IPEC ADVANCE PRACTICE SET-02
PHYSICS-II
SECTION – I
[Questions 1 to 9 are single correct answer type. For each correct answer 3 marks will be
awarded and each incorrect choice 1 mark will be deducted]
1.
A sample has two isotopes A and B with mass number 150. The masses of A and B are 50g and
30g respectively. A is radioactive and B is stable. A decays to C by emitting  particles. The
half life of A is 2hrs. The mass of the sample after 4hrs and number of  particles emitted are
a) 79 gm,1.5 1023
2.
b) 74 gm,1.5 1023
c) 75 gm,3 1023 d) 79 gm,3 1023
The energies of three photons from excited Hydrogen atoms was found to be 1.9eV, 10.2 eV and
12.1 eV. These photons must come from
3.
a) a single atom
b) definitely two atoms
c) definitely three atoms
d) two or three atoms
In the circuit shown in fig. The capacitor of capacitance C = 2  F is uncharged when the key k is
open. The key is then closed for a time interval during which the capacitor becomes charged to a
voltage of 2 V. The amount of heat liberated during this time in the resistor of resistance R2  3
if the emf of the source is E = 6V. neglect internal resistance of battery. The resistance R1 = 7 
a) 7  J
4.
b) 14  J
c) 21 J
d) 28 J
A ray of light is incident at grazing incidence at origin. X-Z plane separates two media. For y  0
it is air and for y  0 it is a medium of continuously varying refractive index. If slope at a point
P(x,y) on the ray is m(y). Then the refractive index as the function of y is
a)   y   1   m  y  
c)   y   1 
5.
b)   y  
2
1
 m  y 
1
1   m  y 
d)   y   1 
2
2
1
 m  y 
2
A charge q is placed at the centre of a cylinder of radius R and length 2R. Then electric flux
through the curved surface of the cylinder is
a)
6.
7.
q
2 o
b)
q
4 o
c)
q
2 o
d)
q
2 2 o
In the plane mirror, the co-ordinates of image of charged particle(initially at origin as shown)
after two and half time periods are (initial velocity V0 is in the xy-plane and the plane of the
mirror is perpendicular to the x-axis. A uniform magnetic field B i exists in the whole space.P0 is
pitch of helix,R0 is radius of helix)
1) 17 P0 ,0, 2 R 0
2) 3P0 , 0, 2 R 0
3) 17.5P0 , 0, 2 R 0
4) 3P0 , 0, 2 R 0
A double convex lens forms a real image of an object on a screen which is fixed. Now the lens is
given a constant velocity 1 m/s along its axis and away from the screen. For the purpose of
forming a sharp image always on the screen, the object is also required to be given an appropriate
velocity. The velocity of the object at the instant the size of the image is half the size of the
object.
a) 1 m/s
8.
b) 2 m/s
c) 3 m/s
d) 4 m/s
A rigid body is placed on a rough inclined plane with initial angle of inclination zero. The angle
of inclination is slowly increased from zero. At some angle of inclination if the body topples and
the angle of inclination is independent of dimensions of the body then the body is (friction is
sufficient to prevent sliding)
9.
a) solid right circular cone
b) solid cylinder
c) solid cube
d) solid cuboid (with all unequal sides )
Two circular rings of same radii are made from similar wire of resistance 36 each.They are
placed in such a way that they cross each other’s centre C1,C2 as shown in figure. Conduction
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joints are made at intersection points A and B of the rings. An ideal cell of emf 20 volts is
connected across AB. The power delivered by cell is
1) 80 watt
2) 100watt
3) 120 watt
4)200watt
SECTION – II
Assertion-Reason type
[This section contains 4 question numbered 10 to 13 Each question contains STATEMENT-1
(Assertion) and STATEMENT-2( Reason) Each question has 4 choices (A), (B), (C) and (D)
out of which ONLY ONE is correct. For each question you will be awarded 3 marks if you have
darkened only the bubble corresponding to the correct answer and zero mark if no bubble is
darkened. In all other cases, minus one (-1) mark will be awarded.]
A) Both Statement - 1 and Statement - 2 are true and Statement - 2 is the correct explanation of
Statement - 1
B) Both Statement - 1 and Statement - 2 are true but Statement - 2 is not the correct explanation
of Statement - 1
C) Statement - 1 is true, Statement - 2 is false
D) Statement - 1 is false, Statement - 2 is true
10.
Statement - 1 :- A body is lying at rest on a rough horizontal. A person accelerating with
acceleration ai (where a is positive constant and i is a unit vector in horizontal direction)
observes the body with respect to him. The block experiences kinetic friction as observed by the
person.
Statement - 2 : -Whenever there is relative motion between the contact surfaces then kinetic
friction acts.
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11.
Statement – 1 :- A car moves along a road with uniform speed. The path of car lies in vertical
plane and is shown in fig. The radius of curvature (R) of the path is same every where. If the car
does not loose contact with road at the high point, It can travel the shown path without loosing
contact with road any where else.
Statement - 2 :- For car to loose contact with road, the normal reaction between car and road
should be zero.
12.
Statement - 1: - A charged particle undergoes uniform circular motion in a uniform magnetic
field. The only force acting on the particle is that exerted by the uniform magnetic field. If now
the speed of the same particle is some how doubled by keeping its charge and external field
constant, then the centripetal force of the particle becomes four times.
Statement - 2:- The magnitude of centripetal force on a particle of mass m moving in circle of
radius R with uniform speed V is
13
mV 2
.
R
Statement - 1:- When a neutron with energy 10.2eV collides with a hydrogen atom in ground
state the electron will be excited to first excited state.
Statement - 2 : - The collision between atoms can be either elastic, inelastic (or) perfectly
inelastic
SECTION –III
[This section contains 2 paragraphs Passage-I (14-16) and Passage-II (17-19). Based on each
paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A),
(B), (C) and (D) out of which ONLY ONE is correct For every correct answer 4 marks will
be awarded and each incorrect answer 1 mark will be deducted.]
Passage – I
A cylinder of mass m1 is free to rotate about a fixed axis. Another cylinder is of mass m2 is not
fixed to any point. A string is wound on two cylinders as shown in the figure. Mass m2 is allowed
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to fall freely under gravity. Assume that the string remains vertical to the ground throughout. The
radius of m1 is R1 and that of m2 is R2
14.
The acceleration of centre of mass of m2 is
 m  m1 
a)  2
g
 m1  m2 
15.


