18-04-20 SR.N-SUPER CHAINA/N-CHAINA Jee-Main GTM-15

Sec: Sr.IIT N-SUPER CHAINA/N-CHAINA Date: 18-04-20 Time: 3 Hrs Max. Marks: 300

Name of the Student: ___________________ H.T. NO:

18-04-20_SR.N-SUPER CHAINA/N-CHAINA_Jee-Main_GTM-15

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Narayana IIT Academy 18-04-20_Sr.IIT_N-SC/N-C _JEE-MAIN_GTM-15_Q’P

SR.IIT_N-SC Page. No. 2

The important thing in life is not the triumph but the struggle.

PHYSICS MAX.MARKS: 100

SECTION – I

(SINGLE CORRECT ANSWER TYPE)

This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its answer,

out of which ONLY ONE option can be correct.

Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct.

1. In the measurement of a physical quantity 2

123

A BX

C D

. The percentage errors introduced in

the measurements of the quantities of A, B, C and D are 2%, 2% 4% and 5% respectively.

Then the minimum amount of percentage of error in the measurement of X is contributed

by

A) A B) B C) C D) D

2. The collision frequency of nitrogen molecule in a cylinder containing at 2.0 atm pressure

and temperature 170 C is approximately: (Take radius of a nitrogen molecule is 1.0 A0)

A) 4.6 x 109 s-1 B) 5.6 x 109 s-1 C)4.6 x 108 s-1 D) 5.6 x 108 s-1

3. A drop of liquid of density is floating half immersed in a liquid of density d. If is the

surface tension, then what is the diameter of the drop of the liquid (Assume angle of

contact to be 180 )

A)

3

g 2 d

B)

6

g 2 d

C)

4

g 2 d

D)

12

g 2 d

4. The equation of an alternating voltage is E 220sin t6

and the equation of the current

in the circuit is I 10sin t6

. Then the impedance of the circuit is

A) 10 ohm B) 22 ohm C)11 ohm D) 17ohm




5. A metal wire of linear mass density of 9.8 g/m is stretched with a tension of 10kgwt

between two rigid support 1 m apart. The wire passes at its middle point between the

poles of a permanent magnet and it vibrates in resonance when carrying an alternating

current of frequency n. The frequency n of the alternating source is

A) 50 Hz B) 100 Hz C) 200 Hz D) 25 Hz

6. Two wires of the same material (Young’s modulus Y) and same length L but radii R and

2R respectively are joined end to end and a weight W is suspended from the combination

as shown in the figure. The elastic potential energy of the system is

A) 2

2

3W L

4 R Y B)

2

2

3W L

8 R Y C)

2

2

5W L

8 R Y D)

2

2

W L

8 R Y

7. A long solenoid has 200 turns per cm and carries a current i. The magnetic field at its

centre is 6.28 X 10-2 Wb/m2. Another long solenoid has 100 turns per cm and it carries a

current i/3.The value of the magnetic field at its centre is

A) 05 x 10-4 Wb/m2 B) 1.05 x 10-2 Wb/m2

C)1.05 x 10-5 Wb/m2 D) 1.05 x 10-3 Wb/m2




8. A linearly polarized electromagnetic wave given as 0ˆE E i cos kz t is incident from

space normally on a perfectly reflecting wall at 0z of some material, the reflected wave

will be give as

A) Er = E0 i kz t B) Er = E0 i cos kz t

C)Er = -E0 i cos kz t D) Er = E0 i sin kz t

9. The escape velocity from the earth is 11 km/s. The escape velocity from a planet having

nine times the radius and one third of density as the earth is __ km/s

A) 11 B) 22 3 C)33 3 D) 44 3

10. If the linear density of a rod of length L varies as A Bx , find the position of its centre

of mass from the origin (Assume negligible thickness)

A)

L 3A 2BL

3 2A BL

B)

L 3A 2BL

3 2A BL

C)

L 3A 2BL

3 2A BL

D)

