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Page 1
Original DPPs
Black Board Problems
for JEE Advanced
Set-1
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Time Allowed : 1:30 Hrs
PHYSICS
Instructions (Q 1 to 3) : Single Option Correct type MCQs
1.
A particle is moving along x-axis back and forth in a box of length L. Assuming de-broglie hypothesis applicable for the
particle, and it is moving with constant speed in the box making perfectly elastic collisions to the walls. The possible
value of momentum of the particle is : (Note : h is plank constant, n is principal quantum number)
nh
nh
nh
2nh
(A)
(B)
(C)
(D)
2L
L
4L
3L
2.
3.
A comet takes 76 years to complete one revolution around the sun. Its eccentricity is 0.9. Find perihelion and aphelion
distance. Take Rearth = 1 AU.
(A) 1.8 AU, 34.2 AU
(B) 3.6 AU, 68.4 AU
(C) 2.4 AU, 45.6 AU
(D) None of these

A nucleus moving with a velocity v emits an -particle. Let the velocities of the -particle and the remaining nucleus


be v1 and v2 and their masses be m1 and m2 :

 
(A) v , v1 and v2 must be parallel to each other

 
(B) None of the two of v , v1 and v2 should be parallel to each other
 




(C) v1 + v2 must be parallel to v
(D) m1 v1 + m2 v2 must be parallel to v
Instructions (Q 4) : Numerical Value Answer type question. Answer to be calculated upto two decimal places
4.
A vessel of volume V = 5.0 litre contains m = 1.4 g of nitrogen at a temperature T = 1800 K. Find the gas pressure in atm,
taking into account that  = 30% of molecules are dissociated into atoms at this temperature.
Instructions (Q 5 to 7) : Single Option Correct type MCQs based on below comprehension passage
AB is a uniform wire of meter bridge, across which an ideal 20 volt cell is connected as shown. Two resistor of 1  and
X  are inserted in slots of metre bridge. A cell of emf E volts and internal resistance r  and a galvanometer is connected
to jockey J as shown.
1
X
E, r
A
J
B
P
20V
5.
If E = 16 volts, r = 4  and distance of balance point P from end A is 90 cm, then the value of X is :
(A) 3 
(B) 6 
(C) 9 
(D) 12 
6.
If E = 16 volts, r = 8  and X = 9 , then the distance of balance point P from end A is :
(A) 10 cm
(B) 30 cm
(C) 60 cm
(D) 90 cm
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7.
If E = 12 volts, X = 9 , then distance of balance point P from end A is :
(A) 20 cm
(B) 50 cm
(C) 70 cm
Page 2
(D) Data insufficient
Instructions (Q 8 to 10) : Single Option Correct type MCQs based on below comprehension passage
1
m and cross sectional radius 1 cm is initially at temperature of 20ºC. At t = 0,
2
it is connected to an ideal battery of emf 500 V. Just after the key k is pressed, the current detected in the resistor was
5 amp. Due to heating effect, the temperature of wire increases. The wire is kept in vaccum, it looses heat by radiation
A straight Nichrome wire of length l =
dQ
= 45 (T – 20ºC) J/sec, where T is the temperature of the wire.
dt
After some time the temperature of the wire acquires steady state, and the value of current through it in steady state is
4.5 A.
at a rate of, –
–
dQ
= 45 (T – 20ºC) J/sec
dt
k
t= 0
500 V
8.
9.
10.
The steady-state temperature of the wire will be :
(A) 50ºC
(B) 70ºC
(C) 90ºC
(D) 100ºC
Temperature coefficient of resistance of the wire used, should be :
(A) 1.57 × 10–3/ºC
(B) 2.2 × 10–3/ºC
(C) 1.57 × 10–5/ºC
(D) 2.2 × 10–5/ºC
At steady state, the spectral energy distribution of radiation coming from the Nichrome wire is as shown. The area
under the curve, and the wavelength corresponding to maximum spectral emissive power will be respectively : (Wien's
constant = b = 3.43 × 10–3 m.K.) (Assume the wire to be perfect black body)
E