 m1  m2 
b) 
g
3
 m1  m2 
2

d) g
The angular acceleration of m1 and m2 are.
 m2  g
 m1  g
a) 1  
 , 2  

 m1  m2  R1
 m1  m2  R2







 g
m2
g
m1
c) 1  
,2  


3
3
 m1  m2  R1
 m1  m2  R2
2

2

16.


 m2  m1 
c) 
g
3
 m1  m2 
2






g

 g
m2
m1
b) 1  
,2  


3
3
 m1  m2  R1
 m1  m2  R2
2

2

d) 1 
g
g
, 2 
R1
R2
The tension in the string is
 mm 
a)  1 2  g
 m1  m2 


 m1m2 
b) 
g
3
 m1  m2 
2

 m1m2 
c) 
g
 3 m1  2 m2 
d)  m1  m2  g
Passage – II
0.01 mole of an ideal diatomic gas is enclosed in an adiabatic cylinder of cross-sectional area
A = 104 m2 . In the arrangement shown in fig, a block of mass M = 0.8kg is placed on a
horizontal support and another block of mass m = 1 kg is suspended from a spring of stiffness
constant k = 16 N/m. Initially, the spring is relaxed and the volume of the gas is V  1.4 104 m3
(Atmospheric Pressure= 1105 N / m 2 )
17.
The initial pressure of the gas is
a) 1105 N / m 2
b) 2 105 N / m 2
c) 3 105 N / m2
d) 4 105 N / m 2
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18.
It the block m is slightly pushed down and released it oscillates harmonically, the angular
frequency is
a) 4 rad/s
19.
b) 5 rad /s
c) 6 rad /s
d) 7 rad /s
When the gas in the cylinder is heated by a heating coil arranged inside the cylinder, the piston
starts moving up and the spring gets compressed so that the block M is just lifted up. The heat
supplied to the gas is (atmospheric pressure = 105 N / m2 , g  10 m / s 2 )
a) 25 J
b) 50 J
c) 75J
d) 100J
SECTION – IV
[This section contains 3 questions. Each questions contains statements given in two columns
which have to be matched. Statements (A, B, C D) in Column - I have to be matched with
statements (p, q, r, s) in Column - II. The answer to the question have to be appropriately
bubbled, For every correct answer 6 marks]
20.
Two blocks of same mass m = 10kg are placed on rough horizontal surface and are connected by
a massless string as shown in fig. Initially tension in the massless string is zero and the string is
 