L 3A 2BL

3 2A BL

11. The equivalent resistance of the circuit across AB is given by

A) 4 B) 13 C) 4 or 13 D) 4 or zero

12. A fish looking up through the water sees the outside world contained in a circular horizon.

If the refractive index of the water is 4

3 and fish is 12 cm below the surface, the radius of

this circle in cm is




A) 36

5 B) 4 5 C)

36

7 D) 36 7

13. Electron in Hydrogen atom first jumps from third excited state to second excited state and

then from second excited state to the first excited state. The ratio of wavelengths of

emitted photons I1 : I2 emitted in the two cases is

A) 27/5 B) 20/7 C)7/5 D) 27/20

14. A thin wire of length L is made of an insulating material. The wire is bent to form a

circular loop, and a positive charge q is distributed uniformly around the circumference of

the loop. The loop is then set in to rotation with angular speed around an axis through

its centre. If the loop is in the region where there is uniform magnetic field B

directed

parallel to the plane of the loop, calculate the magnitude of the magnetic torque on the

loop.

A) 2

2

q L B

8

B)

2

2

q L B

4

C)

2

2

q L B

2

D)

2

2

q L B

15. Two particles A and B are projected simultaneously from the two towers of height 10 m

and 20 m respectively. Particle A is projected with an initial speed of 10 2 m/s at an

angle of 450 with horizontal, while particle B is projected horizontally with speed 10m/s.

If they collide in air, what is the distance d between the towers?

A) 10 m B) 20 m C)30 m D) 40 m

16. At a given time the position vector of a particle moving in a circle with a velocity

ˆ ˆ ˆ3i 4 j 5k is ˆ ˆ ˆi 9 j 8k . Its angular velocity about origin at that time is

A) ˆ ˆ ˆ13i 29j 31k

146

B)

ˆ ˆ ˆ13i 29j 31k

146

C)

ˆ ˆ ˆ13i 29j 31k

146

D)

ˆ ˆ ˆ13i 29j 31k

146




17. The capacitor shown in figure has been charged to a potential difference of V volt so that

it carries a charge C V with both the switches S1 and S2 remaining open. Switch S1 is

closed at t = 0.At t = R1 C, switch S1 is opened and S2 closed. Find the charge on the

capacitor at t = 2R1C + R2C

A) CV

CE 1 ee

B) 2 CVCE 1 e

e

C)2

1 CVCE 1

e e

D)

2

1 CVCE 1

e e

18. Calculate the linear acceleration of the blocks in the given figure. Mass of block A =

10kg, mass of block B = 8 kg, mass of disc shaped pulley = 2kg (take g= 10m/s(2))

A) 20

19 m/s2 B)

19

20 m/s2 C)

29

20 m/s2 D)

20

29 m/s2

19. An electron of mass ‘m’ and charge ‘e’ initially at rest gets accelerated by a constant

electric field ‘E’. The rate of change of de- Broglie wavelength of this electron at time ‘t’

ignoring relativistic effects is

A) 2

h

eEt

B)

eEt

E

C)

2

mh

eEt

D)

h

e.E




20. A small block of mass 10 kg is fastened to one end of a light string and a second block

(m1) of mass 20 kg to the middle point, the other end of the string fastened to a fixed point

on a smooth horizontal table. The blocks are then projected such that the two portions of

the string are always in the same straight line and the blocks describes horizontal circles

on the table as shown in figure below.

m1

L Lm2

The tension in the string portion between blocks is 1T and tension between point O and the

block of mass m1 is 2T . The value of 1

2

T

T is

A) 1 B) 2 C)0.5 D) 0.25

SECTION-II

(Numerical Value Answer Type)

This section contains 5 questions. The answer to each question is a Numerical value. If the numerical value has

more than two decimal places, round-off the value of Two decimal places. Answer to each question will be

evaluated according to the following marking scheme:

Marking scheme: +4 for correct answer, 0 in all other cases.

21. Two infinite line charges, each having uniform charge density, pass through the midpoints

of two pairs of opposite faces of a cube of edge ‘L’ as shown in figure. The modulus of

the total electric flux due to both the line charges through the face ABCD is0

Ln

. Find n.




22. Two long parallel wires carrying current 2.5 amperes and I ampere in the same direction

(directed into the plane of the paper) are held at P and Q respectively such that they are

perpendicular to the plane of paper. The points P and Q are located at a distance of 5

metres and 2 metres respectively from a collinear point R (see figure). An electron

moving with a velocity of 54 10 /m s along the positive x -direction experiences a force of

magnitude 203.2 10 N at the point R . Find the value of I (in ampere).