(A) 225000 Watt./m2, 10 m
(C) 112500 Watt/m2, 20 m
(B) 112500 Watt/m2, 10 m
(D) 225000 Watt/m2, 20 m
CHEMISTRY
Instructions (Q 1 to 4) : Single Option Correct type MCQs
1.
For an ideal monoatomic gas during any process T = kV, find out the molar heat capacity of the gas during the process.
(Assume vibrational degree of freedom to be active) :
(A)
2.
5
R
2
(B) 3R
(C)
7
2
(D) 4R
For the reaction [Ag(CN)2]¯  Ag+ + 2CN¯ ; Kc at 25°C is 4 × 10–19. The equilibrium concentration of Ag+ is, in a
solution which is 0.1 M in KCN & 0.03 M in AgNO3 originally :
(A) 7.5 × 10–16 M
(B) 7.5 × 10–18 M
(C) 1.25 ×1019 M
(D) 1.25 × 10–17 M
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Page 3
3.
Aqueous solution of ‘A’ + KI (excess)  Black ppt. (B) + Colourless solution (C). The hybridisation of central atom in
(C) is :
(A) sp
(B) sp2
(C) sp3
(D) dsp2
4.
A mixture of hydrocarbon C2H2, C2H4 & CH4 in mole ratio of 2 : 1 : 2 is burnt completely in the presence of air containing
80% N2 & 20% O2 by volume. The mass of air required for the complete combustion of the one gm of mixture is :
(A)
1728
112
(B)
1528
73
(C)
1920
120
(D)
112
1728
Instructions (Q 5 to 7) : Single Option Correct type MCQs based on below comprehension passage
H 2O
Quick lime 

Cl2 is

 (B) + H2O
(A)
(dried)
5.
6.
7.
Passed
(B) on reaction with NH3 & PH3 produces _____ & ______ respectively :
(A) N2 & P4
(B) NCl3 & PCl3
(C) N2 & PCl3
(D) NCl3 & PCl5
The oxidation states of Cl-atoms are :
(A) + 1, + 1
(B) + 1, 0
(D) – 1, – 1
(C) – 1, + 1
When aqueous solution of (A) reacts with gas mixture (D) and turns milky. (D) may consist of :
(A) CO2 + H2
(B) SO2 + N2
(C) CO2 + SO2
(D) All of the three
Instructions (Q 8 to 9) : Multiple Option Correct type MCQs.
8.
Which of the following property gets changed due to the interstitial carbide formation by the transition elements :
(A) Metallic lustre
(B) Malleability
(C) Ductility
(D) Electrical conductivity
9.
Which of the following reagents or process are suitable to distinguish MeOH & EtOH ?
OH
+
COOH & H
(A) NaOI
(B)
(C) Anhydrous ZnCl2 + conc. HCl
(D) Victor Mayor's process
Instructions (Q 10) : Numerical Value Answer type question. Answer to be calculated upto two decimal places.
10.
A sample of water contains 12% w/w MgSO4 and 9.5% w/w MgCl2. If the sulphate dissociates to 80% extent and chloride
to 60% extent then calculate the boiling point of the solution.
Given : Kb[H2O] = 0.785 K-Kg/mole–1 .
[Express your answers in Kelvin scale.]
MATHEMATICS
Instructions (Q 1 to 5) : Single Option Correct type MCQs
1.
The centre of a square ABCD is at Z = 0. If A is Z1, then the centroid of  ABC is
(A) Z1 (cos  ± i sin )
(B)
Z1
(cos  ± i sin )
3