horizontal. A horizontal force F = 40 sin  t  is applied as shown on the block A for a time
6 
interval t = 0 to t = 6 Sec. Here F is in newton and t is in second. Friction coefficient between
block A and ground is 0.20 and between B and the ground is 0.30. (g = 10 m/ s2).
Match the statements in column – I with time intervals (in seconds) in Column - II
Column– I
A)
Frictional force between block B and ground is
Column– II
p)
0 t 1
q)
1<t<3
zero in the time interval
B)
Tension in the string is non zero in the time
interval
C)
Acceleration of block A is zero in time interval
r)
3<t<5
D)
Magnitude of frictional force between A and
s)
5<t<6
ground is decreasing in the time interval
21.
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Two Particles A and B each of charge q are placed along y-axis in gravity free space as shown. A field
(electric or magnetic) is applied along the z-axis at t=0. At the same instant B is projected with a velocity
V0 i .The nature of the field and the effects are given in Column-I and Column-II respectively.
Match Column-I to Column-II.
Column– I
Column– II
A) An electric field uniform in space and
constant with time.
B) A magnetic field uniform in space and
constant with time.
C) A magnetic field uniform in space varying with
time.
D) A magnetic field non uniform in space
(varying radially from origin) but constant with
time
22.
p)
q)
r)
s)
changes the speed of both
A and B.
exerts force on both A and B
moves B with uniform speed
in circular. Path
changes the velocity of both
A and B
Match column I with column II in regard to the units of the physical quantities mentioned
in column I and units of expressions in column II
Column– I
Column– II
2
A) Frequency
p)
o E
B) Energy density
q)
B2
o
C)
Pressure
r)
D)
Energy of a particle per unit
angular momentum
s)
Here , o - Permittivity of free space,
E - Electric field strength
R - Resistance
L – Inductance
1
RC
R
L
o - Permeability of free space
B – Magnetic flux density
C – Capacitance
CHEMISTRY
SECTION – I
[Questions 23 to 31 are single correct answer type. For each correct answer 3 marks will be awarded
and each incorrect choice 1 mark will be deducted]
23.
a)
b)
c)
d)
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24.
25.
alcKOH .( E )
2
Trans-1-chloro-2 – methylcyclohexane 
.Predominant product is
a)
b)
c)
d)
The gas evolved when K 4  Fe  CN 6  was treated with dil H2SO4 is
a) CO
26.
b) HCN
c) N2
d) CO2
I mole of an ideal gas at 25oC is subjected to expand reversibly ten times of its initial volume. Then
the change in entropy of expansion is
a) 19.15JK  mol 1
27.
b) 29.15JK  mol 1
c) 9.15JK  mol 1
d) 39.15JK  mol 1
5 moles of a mixture Mohr’s salt and Fe2(SO4)3 requires 500 ml of 1M K2Cr2O7 for complete
oxidation in acidic medium. The mole % of the Mohr’s salt in the mixture is
a) 10
28.
b) 30
c) 40
d) 60
The reaction A( g )  2 B( g )  C ( g ) in an elementary reaction. In an experiment involving this
reaction, the initial partial pressures of A and B are PA =0.40 atm and PB =1.0 atm respectively.
When PC =0.3atm,the rate of the reaction relative to the initial rate is:
a)
29.
1
12
1
25
c)
1
50
d)
1
75
Calomel on reaction with NH 4OH gives
a) HgNH2Cl
30.
b)
b) NH2  Hg  Hg  Cl
In the radioactive decay of
Z
c) Hg2O
d) HgO
X A , which of the following could be considered as incorrect
statement?
a)  - decay involves the decrease of both A and Z by 2
b)  - decay involves the increase of Z by one, A remaining constant
c) K – electron capture results in the decrease of Z by one with no change in A and emission of
 -rays
d)  - ray emission is followed by the emission of  or  - particles
31.
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A exhibits how many geometrical isomers
a) 1
b) 2
c) 3
d) 4
SECTION – II
Assertion-Reason type
[This section contains 4 question numbered 32 to 35 Each question contains STATEMENT-I
(Assertion) and STATEMENT-II ( Reason) Each question has 4 choices (A), (B), (C) and (D)
out of which ONLY ONE is correct. For each question you will be awarded 3 marks if you have
darkened only the bubble corresponding to the correct answer and zero mark if no bubble is
darkened. In all other cases, minus one (-1) mark will be awarded.]
A) Both Statement - I and Statement - II are true and Statement - II is the correct explanation of