23. A tyre pumped to pressure of 6 atmosphere suddenly bursts. Room temperature is 250 C.

calculate the temperature of escaping air. 1.4γ (Assume reversible adiabatic process)

(Take 2/76 0.6 )

24. In the Young’s double slit experiment, maximum number of bright bands observed

(inclusive of the central bright band) is found to be 11. If λ is the wavelength of the

monochromatic light used, the distance between the slit is n λ. Find n.

25. In the figure shown the potential drop across the series resistor of 2k is x volt. Find x.




CHEMISTRY MAX.MARKS: 100

SECTION – I


This section contains 20 multiple choice questions. Each question has 4 options (1), (2), (3) and (4) for its

answer, out of which ONLY ONE option can be correct.


26. The solubility product of Mg(OH)2 is 9.0 x 10-12. The pH of an aqueous saturated solution

of Mg(OH)2 is (log1.8 = 0.26, log 3 = 0.48)

A) 3.58 B) 10.42 C)3.88 D) 6.76

27. The correct order of the spin-only magnetic moments of the following complexes is:

(I) [Fe(H2O)6]Cl2 (II) Na3[Fe(CN)6] (III) [Fe(en)3]Cl2 (IV) Ni(CO)4

A) III > I > IV > II B) I > II III > IV

C) I > IV III > II D) III > I > II > IV

28. Three gases O2, H2 and CO2 are taken in three different containers A, B and C

respectively at same pressure containing charcoal. The graph that represents the correct

behaviour of pressure with time is

A) B)

C) D)




29. The number of sp2 hybrid orbitals in benzoic acid is?

A) 18 B) 21 C)24 D) 30

30. In the following reaction A is

A) B)

C) D)

31.

P, Q respectively are

A)

B)




(C)

D)

32. Among the statements (a-d) correct ones are

(a) Beryllium is not readily attacked by acids

(b) BeSO4 is readily soluble in H2O

(c) Beryllium exhibits co-ordination number more than four

(d) BeO is purely acidic in nature

A) a, b, d B) b, c C)a, b D) a, c, d

33. A compound X, of boron reacts with NH3 on heating to give another compound Y.

B3N3H3Cl3 on reaction with LiBH4 also gives Y the compound X can be prepared by

treating BF3 with LiAlH4 compound X and Y respectively are

A) B3N3H6, B2H6 B) BF3, B3N3H6 C)B2H6, B3N3H6 D) B2O3, B3N3H6




34. Which of the following reactions produce meso product

A) 4

3

i)OsO

ii) aq.NaHSO

B) 2 4Br (CCl )

C)

