Allen DLP JEE Mains Leader Course AIOT Paper WITH Solution DATE 22-12-2019 PDF

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Download Allen DLP JEE Mains Leader Course AIOT Paper WITH Solution DATE 22-12-2019 PDF

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)0000CJA102119025)

(0000CJA102119025)

DISTANCE LEARNING PROGRAMME (Academic Session : 2019 - 2020)

Test Pattern JEE(Main) AIOT 22-12-2019

JEE(Main) : LEADER TEST SERIES / JOINT PACKAGE COURSE 12th Undergoing/Pass Students Paper : Physics, Chemistry & Mathematics Read carefully the Instructions this Test Booklet.

1.

Immediately fill in the form number on this page of the

2.

Test Booklet with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited. The candidates should not write their Form Number anywhere else (except in the specified space) on the Test Booklet/Answer Sheet.

3. 4. 5.

6.

The test is of 3 hours duration. The Test Booklet consists of 75 questions. The maximum marks are 300. There are thr ee parts in the que stion paper 1,2,3 consisting of Physics, Chemistry and Mathematics having 25 questions in each subject and each subject having Two sections. (i) Section-I contains 20 multiple choice questions with only one correct option. Marking scheme : +4 for correct answer, 0 if not attempted and –1 in all other cases. (ii) Section-II contains 5 Numerical Value Type questions Marking scheme : +4 for correct answer and 0 in all other cases. Use Blue/Black Ball Point Pen only for writting particulars/marking responses on Side–1 and Side–2 of the Answer Sheet. Use of pencil is strictly prohibited.

7.

No candidate is allowed to carry any textual material, printed or written, bits of papers, mobile phone any electronic device etc, except the Identity Card inside the

examination hall/room. Rough work is to be done on the space provided for this purpose in the Test Booklet only. 9. On completion of the test, the candidate must hand over the Answer Sheet to the invigilator on duty in the Room/ Hall. However, the candidate are allowed to take away this Test Booklet with them. 10. Do not fold or make any stray marks on the Answer Sheet. 8.

Name of the Candidate (in Capitals) Form Number

: in figures

Candidate’s Signature :

Invigilator’s Signature :

Your Target is to secure Good Rank in JEE(Main) 2020 +91-744-2757575

[email protected]

www.dlp.allen.ac.in, dsat.allen.ac.in

ALLEN

PART 1 - PHYSICS SECTION–I : (Maximum Marks : 80) 

This section contains TWENTY questions.



Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.



For each question, darken the bubble corresponding to the correct option in the ORS.



For each question, marks will be awarded in one of the following categories : Full Marks : +4 If

only

th e

bubble

corresponding to the c orrect option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases 1.

AM radio band has carrier frequency from 500 kHz to 1500 kHz. Assuming a fixed inductance in a simple LC circuit, what is ratio o f highest capacitanc e to lowest capacitance required to cover this frequency range ? (A) 3

(B) 6 (C) 9

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

(D) 12

0000CJA102119025

ALLEN 2.

Water is flowing in a pipe as depicted in the figure. The pressure at the diameter of 3 cm is p2 and velocity there is v 2 :5

5

d2 = 3 cm

p1 = 10 Pa d1 = 5 cm

1.5m

d2 = 3 cm

p1 = 10 Pa d1 = 5 cm

1.5m

v1 = 4 m/s

v1 = 4 m/s

(A) v2 > 4 m/s and p2 < 105 Pa (B) v2 > 4 m/s and p2 > 105 Pa (C) v2 < 4 m/s and p2 < 105 Pa (D) v 2 < 4 m/s and p2 > 105 Pa 3.

A ball falls on a wedge. The wedge is initially at rest. Friction is absent everywhere. The collision is elastic :-

45° 45°

(A) Mechanical energy as well as momentum is conserved in all direction. (B) Mechanical energy is conserved but mo mentum is no t conser ved in all directions. (C) Mechanical energy as well as momentum is not conserved. (D) Mechanical energy is not conserved but momentum is conserved in all directions. All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

0000CJA102119025

ALLEN scale and pitch is 0.5 mm. When we fix a wire between it's jaws, it reads 2 divisions on main scale and 48 divisions on circular scale. If the screw gauge has no zero error, radius of wire is :-

5.