Statement - I
B) Both Statement - I and Statement - II are true but Statement - II is not the correct explanation
of Statement - I
C) Statement - I is true, Statement - II is false
D) Statement - I is false, Statement - II is true
32.
STATEMENT – I :- In close packing of spheres, a tetrahedral void is surrounded by 4 spheres
where as anoctahedral void is surrounded by 6 spheres.
STATEMENT – II :-A tetrahedral void has a tetrahedral shape where as an octahedral void has
an octahedral shape.
33.
STATEMENT – I :- Fumaric acid and maleic acid exhibits geometrical isomerism.
STATEMENT – II :- Maleic acid has more boiling point than fumaric acid.
34.
STATEMENT – I :- Glucose under goesmutarotation
STATEMENT – II :- Glucose is a reducing sugar.
35.
STATEMENT – I :- The stability of alkali metal peroxides increases with increasing atomic
number.
STATEMENT – II :- Bigger cations form more stable lattice with bigger anions.
SECTION –III
[This section contains 2 paragraphs Passage-I (36-38) and Passage-II (39-41). Based on each
paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A),
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(B), (C) and (D) out of which ONLY ONE is correct For every correct answer 4 marks will
be awarded and each incorrect answer 1 mark will be deducted.]
Passage – I:
Molar conductance of electrolytes increases with dilution. The relative increase in molar
conductance for strong electrolyte is not so large as observed in case of weak electrolytes. For
strong electrolytes molar conductivity  increases slowly with dilution and follows the following
relation   o  b C
 and  o are conductivities at dilution V and infinite dilution respectively. The above equation
is known as Debye – Huckel – Onsagar equation and is found to hold good at low concentration.
36.
According to Kohlrausch law the limiting value of equivalent conductivity of an electrolyte A2B is
given by:
1
a) A    B2
b) A    B2
c) A     B2
d) 2A     B2
2
37.
For which electrolyte the evaluation of  is not possible by extrapolation of  vs C curves to
zero concentration .
a) KCl
b) NH4OH
c) NaCl
d) K2SO4
The variation of equivalent conductance of strong electrolyte with concentration is correctly
shown in figure.
a)
b)
c)
d)
38.
Passage – II:
Aromatic compounds mainly under go electrophilic substitution reactions. The
orientation of these substitution reaction is governed by the type of functional group attached
to the benzenering. In general electron with drawing groups direct the incoming electrophile to
the meta position and electron releasing groups the direct the incoming electrophile to the
ortho and para position.
39.
a)
b)
c)
d)
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40.
Which of the following gives high percentage of meta product ?
a)
b)
c)
d)
41.
b)
c)
d)
a)
SECTION – IV
[This section contains 3 questions. Each question contains statements given in two columns
which have to be matched. Statements (A, B, C D) in Column - I have to be matched with
statements (p, q, r, s) in Column - II. The answer to the question have to be appropriately
bubbled, For every correct answer 6 marks]
42.
Match the following
Column –I
A)
B)
C)
D)
43.
NaCl
CaSO4
BaSO4
p)
q)
r)
s)
CuSO4  5H 2O
Column –II
a  b  c and       90o
a  b  c and       90o
a  b  c and       90o
a  b  c and       90o
Match the underlined substance in the reactions listed in column I with their equivalent
masses listed in column II.(M = molecular mass of the substance in question)
Column– II
Column– I
44.
A)
p)
B)
q)
C)
r)
D)
s)
M
6
M
2
M
M
3
Match the following
Column –I
Column –II
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a)
Bakelite
p)
Butadiene and styrene
b)
Buna – S
q)
Reducing sugar
c)
Lactose
r)
Phenol-formaldehyde resin
d)
Tryptophane
s)
Amino acid
MATHEMATICS
SECTION – I
[Questions 45 to 53 are single correct answer type. For each correct answer 3 marks will be
awarded and each incorrect choice 1 mark will be deducted]
45.
In ABC orthocentre is (6,10) circumcentre is (2,3) and equation of side BC
is 2x+y=17.Then the radius of the circumcircle of ABC is
a) 4
46.
b) 5
c) 7
d) 3
The inclination to the major axis of the diameter of an ellipse the square of
whose length is the harmonic mean between the squares of the major and
minor axes is
a)
47.
49.
b)

