 𝑏2

(c) 𝛼 = 2𝑎𝑏, 𝛽 = 𝑎2 + 𝑏2

(d) 𝛼 = 𝑎2 + 𝑏2 , 𝛽 = 𝑎𝑏

62. 𝐴 = 𝑎 𝑏𝑏 𝑎

, 𝐴2 = 𝛼 𝛽𝛽 𝛼

then

(a) 𝛼 = 𝑎2 + 𝑏2 , 𝛽 = 2𝑎𝑏

(b) 𝛼 = 𝑎2 + 𝑏2 , 𝛽 = 𝑎2 − 𝑏2

(c) 𝛼 = 2𝑎𝑏, 𝛽 = 𝑎2 + 𝑏2

(d) 𝛼 = 𝑎2 + 𝑏2 , 𝛽 = 𝑎𝑏

63. જો 𝑎1 , 𝑎2 , 𝑎3 , .......... 𝑎𝑛 સભગ ણોત્તય શ્રેણીભાું

હોમ તો

𝐷 =

log 𝑎𝑛 log 𝑎𝑛+1 log 𝑎𝑛+2

log 𝑎𝑛+3 log 𝑎𝑛+4 log 𝑎𝑛+5


=...........

(a) 0 (b)1

(c) 2 (d) 4

63. If 𝑎1 , 𝑎2 , 𝑎3 , ..........𝑎𝑛 are in G.P. , Then

𝐷 =

log 𝑎𝑛 log 𝑎𝑛+1 log 𝑎𝑛+2



=...........

(a) 0 (b)1

(c) 2 (d) 4

64. 504

+ 56 − 𝑟

3 6

𝑟=1 = .........

(a) 553

(b) 564

(c) 554

(d) 563

64. 504

+ 56 − 𝑟

3 6

𝑟=1 = .........

(a) 553

(b) 564

(c) 554

(d) 563

Mathematics


65. જો a + 2b + c n ના નલસ્તયણભાું દોની સુંખ્મા 66

હોમ તો nr ની ભહતભ કકભત = ...........

(a) 252 (b) 126

(c) 33 (d) આભાુંથી કોઈણ નનહ.

65. If in the expansion of a + 2b + c n there

are 66 terms, then maximum value of

nr is ............

(a) 252 (b) 126

(c) 33 (d) None of this

66. જો 𝑝 , 𝑞 , 𝑟 ત્રણ ધન સુંખ્માઓ છે, તો

𝑝𝑞 𝑝+𝑞 +𝑞𝑟 𝑞+𝑟 +𝑟𝑝 𝑟+𝑝

𝑝𝑞𝑟 ન ું રઘ તભ ભૂલ્મ

.... છે.

(a) 1 (b) 3 (c) 6 (d) 9

66. If 𝑝 , 𝑞 , 𝑟 are three positive numbers, then minimum value of

𝑝𝑞 𝑝+𝑞 +𝑞𝑟 𝑞+𝑟 +𝑟𝑝 𝑟+𝑝

𝑝𝑞𝑟

(a) 1 (b) 3 (c) 6 (d) 9

67. lim

𝑛 → ∞

1𝑝 +2𝑝 +3𝑝 +⋯..+𝑛𝑝

𝑛𝑝−1 =......

(a) 1

p+1 (b)

1

1−p

(c) 1

p−

1

p−1 (d)

1

p+2

67. lim

𝑛 → ∞

1𝑝 +2𝑝 +3𝑝 +⋯..+𝑛𝑝

𝑛𝑝−1 =......

(a) 1

p+1 (b)

1

1−p

(c) 1

p−

1

p−1 (d)

1

p+2

68. જો 𝑥 = cos 𝜃 + log tan𝜃

2 , 𝑦 = sin 𝜃 તો 𝜃

ની કઈ કકભતો ભાટે 𝑑2𝑦

𝑑𝑥 2= 0 થામ?

(a) θ = nπ ; n ∈ z

(b) θ = 2n + 1 π

2 ; n ∈ z

(c) θ = 2n + 1 π; n ∈ z

(d) θ = 2nπ ; n ∈ z

68. If 𝑥 = cos 𝜃 + log tan𝜃

2 , 𝑦 = sin 𝜃 then

for which value of , 𝑑2𝑦

𝑑𝑥2 becomes zero.

(a) θ = nπ ; n ∈ z

(b) θ = 2n + 1 π

2 ; n ∈ z

(c) θ = 2n + 1 π; n ∈ z

(d) θ = 2nπ ; n ∈ z

69. જો 𝑥𝑚 ∙ 𝑦𝑛 = (𝑥 + 𝑦)𝑚+𝑛 તો 𝑑𝑦

𝑑𝑥=.......