(A) 2.48 mm

(B) 1.24 mm

(A) 2.48 mm

(B) 1.24 mm

(C) 0.62 mm

(D) 0.31 mm

(C) 0.62 mm

(D) 0.31 mm

As a ball rolls down the inclined plane, the power of gravitational force Pg and frictional force Pf thereafter :(A) Pg increases with time and P f remains constant with time. (B) Pg as well as P f remain constant with time. (C) Pg as well as Pf increase with time. (D) P g remains constant and P f decreases with time.

6.

If rotating annular disc is heated, what happens to its angular momentum and angular velocity ? (A) Angular momentum decreases, angular velocity decreases. (B) Angular momentum remains constant, angular velocity increases. (C) Angular momentum remains constant, angular velocity decreases. (D) Angular momentum increases, angular velocity remains constant.

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

0000CJA102119025

7.

ALLEN

An optical fibre with core having variable refractive index and cladding hav ing constant refractive index is shown. A ray is incident at the centre of core from air as shown. The path followed by ray inside core can be :-

i0

i0

Core

Core

cladding

Refractive index

Refractive index

n core = n(r)

ncore = n(r)

ncladding = constant

n cladding = constant

Radius

Radius

(A)

(C)

q q

cladding

(B)

(A)

(D) None of these

(C)

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

(B)

q q

0000CJA102119025

8.

9.

ALLEN

The frequency of an organ pipe closed at one end in fundamental mode is f0. The frequency of second overtone is :(A) 2f0 (B) 3f0 (C) 4f0 (D) 5f0 A car is moving straight towards a stationary observer. The car is de cele rating at a constant rate such that it comes to halt before reaching the observer. The horn of car is sounding at a frequency of 1000 Hz. The frequency heard by observer as a function of time is :-

(A) 2f0

1000H g

(A)

(D) 5f0

1000Hg

t

t f

f

1000Hg

1000H g

(B)

(B)

t

t

f

f

(C)

(C) 4f0

f

f

(A)

(B) 3f0

1000H g

(C)

1000H g

t

t

f

f

1000H g

1000H g

(D)

(D) t

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

t 0000CJA102119025

ALLEN 10.

The moving coil of a galvanometer made of 200 turns of thin wire is suspended from an elastic thread. The area of coil is 1 cm2 magnetic field is 15 mT. When a current of 5µA is passed through it, it turns through 15° (in equilibrium position). What is the torsional constant of the wire (in SI units)?

11.

(A)

18 ´10 -9 Nm / rad. p

(A)

18 ´ 10-9 Nm / rad. p

(B)

4 ´ 10 -8 Nm / rad. p

(B)

4 ´10 -8 Nm / rad. p

(C)

3 ´10 - 9 Nm / rad. 2p

(C)

3 ´10 -9 Nm / rad. 2p

(D)

15 ´10- 6 Nm / rad. 2p

(D)

15 ´ 10-6 Nm / rad. 2p

A particle of mass 4 kg executes SHM such that its energy of SHM is 36 J. Its velocity at t = 0 is –3 m/s and displacement from the mean position is +20 cm. The equation of its motion is :-

3p ö æ (A) x = 20 2 sin ç15t + ÷cm 4 ø è 5p ö æ ÷cm (B) x = 40sin ç20t + 6ø è 2p ö æ ÷cm (C) x = 40sin ç15t + 3 ø è

3p ö æ (A) x = 20 2 sin ç15t + ÷ cm 4ø è 5p ö æ (B) x = 40sin ç 20t + ÷ cm 6 ø è 2p ö æ ÷ cm (C) x = 40sin ç15t + è 3 ø

(D) None of these All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

0000CJA102119025

ALLEN 12.

A charged bead (charge +4 µC) is threaded on a fixed smooth circular ring of radius 2m in gravity free space. Another charge +4µC is fixed at 1m from centre as shown. The bead is projected with just sufficient velocity to complete the circular path. If mass of bead is 100 gm, what is initial speed v0 ?