3
c)
2
3
c)
3e
2
d)

2
(1  x)1/ x  e
is
x 0
x
The value of lim
a)
48.

4
e
2
If I  
b) 
dx


sin  x   cos x
3

e
2
d) 
2e
3
, then I equals


a) 2 log sin x  sin  x    C
3



b) 2 log sin  x   sec x  C
3



c) 2 log sin x  sin  x    C
3

d) None of these
If [.] stands for the greatest integer function, the value of
10
[ x 2 ] dx
4 [ x2  28x  196]  [ x 2 ] is
a) 0
50.
b) 1
c)3
d) 7
If cos x  tan y,cos y  tan z and cos z  tan x then sinx equals
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a) sin y
51.
b) sin z
c) 2 sin180
d) 2 cos180
The equation to the curve which is such that portion of the axis of x cutoff
between the origin and the tangent at any point is proportional to the
ordinate of that point is (constant of proportionality is K)
52.
a) x=y(C-K log y)
b) log x = Ky2+C
c) x2=y(C- K log y)
d) None of these
The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines
of its angles. If the side a is 1,then A is
a)
53.

6
b)

3
c)

2
d)
2
3
The probability of a bomb hitting a bridge is ½ and two direct hits are
needed to destroy it. The leastnumber of bombs required so that the
probability of the bridge being destroyed is greater than 0.9 is
a) 7
b) 9
c) 8
d) 10
SECTION – II
Assertion-Reason type
[This section contains 4 question numbered 54 to 57 Each question contains STATEMENT-1
(Assertion) and STATEMENT-2( Reason) Each question has 4 choices (A), (B), (C) and (D)
out of which ONLY ONE is correct. For each question you will be awarded 3 marks if you have
darkened only the bubble corresponding to the correct answer and zero mark if no bubble is
darkened. In all other cases, minus one (-1) mark will be awarded.]
A) Both Statement - 1 and Statement - 2 are true and Statement - 2 is the correct explanation of
Statement - 1
B) Both Statement - 1 and Statement - 2 are true but Statement - 2 is not the correct explanation
of Statement - 1
C) Statement - 1 is true, Statement - 2 is false
D) Statement - 1 is false, Statement - 2 is true
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54.
STATEMENT 1: If f ( x) 
cos x
, x  (2 , 2 ) ,then f(x) is an odd function.
 x  1
 2   2
Where [.] denotes greatest integer function.
STATEMENT 2: Odd functions are symmetric about y-axis
55.
STATEMENT 1: a  2i  j  k and b  i  3k If c is a unit vector, then the
maximum value of the scalar triple product [a b c] is 63
STATEMENT 2: If u and v and two vectors then the scalar product u.v  u v
56.
STATEMENT 1: The differential equation of all circles in a plane must be of
order 3.
STATEMENT 2: There is only one circle passing through three non collinear
points
57.
STATEMENT 1: The graph y  x3  ax 2  bx  c has no extremum, if a 2  3b,(a, b, c  R)
STTAEMENT 2: If f  (x) vanishes at x=a then f(x) has extremum at x=a
SECTION –III
[This section contains 2 paragraphs Passage-I (58-60) and Passage-II (61-63). Based on each
paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices A),
B), C) and D) out of which ONLY ONE is correct For every correct answer 4 marks will be
awarded and each incorrect answer 1 mark will be deducted.]
PASSAGE: I
Differentiate I w.r.t. the parameter within the sign of integrals taking variable of the integrand as
constant. Now, evaluate the integral so obtained as usual as a function of the parameter and then
integrate the result to get I. Constant of integration can be computed by giving some arbitrary
values to the parameter and the corresponding value of I.
xa 1
0 log x dx is
1
58.
The value of
a) log(a-1)
b) log(a+1)
c) a log (a+1)
d) None of these