2 6i)B D /THF

ii)DCl

D) Both a and b

35. Which of the following is not true?

A) Acid rain is mostly because of oxides of nitrogen & sulphur

B) Chlorofluorocarbons are responsible for ozone layer depletion

C) Greenhouse effect is responsible for global warming

D) Ozone layer does not permit IR radiation from the sun to reach the earth

36. A, B and C are three Biomolecules. The results of tests performed on them given below

Molisch’s test Benedict’s test Ninydrin test

A Positive Negative Negative

B Positive Positive Negative

C Negative Negative Positive

A) A = Fructose B = Starch C = Arginine

B) A = Sucrose B = Arginine C = Starch

C)A = Starch B = Sucrose C = Alanine

D) A = Starch B = Glucose C = Arginine

37. Which of the following metal when treated separately with an excess of (a) dilute HCl, (b)

aqueous NaOH gives out H2 in 1:1 volume ratio

A) Al B) Zn C)Cu D) Mn




38. In the figure shown below, reactant A (represented by circle) is in equilibrium with

product B (represented by square). The equilibrium constant for process is, 2A B

A) 1 B) 1

6 C)6 D) 2

39. The correct order of basicities of the following compounds is

(I) (II) 3 2 2CH CH NH

(III) 3 2CH NH (IV) 3 2

O||

CH C NH

A) II > I > III > IV B) I > III > II > IV

C)III > I > II > IV D) I > II > III > IV

40. The true sentence among the following is

A) G is a function of temperature but G is not a function of temperature

B) Both G and G are functions of temperature

C)Both G and G are not functions of temperature

D) G is not a function of temperature but G is a function of temperatures

41. The isomer(s) of [Ni(NH3)3Cl3] that has/have a Cl–Ni–Cl angle of 180°, is/are:

A) cis and trans both B) facial isomer only

C)Meridional and trans both D) meridional isomer only




42. Which one of the following sets forms the biodegradable polymer

A) CH2 = CH-CN and CH2 = CH-CH = CH2

B) H2N – CH2 – COOH and H2N – (CH2)5 – COOH

C)HO – CH2 – CH2 – OH and

D)

43. Amongst the following, the solution with the highest ionic conductance at 298K is

A) 30.1M CH COOH B) Distilled water C) 0.1M NaCl D) 0.1M Glucose

44. Which of the following has the shortest C-Br bond length

A) B) C) D)

45. The first, second and third ionisation enthalpies of a metal are 738, 1450 and 7730

kJ –1mol , respectively. How many moles of HCl and H2SO4, respectively, will be needed

to react completely with 2 moles of the metal hydroxide?

A) 6 and 3 B) 2 and 2 C)4 and 2 D) 1 and 1




SECTION-II



more than two decimal places, round-off the value of Two decimal places.

Answer to each question will be evaluated according to the following marking scheme:


46. The number of bonds between sulphur and oxygen atoms in sulphate and disulphate ions

is ______.

47. The generation time of any substance is the time in which its concentration doubles. The

growth of a certain bacteria follows first order kinetics. If the population of bacteria

triples in 96 hours, what is the generation time (in hours) for it? (log2 = 0.3, log3= 0.48)

48. A quantity of 75.2 g of phenol is dissolved in 1 kg of a solvent (Tf = 273) of kf =14 K–kg

/mol. If the above solution at its freezing point is in equilibrium with a cylinder containing

an ideal gas (1 mole of 8.2 dm3 at 2.66 atm). The percentage of phenol that dimerizes

is________. (kf =14 K–kg /mol).

49. 5.2 mg of O2 is dissolved into a litre of water of density 1.04 g/mL. The concentration of

O2 in ppm is ______.

50. 3

3

1.H O

2.CrO /HA

3. PhMgBr

4. HB

Percentage of Hydrogen in A is_______.




MATHEMATICS MAX.MARKS: 100

SECTION – I


This section contains 20 multiple choice questions. Each question has 4 options (1), (2), C)and (4) for its

answer, out of which ONLY ONE option can be correct.


51. If : 2A x R x and : 2 3B x R x ; then:

A) 2,5A B R B) 1, 2B A

C) (2,5)A B R D) ( 2, 1)A B

52. If 12 distinct balls are to be placed in 3 distinct boxes, then the probability that one

particular box contains exactly 3 balls is

A) 11

55 2

3 3

B) 5510

2

3

C)22012

1

3

D) 2211

1

3

53. If x = sin-1 t and y = log (1 – t2); then 2

21

2t

d y

dx is

A) 8

3 B)

8

3 C)

3

4 D)

3

4

54. Let f and g be differentiable functions on R such that gof is the identity function, If for

some a,b R, f(a) =b, f ’ (a) = 5 and f ’’ (a) = – 5 , then g’’(b) is equal to

A) 1

25 B)

1

5 C)

1

25 D)

1

5

55. In the expansion of 20

1

sin cos

x

x

, 1l is coefficient of 2x and 2l is coefficient of 2x then

the value of 1

2

l

l at

4

A) 1 B) 2 (3)3 D)4

56. If the two equations x2 – cx + d = 0 and x2 – ax + b = 0 have one common root and the

second equation has equal roots, then 2(b + d) =

A) 0 B) a + c C)ac D) – ac




57. Let a function f : [0, 5] R be continuous, f(1) = – 2 and F be defined as F(x) =

2

1

( )x

t g t dt , where g(t) = 1

( )t

f u du , then for the function F, the point x = 1 is :