(C) Z1  cos  i sin 
2
2

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(D)
Z1 


 cos  i sin 
3
2
2
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2.
3.
The number of non-zero solutions of the equations x2 – 5x – (sgn x)6 = 0 is
(A) 1
(B) 2
(C) 3
Page 4
(D) 4
Consider a real valued function f (x) satisfying 2f (xy) = (f (x)) y + (f (y))x  x, y  R and f (1) =    0, then the value of
n
( – 1)
 f (k ) is :
k 1
(A) n
4.
5.
(B) n + 1
(C) n – 1 + 
(D) n + 1 – 
From any point P on the line 5x + 4y = 20 tangents are drawn to the circle x2 + y2 = 4 meeting at Q and R, then the lows
of the circumcentre of triangle PQR is :
(A) 5x + 4y = 10
(B) 5x – 4y = 10
(C) 5x + 4y = 30
(D) 5x + 4y = 40
2
2
If the tangent and normal at ‘’ on the ellipse x  y  1 meets the y-axis at T and T' respectively, then the circle on TT'
16 9
as a diameter passes through the point :
(A) ( 7, 0)
(B) (0, 7)
(C) ( 7, 7)
(D) None of these
Instructions (Q 6) : Multiple Option Correct type MCQs.
6.
The value of x in (0, /2) satisfying the equation,
(A)

12
(B)
5
12
3 1
3 1

= 4 2 is :
sin x
cos x
(C)
7
24
(D)
11
36
Instructions (Q 7 to 9) : Asserstion - Reason type MCQs.
This section contains 3 questions. Each question contains STATEMENT-1 (Assertion) and STATEMENT -2 (Reason).
Each question has 4 choices (A), (B), (C) and (D) as given below, out of which ONLY ONE is correct :
(A) Statement 1 is True, Statement 2 is True; Statement 2 is a correct explanation for Statement 1
(B) Statement 1 is True, Statement 2 is True; Statement 2 is not a correct explanation for Statement 1
(C) Statement 1 is True, Statement 2 is False
(D) Statement 1 is False, Statement 2 is True
7.
Statement-1 : The circle C1 : x2 + y2 – 6x + 9 = 0 bisects the circumference of the circle C2 : x2 + y2 – 8x – 6y + 23 = 0
Statement-2 : Centre of the circle C1 lies on the circumference of C2.
8.
Statement 1: The plane x – 2y + 7z + 21 = 0 contains the line
x 1 y  3 z  2


3
2
1
Statement 2: Both (–1, 3, –2) and (–4, 5, –1) which are the two points on the line satisfy the equation of the plane.
9.
j  k
Statement 1: A unit vector coplanar with a  iˆ  ˆj  2kˆ and b  iˆ  2 ˆj  kˆ and perpendicular to c  iˆ  ˆj  kˆ is
.
2
Statement 2: a  (b  c ) is coplanar with b and c , and is perpendicular to a .
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Page 5
Instructions (Q 10) : Matrix Match type MCQs.
10.
Column-I
(A) Lim
x0
Column-II
(3sin x  sin 3x )4
(sec x  cos x)6
is equal to
(P) 96
(B) Given that x, y, z are positive reals such that xyz = 32. The minimum value of
(Q) 144
x2 + 4xy + 4y2 + 2z2 is equal
(C) The number of ways in which 6 men can be seated so that 3 particular men are (R) 216
consecutive is
(D) The number N = 6log10 40  5log10 36 is
(S) 256
*
*
*
*
*
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available on
Page 6
Original DPPs
Black Board Problems
for JEE Advanced
Set-1
To know the story of Original DPPs, watch https:/bit.ly/originalDPP
ANSWER KEY
PHYSICS
1. (A)
5. (C)
9. (B)
2. (A)
6. (D)
10. (A)
3. (D)
7. (C)
4. (1.90)
8. (B)
2. (B)
6. (C)
10. (377.00)
3. (C)
7. (D)
4. (A)
8. (B, C)
CHEMISTRY
1. (A)
5. (C)
9. (A, B)
MATHEMATICS
1. (D)
5. (A)
9. (A)
2. (A)
3. (D)
6. (A, D)
7. (B)
10. [(A)  S; (B)  P; (C)  Q; (D)  R]
*
*
*
*
4. (A)
8. (A)
*
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