1m

2m

1m 4µC

2m 4µC

4µC

4µC

(A) 80 3 cm / s

(A) 80 3 cm / s

(B) 40 2 cm / s

(B) 40 2 cm / s

(C) 10 m/s

(C) 10 m/s

(D) 4 5m / s

(D) 4 5m / s

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

0000CJA102119025

ALLEN 13.

Unpolarized light of equal intensity is incident on four pairs of polarizing filters. Rank in order, from largest to smallest, the intensities I a to I d transmitted through the second polarizer of each pair :pass axis 30°

pass axis 30°

pass axis 30°

pass axis 30°

(a)

60° 60°

pass 30° axis

pass axis

pass 30° axis

pass axis

(b)

(b)

30° 30° 60° pass axis

pass axis

60° pass axis

pass axis

(c)

(c)

30° 30° pass axis

pass axis

pass 30° axis

(d)

(d)

(A) a > b = c > d (C) b > c > a > d

pass 30° axis

(B) d > a > b = c (D) a > b > c > d

(A) a > b = c > d (C) b > c > a > d

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

(B) d > a > b = c (D) a > b > c > d 0000CJA102119025

14.

15.

16.

ALLEN

Rutherford's planetary model of atom was rejected because :(A) this would suggest that atom was mostly empty. (B) such a nucleus cannot undergo b– decay. (C) the accelerating electron would rapidly lose energy. (D) it cannot explain atomic spectra. Assume pupil diame ter to be 2.5 m m. Assume light of wavelength 500 nm. What is the minimum distance between two point objects that can be seen clearly by the eye when kept at least distance of distinct vision? (A) 0.61 mm (B) 0.061 mm (C) 0.122 mm (D) 0.0122 mm In the circuit shown, the battery is ideal. What is the total power consumed by the circuit approximately ?

(C) 0.122 mm

200V, 40W

200V, 40W

200V,100W

200V,100W

200V, 40W

(C) 28 W

200V, 40W

200V

200V

(A) 140 W (B) 44 W

(D) 0.0122 mm

(D) 56 W

(A) 140 W (B) 44 W

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

(C) 28 W

(D) 56 W 0000CJA102119025

ALLEN 17.

In a carnot's cycle, we use a monoatomic gas. The volume V is :-

P

P

3

1m

18.

1m3

V 2m3 4m3

(A) 1.5 m3

(B) 2.4 m3

(C) 2 m3

(D) 1.8 m3

(A) 1.5 m3 (C) 2 m3

3

3

V 2m 4m

(B) 2.4 m3 (D) 1.8 m3

A capillary tube is inserted in a liquid. Liquid rises in the capillary to height h. Which of the following cannot change the value of h ?

(A) Increasing the temperature. (B) Dissolving some detergent in the liquid. (C) Increasing atmospheric pressure. (D) Decreasing the leng th of the tube protruding out of liquid. All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

0000CJA102119025

19.

ALLEN

We have attached a variable resistor in an L-R circuit connected to an AC source as shown. At what value of R will power dissipated in it be maximum ? L=

5 H 100p

L=

~ V = 200 cos(100pt)

~ V = 200 cos(100 pt)

20.

(A) 5 2W

(B)

(C) 5W

(D)

5 2

W

5 W 2

5 H 100 p

(A) 5 2W

(B)

(C) 5W

(D)

5 2

W

5 W 2

A converging lens and a diverging lens share the same principal axis. Their focal lengths are f1 & f2 respectively. What should be the distance between them so that a beam parallel to principal axis emerges parallel to principal axis ? f1

(A) f1 + f2 (C) |f1| + |f2|

f1

f2

(B) f1 – f2 (D) f2 – f 1

(A) f1 + f2 (C) |f1| + |f2|

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

f2

(B) f1 – f2 (D) f2 – f 1 0000CJA102119025

ALLEN SECTION-II : (Maximum Marks: 20) 

This section contains FIVE questions.



Th e answer to each que stion is a NUMERICAL VALUE.