2
59.
The value of
 log(sin
2
  k 2 cos 2  ) d , where k  0 , is
0
a)  log(1  k )   log 2
b)  log(1  k )
c)  log(1  k )   log 2
d)  log(1  k )  log 2

60.

dx
dx

If 
, then the value of 
is

3
2
(a  cos x)
a 1
0 ( 10  cos x )
0
Address: First floor, M-5, City Centre, Sector-IV, Bokaro Steel City - 827 004 :7543095676
a)

81
b)
7
81
c)
7
162
d)None of these
PASSAGE:II
A player throws a fair cubical die and scores the number appearing on the die. If he throws a
one,he gets further throw let Pr denote the probability of getting a total score of exactly r
61.
If 2  r  6 , Pr equals
1
a) 1   
6
62.
r 1
1 1
b) 1   
5   6 
r 1
1 1
1   
5   6 
r 1



5
c)  
6
r
d) None of these
If r>6,Pr equals
1
a) 1   
6
r 1
b)



c)
1  1 
 
5  6 
r 6
1
 
6
r 1

 d) None of these


63.
Sum of the series S=  Pr is
r 1
a) 1
b)
1
6
c)
1
5
d)
2
3
SECTION –III
[This section contains 3 questions. Each questions contains statements given in two columns
which have to be matched. Statements (A, B, C D) in Column - I have to be matched with
statements (p, q, r, s) in Column - II. The answer to the question have to be appropriately
bubbled, For every correct answer 6 marks]
64.
Z1,Z2,Z3 are vertices of a triangle. Match the condition in List-I with type of
triangle in List-II
List-I
Z  Z  Z  Z 2 Z 3  Z 3 Z1  Z1Z 2
A)
2
1
2
2
2
3
 Z  Z1 
Re  3
0
 Z3  Z 2 
 Z  Z1 
Re  3
0
 Z3  Z 2 
Z 3  Z1
i
Z3  Z 2
B)
C)
D)
p)
List-II
right angled
q)
obtuse angled
r)
isosceles and right angled
s)
equilateral
65.
Column-I
Column-II
Address: First floor, M-5, City Centre, Sector-IV, Bokaro Steel City - 827 004 :7543095676
A)
Area enclosed by y=[x] and y={x} where [.] & {.}represent greatest
integer and fractional part functions
p)
B)
Area bounded by the curves
y 2  x3and y  2 x
The smaller area included between the curves
q)
32
sq.unit
5
1 sq.unit
r)
12 sq.unit
s)
2
Sq.unit
3
C)
x
y  1 and x  y  1
Area enclosed by  x    y   2 Where [.] denotes greatest integer
function.
D)
66.
A)
B)
C)
D)
LIST-I
Radius of the largest circle which passes
through the focus of the parabola y2=4x and
contained in it, is
The shortest distance between parabola
y2=4x and y2=2x-6 is d then d2 is
The harmonic mean of the segments of a focal
chord of a parabola y2=12x is
Tangents drawn from P to the parabola y2=16x
meet at A and B are perpendicular then the least value of AB is
p)
LIST-II
16
q)
5
r)
6
s)
4
Address: First floor, M-5, City Centre, Sector-IV, Bokaro Steel City - 827 004 :7543095676