A) a point of inflection B) a point of local maxima

C)a point of local minima D) not a critical point

58. Let [t] denotes the greatest integer t and 0

5lim

x

xx

= A. Then the function,

f(x) = [x2] sin x is continuous when x is equal to

A) A B) 2A C) 3A D) 4A

59. If f(x) = 2

1 0

1

a

ax a

ax ax a

, then f(2x) – f(x) is not divisible by

A) x B) a C)2a + 3x D) x2

60. Given :

x 0 x 3

f (x) 3 x 3

6 x 3 x 6

and 6

g(x)x 1

, then the area (in sq. units) of the

region bounded by the curves y = f(x) and y = g(x) between the lines x = 2 and x = 3, is

A) 5 4

6log4 3

B)

5 46log

2 3

C)

5 43log

2 3

D)

5 26log

2 3

61. The following system of linear equations 2 6 8x py z , 2 5x y qz , 3 4x y z

A) has no solution if 2, 3p q

B) has unique solution if p =2 , q = 3

C)has infinitely many solution if p = 2 , q R

D) has trivial solution only

62. If (p ~ r) (~p q) is false then the truth value of p, q and r, respectively

A) T, F, F B) F, F, T C) F, T, T D) T, F, T




63. An ellipse with co-ordinate axis as the axis passes through the point (4, -1). If this ellipse

touches the line 4 10 0x y then its eccentricity can be

A) tan 300 B) cos600 C) sin1200 D) cot 2400

64. If 2z z z z then range of z is

A) 1, 2 B)

1,1

2

C) [1, 2] D) 2, 2

65. 2

0

( 1) tann n

n

x

and 2

0

cos n

n

y

, where 04

. If ( )y f x then domain of f(x) is

A) R B) R – {0} C) R – {1} D) (1/2,1)

66. 2 2

2

dy x y

dx xy If y(3) = a , y(2) = 1, then a possible value of a is

A) 3

2 B)

2

3 C)

3

2 D)

3

2

67. If (2, -8) is at one end of a focal chord of the parabola y2 = 32x, then equation of normal

to the parabola at the other end of the focal chord is

A) 2x + y = 32 B) x + y = 64 C)2x + y = 96 D) x + 2y = 96

68. Let an be the nth term of G.P. of positive terms. If p = 25

12 1

1

( 1)

nn

n

a and q = 25

12

1

( 1)

nn

n

a ,

then p

q =

A) 0 B) 1

2

a

a C) 1 D) 25

24

a

a

69. The probability distribution of a discrete random variable X is given below

X 2 3 4 5

P(X) 5

k

7

k

9

k

11

k

then E(X) is

A) 6 B) 1 D) 1

6 D)

61

16




70. cos sin 1

sin

x

x x xdx

e x x = log |f(x)| + g(x) + c, where c is constant of integration and f(x) is

positive, then f(x) + g(x) may be equal to

A) ex + sin x + 2x B) ex + sin x C) ex - sin x D) ex + sin x + x

SECTION-II



more than two decimal places, round-off the value of Two decimal places.

Answer to each question will be evaluated according to the following marking scheme:


71. Let 2 2

a i j k and

b i j . If

c is a vector such that .

a c c ,

c a = 2 2 and the

angle between

a b and c is 300 then 2 ( )

a b c is

72. If rC = 41rC and C0 + 6 C1 + 11 C2 +..........+ 206 C41 = k (240) then value of k is

_________.

73. If circles x2 + y2 – 10x + 4y – 20 = 0 and x2 + y2 + 14x – 6y + 22 = 0 touch each other at

(a, b) then 13(b – a) = ________.

74. The largest term common to the sequences 1, 11, 21, 31, . . . . . . . to 100 terms and 31, 36,

41, 46, .. . . . . . . . . to 100 terms is ________.

75. If distance between the planes 2x – 3y + 5z +7 = 0 and the plane containing the lines

3 4 1

2 3 1

x y z and

2 1

1 4 2

x y z is equal to

38

k, then k is_______.

18-04-20 SR.N-SUPER CHAINA/N-CHAINA Jee-Main GTM-15

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Transcript of 18-04-20 SR.N-SUPER CHAINA/N-CHAINA Jee-Main GTM-15