(a) y

x (b)

x+y

xy

(c) xy (d) x

y

69. If 𝑥𝑚 ∙ 𝑦𝑛 = (𝑥 + 𝑦)𝑚+𝑛 then 𝑑𝑦

𝑑𝑥=.......

(a) y

x (b)

x+y

xy

(c) xy (d) x

y

Mathematics


70. ઉગભબફદ થી 𝑥 = 𝑎 sint −𝑏 sin𝑎𝑡

𝑏 ,

𝑦 = 𝑎 𝑐𝑜𝑠𝑡 − 𝑏 cos 𝑎𝑡

𝑏 , 0 < 𝑏 < 𝑎, 𝑎

યના કોઈણ બફદ ન ું ભહતભ અુંતય .......

(a) a − b (b) a + b

(c) a2 + b2 (d) a2 − b2

70. For 0 < 𝑏 < 𝑎,Maximum distance of any point from origin to

𝑥 = 𝑎 sint − 𝑏 sin𝑎𝑡

𝑏 ,

𝑦 = 𝑎 𝑐𝑜𝑠𝑡 − 𝑏 cos𝑎𝑡

𝑏, Is _______.

(a) a − b (b) a + b

(c) a2 + b2 (d) a2 − b2

71. 𝑦 = 𝑥2 − 5𝑥 + 6 લક્ર યના 2 , 0 અને 3 , 0

બફદ આગના સ્ળશકો લચ્ચેનો કોણ .....

(a) π

2 (b)

π

3

(c) π

6 (d)

π

4

71. Angle between two tangents on curve 𝑦 = 𝑥2 − 5𝑥 + 6 at point (2,0) and (3,0) is ........ .

(a) π

2 (b)

π

3

(c) π

6 (d)

π

4

72. 𝑑𝑥

𝑥2010 1+𝑥2010 (2010 )−1 = .......

(a) −1

2011 1 + 𝑥−2010 2009×(2010)−1

+ 𝑐

(b) −1

2009 1 − 𝑥−2010

2009

2010 + 𝑐

(c) 1

2011 1 +

1

𝑥2010

2009

2010+ 𝑐

(d) −1

2009 1 + 𝑥−2010

2009

2010 + 𝑐

72. 𝑑𝑥

𝑥2010 1+𝑥2010 (2010 )−1 = .......

(a) −1

2011 1 + 𝑥−2010 2009×(2010)−1

+ 𝑐

(b) −1

2009 1 − 𝑥−2010

2009

2010 + 𝑐

(c) 1

2011 1 +

1

𝑥2010

2009

2010+ 𝑐

(d) −1

2009 1 + 𝑥−2010

2009

2010 + 𝑐

73. 𝑥 + 3 3 + 𝑐𝑜𝑠2 𝑥 + 3𝜋 𝑑𝑥−

𝜋

2

−3𝜋

2

ની કકભત ..............

(a) π4

32 (b)

π4

32+π

2

(c) π

2 (d)

π

4− 1

73. 𝑥 + 3 3 + 𝑐𝑜𝑠2 𝑥 + 3𝜋 𝑑𝑥−

𝜋

2

−3𝜋

2

= ....

(a) π4

32 (b)

π4

32+π

2

(c) π

2 (d)

π

4− 1

Mathematics


74. જેનો x, y બફદ એ ઢા sin 2y

x+tan y હોમ તેલા 1 ,

π

4

બફદ ભાુંથી સાય થતા લક્રન ું સભીકયણ

(a) x = tany (b) y = tanx

(c) x = 2 tany (d) y = 2 tanx

74. If slope of any tangents to (x , y) is sin 2y

x+tan y

then equation of curve passing through

1 ,π

4 is ..........

(a) x = tany (b) y = tanx

(c) x = 2 tany (d) y = 2 tanx

75. નીચેનાભાુંથી ..... નલકર સભીકયણ dy

dx

2

+ xdy

dx= y

ન ું સભાધાન કયે છે.

(a) y = 3x + 9 (b) y = 3x − 9

(c) x2 + 9y = 0 (d) x2 − 4y = 0

75. From following equation ______ is the

solution of diff. eq. dy

dx

2

+ xdy

dx= y.