Fo r each que stion, enter the cor rect numerical value (If the numerical value has more than two decimal places, truncate/ round-off the value to TWO decimal places; e.g. 6.25, 7.00, –0.33, –.30, 30.27, –127.30, if answer is 11.36777..... then both 11.36 and 11.3 7 will b e corre ct) b y darken the corresponding bubbles in the ORS. For Example : If answer is –77.25, 5.2 then fill the bubbles as follows. + 0



1 2 3

1 2 3

1 2 3

4 5 6 7

4 5 6 7

4 5 6

8 9

8 9

8 9

0 • 1 • 2 • 3 • 4 •

0

0

1

1 2 3

1 2 3

1 2 3

1 2 3

4

4 5 6 7

4 5 6 7

8 9

8 9

3

4 5 • 5 6 • 6 • 7

6 7

4 5 6 7

8 • 8 9 • 9

8 9

8 9

–

+

0 •0 1 • 1 2 • 3 • 3 4 • 4

0 •0 1 • 1

0 1

1

1

1

0 • 0 1 • 1

1

1 2 3

• 5 6 • 6 7 • 7

4 5 6 7

8 • 8 9 • 9

8 9

–

1

1

0 1

2 3 4

2 3 4

2 3 4

2 • 3 • 3 4 • 4

2 3 4

2 3 4

2 3 4

2 3 4

2 • 3 • 3 4 • 4

2 3 4

5 6 7 8

5 6 7 8

5 6

6 7 8

5 6 7 8

5 6 7 8

5 6 7 8

9

9

9

9

9

9

• 5 6 • 6 7 • 7 8 • 8 9 • 9

5 6 7 8

9

5 • 5 6 • 6 • 7 8 • 8 9 • 9

8

9

Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 I f ONLY th e corre ct numerical value is entered as answer.

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

0000CJA102119025

ALLEN 1.

250 98

Cf is split into two parts of almost equal

1.

250

mass. What is the order of magnitude for potential energy of interaction of the two parts when they are just touching each other? (in 10n eV). Fill n in OMR sheet. 2.

A parallel plate capacitor has a capacitance of 120 pF (without dielectric) and plate area of 100 cm2. The space between the plates is now filled with Mica (k = 5.0). The potential difference between the plates is 50 V. What is modulus of charge induced on either surface of mica (in nC) ?

3.

An ice cube at 0°C measures 10 cm of a side. It sits on top of a copper block with square cross section 10 cm × 10 cm and length of 20cm. The other end of the block of copper is in contact with large pool of water kept at 90° C. Conductivity of copper is 400 W/mK and density of ice is 0.9 gm/cc. In what time (in sec) is ice completely melted? Assume that ice cube melts only from surface in contact with copper. (J = 4.2 J/cal)

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

0000CJA102119025

ALLEN d 0 is placed near a long str aight wire carrying current I 0. When this current is turned off, a momentum p0 is imparted to the frame. What momentu m wo uld be imparted to the frame if the initial current is 3I0 and diameter of wire is 2d 0 . If your answer is np0, fill n in OMR sheet.

I0

5.

I0

A man of mass 80 kg is standing on the rim of a circular platform rotating about its axis with an angular velocity of 1.2 rad/s. If the man moves to the centre of the platform, what is the work done (in J) by the man in the process ? The mass of the platform is 200kg and its radius is 2m.

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

0000CJA102119025

ALLEN

PART 2 - CHEMISTRY SECTION–I : (Maximum Marks : 80) 

This section contains TWENTY questions.



Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.



For each question, darken the bubble corresponding to the correct option in the ORS.



For each question, marks will be awarded in one of the following categories : Full Marks : +4 If only the bubble corresponding to the c orrect option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : –1 In all other cases

1.

40 ml of CH3 COOH solution is mixed with V ml of 0.4 M-NaOH solution. If the pH of resulting solution at equivalence point is 9.0 , the initial concentration of CH3COOH solution is [K a of CH 3 COOH = 2 × 10 –5 , log 2 = 0.30] (A) 0.2 M

(A) 0.2 M

(B) 0.1 M

(B) 0.1 M

(C) 0.4 M

(C) 0.4 M (D) 0.8 M

All India Open Test/Leader Test Series/Joint Package Course/JEE(M ain)

0000CJA102119025

ALLEN 2.

Select the most appropriate method for formation of

2.

O

O Cl

(A)

ONa +

(B)

ONa

(C)

ONa +

(D) 3.

I +

Cl ONa +

+

(B)

Cl

Br

(C)

ONa

(D)

ONa

+

Cl

ONa +

Br ONa

I +

...