(a) y = 3x + 9 (b) y = 3x − 9

(c) x2 + 9y = 0 (d) x2 − 4y = 0

76. કોણના નળયોબફદ ઓ acost , a sint ,

( b sint, −bcost) અને ( 1 , 0) આેર છે. જમાું t

પ્રચર છે. નત્રકોણના ભધ્મકેન્દ્રનો બફદ ગણ

(a) 3x − 1 2 + 3y 2 = a2 − b2

(b) 3x − 1 2 + 3y 2 = a2 + b2

(c) 3x + 1 2 + 3y 2 = a2 + b2

(d) 3x + 1 2 + 3y 2 = a2 − b2

76. If vertices of triangle are acost , a sint , ( b sint,−bcost) And ( 1 , 0) then find the locus of the centroid of triangle, where t is constant .

(a) 3x − 1 2 + 3y 2 = a2 − b2

(b) 3x − 1 2 + 3y 2 = a2 + b2

(c) 3x + 1 2 + 3y 2 = a2 + b2

(d) 3x + 1 2 + 3y 2 = a2 − b2

77. A(3,4) ભાુંથી સાય થતી યેખાના અક્ષો લચ્ચે અુંતયામેરા અુંત:ખુંડો A આગ દ બાગે તેલી યેખાન ું

સભીકયણ ...........

(a) 3x − 4y + 7 = 0

(b) 4x − 3y = 24

(c) 3x + 4y = 25

(d) x + y = 7

77. Find the equation of line which is passing through A ( 3 , 4 ) and whose intercepts intersect at A equally .............

(a) 3x − 4y + 7 = 0

(b) 4x − 3y = 24

(c) 3x + 4y = 25

(d) x + y = 7

Mathematics


78. x2 − 3xy + λy2 + 3x − 5y + 2 = 0, λ ∈ R યેખામ ગ્ભ દળાશલે છે. θ એ ફે યેખાઓ લચ્ચેનો કોણ દળાશલે

છે તો cosec2 θ = ............

(a) 3 (b) 9

(c) 10 (d) 100

78. Lines are x2 − 3xy + λy2 + 3x − 5y + 2 =0, λ ∈ R , θ is the angle between given lines then cosec2 θ =__________

(a) 3 (b) 9

(c) 10 (d) 100

79. લત શ x2 + y2 = 81 ની m ઢાલાી જીલા યલરમ

y2 = 12 x ને સ્ળે , તો m ની કકભતોનો ગણ

.......... છે. (a) −∞, −1 ∪ (1 , ∞ )

(b) −∞, ∞

(c) −∞, 2−1

3 ∪ 2−1

3 , ∞

(d) આભાુંથી એકણ નનહ.

79. If slope of chord is m and this chord to the circle 𝑥2 + 𝑦2 = 81 touches the parabola 𝑦2 = 12 𝑥 then m = ..........

(a) −∞, −1 ∪ (1 , ∞ )

(b) −∞, ∞

(c) −∞, 2−1

3 ∪ 2−1

3 , ∞

(d) 𝑁one of this

80. યલરમ યના બફદ (bt21 , 2bt1) આગનો

અબીરુંફ યલરમને પયીથી (bt22 , 2bt2) બફદ ભાું છે

તો ...........

(a) t2 = −t1 −2

t1 (b) t2 = −t1 +

2

t1

(c) t2 = t1 −2

t1 (d) t2 = t1 +

2

t1

80. If normal of the parabola at (bt2

1 , 2bt1) intersect the parabola , at

(bt22 , 2bt2) then ...........

(a) t2 = −t1 −2

t1 (b) t2 = −t1 +

2

t1

(c) t2 = t1 −2

t1 (d) t2 = t1 +

2

t1

81. ઉલરમ x2 + 4y2 = 64 ભાું અુંતગશત ભહતભ

ક્ષેત્રપલાા રુંફચોયસની ફાજ ઓ ......... છે.

(a) (6 2 , 4 2 ) (b) (8 2 , 4 2 )

(c) (8 2 , 8 2 ) (d) (16 2 , 4 2 )

81. rectangle inscribed in a ellipse x2 + 4y2 = 64 when sides of the rectangle are ______ .

(a) (6 2 , 4 2 ) (b) (8 2 , 4 2 )

(c) (8 2 , 8 2 ) (d) (16 2 , 4 2 )

Mathematics


82. x2

36−

y2

12= 1 અનતલરમના અનુંત સ્ળશકો લચ્ચેનો

ખૂણો = ............

(a) π

4 (b)

π

3

(c) π

6 (d) એક ણ નનહ.

82. Angle between infinite tangents to the

Hyperbola x2

36−

y2

12= 1 is .........

(a) π

4 (b)

π

3

(c) π

6 (d) None of this

83. ∆ ABC મ ાં m∠C =π

2 , A , B , C ના સ્થાન સદદળો

અન ક્રભ ે 2𝑖 − 𝑗 + 𝑘 , 𝑖 − 3𝑗 − 5𝑘 અને a𝑖 − 3𝑗 + 𝑘 તો a ની કકભતો ભેલો.

(a) 2 અને 1 (b) −2 અને − 1

(c) −2 અને 1 (d) 2 અને − 1

83. In ∆ ABC , m∠C =π

2 , If A (2 , -1 , 1 )

B ( 1 ,-3 , -5) and C ( a , -3 , k ) then a = .............

(a) 2 and 1 (b) −2 and − 1

(c) −2 and 1 (d) 2 and − 1

84. જો સભતર x + y + z = 3 ગોરક

x2 + y2 + z2 − 2x − 2y − 2z − 6 = 0 ને સ્ળે

તો λ = ......... (a) 3 + 3 (b) 3 − 3

(c) 3(3 + 2 ) (d) − 3 − 3

84. If plane x + y + z = 3 touches the sphere

x2 + y2 + z2 − 2x − 2y − 2z − 6 = 0 then

λ = ......... (a) 3 + 3 (b) 3 − 3

(c) 3(3 + 2 ) (d) − 3 − 3

85. યેખાઓ x = 1 + s , y = −3 − λs , z = 1 + λs ∶ અને x =

1

2t , y = 1 + t , z = 2 − t જમાું s અને

t , પ્રચરો છે યેખાઓ સભતરીમ હોમ તો λ = ....... (a) −2 (b) −1

(c) −1

2 (d) 0

85. Lines: x = 1 + s , y = −3 − λs , z = 1 + λs ∶ and x =

1

2t , y = 1 + t , z = 2 − t where

s and t are constant , If lines are

coplanar then λ = ....... (a) −2 (b) −1

(c) −1

2 (d) 0

Mathematics


86. સભૂહ A ભાું 100 અલરોકન જેભકે 101 , 102 ,

...... , 200 છે અને સભૂહ B ભાું 100 અલરોકન

જેભકે 151 , 152 , ....... , 250 છે. VA અને VB

તેભના નલચયણ છે તો VA

VB= .............

(a) 1 (b) 9

4

(c) 4

9 (d)

2

3

86. A has 100 observations like 101 , 102 , ..... 200 and B has also 100 observations like 151 , 152, .... 250. 𝑉𝐴 𝑎𝑛𝑑 𝑉𝐵 are

varience then 𝑉𝐴

𝑉𝐵= .........

(a) 1 (b) 9

4

(c) 4

9 (d)

2

3

87. દ્વિદી સુંબાલના નલતયણભાું ભધ્મક અને નલચયણ અન ક્રભે 4 અને 2 છે. ક ર n ભાુંથી 2 સપતા ભલાની

સુંબાલના ............

(a) 128

256 (b)

216

256

(c) 37

256 (d)

28

256

87. If Mean is 4 and Variance is 2 for probability distribution then out of n what is the probability for exactly 2 ?

(a) 128

256 (b)

216

256

(c) 37

256 (d)

28

256

88. α ,β ભાટે π < α − β < 3π

જો sinα + sinβ = −21

65 , cosα + cosβ = −

27

65

તો cos α−β

2 = …… ….

(a) 6

65 (b)

3

130

(c) −3

130 (d) −

6

65

88. For α & β , π < α − β < 3π

If sinα + sinβ = −21

65 , cosα + cosβ = −

27

65

Then cos α−β

2 = … ……

(a) 6

65 (b)

3

130

(c) −3

130 (d) −

6

65

89. જો α + β =π

2 , β + γ = α તો tanα = ........

(a) 2( tanβ + tanγ ) (b) tanβ + tanγ

(c) tanβ + 2tanγ (d) 2tanβ + tanγ

89. If α + β =π

2 , β + γ = α then tanα = ......

(a) 2( tanβ + tanγ ) (b) tanβ + tanγ

(c) tanβ + 2tanγ (d) 2tanβ + tanγ

90. cot−1( 𝑐𝑜𝑠𝛼) − tan−1 𝑐𝑜𝑠𝛼 = 𝑥 તો sinx = .............

(a) tan2 𝛼

2 (b) cot2 𝛼

2

(c) tan 𝛼 (d) cot 𝛼

90. cot−1( 𝑐𝑜𝑠𝛼) − tan−1 𝑐𝑜𝑠𝛼 = 𝑥 then sinx = .............

(a) tan2 𝛼

2 (b) cot2 𝛼

2

(c) tan 𝛼 (d) cot 𝛼

Mathematics


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28 5FGF D]lãT K[P Test Booklet Code 1 : PHYSICS ......2. The Answer Sheet is kept inside this Test...

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