| 1.
Consider the two curves
C1 : y2 = 4x
C2 : x2 + y2 - 6x + 1 = 0
then,
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|
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A
)
|
C1 and C2 touch each other only at one point
|
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B
)
|
C1 and C2 touch each other exactly at two points
|
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C
)
|
C1 and C2 intersect (but do not touch) at exactly two points
|
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D
)
|
C1 and C2 neither intersect nor touch each other
|
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| 2.
If 0 < x < 1, then
|
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A
)
|
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1
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C
)
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x
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D
)
|
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| 3.
The edges of a parallelopiped are of unit length and are parallel
to non-coplanar unit vectors a , b , c
such that
Then, the volume of the parallelopiped is
|
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A
)
|
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1
|
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B
)
|
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1
|
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2
|
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C
)
|
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2
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D
)
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1
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| 4.
Let a and b non-zero real numbers. Then, the equation
(ax2 + by2 + c)(x2 - 5xy + 6y2) = 0
represents
|
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A
)
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Four straight lines, when c = 0 and a, b are of the same sign
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B
)
|
Two straight lines and a circle, when a = b, and c is of sign opposite to that of a
|
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|
C
)
|
Two straight lines and a hyperbola, when a and b are of
the same sign and c is of sign opposite to that
of a
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D
)
|
A circle and an ellipse, when a and b are of the same
sign and c is of sign opposite to that of a
|
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| 5.
Let
|
g(x) =
|
(x - 1)n
|
|
logcosm(x - 1)
|
0 < x < 2 , m and n are integers, m ≠ 0, n > 0, and let p be the left hand derivative
of |x - 1| at x = 1.
If
then
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| 6.
The total number of local maxima and local minima of the function
is
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| 7.
A straight line through the vertex P of a triangle
PQR intersects the side QR at the point S and the circumcircle
of the triangle PQR at the point T. If S is not
the centre of the circumcircle, then
|
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A
)
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B
)
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C
)
|
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D
)
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| 8.
Let P(x1, y1) and
Q(x2, y2), y1 < 0, y2 < 0,
be the end points of the latus rectum of the ellipse x2 + 4y2 = 4.
The equations of parabolas with latus rectum PQ are
|
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|
A
)
|
x2 + 2y =
3 +
|
|
|
B
)
|
x2 - 2y =
3 +
|
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|
C
)
|
x2 + 2y =
3 -
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|
D
)
|
x2 - 2y =
3 -
|
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| 9.
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A
)
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Sn <
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π
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3
|
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B
)
|
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Sn >
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π
|
|
3
|
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|
C
)
|
|
Tn <
|
π
|
|
3
|
|
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D
)
|
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Tn >
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π
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3
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| 10.
Let f(x) be a non-constant twice differentiable function
defined on (- ∞, ∞) such that f(x) = f(1 - x) and
then,
|
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|
A
)
|
f'(x) vanishes at least twice on [0, 1]
|
|
|
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|
C
)
|
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|
D
)
|
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| 11.
Let f and g be real valued functions defined on interval (-1, 1)
such that g''(x) is continuous, g(0) ≠ 0,
g''(0) ≠ 0, g''(0) - 0, and f(x) = g(x)sin x
STATEMENT-1 :
|
lim
|
[g(x)cot x - g(0)cosec x] = f''(0)
|
|
x→0
|
and
STATEMENT-2 :
f'(0) = g(0).
|
|
|
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
|
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| 12.
Consider three planes
P1 : x - y + z = 1
P2 : x + y - z = -1
P3 : x - 3y + 3z = 2
Let L1, L2, L3 be the lines
of intersection of the planes P2 and P3,
P3 and P1,
P1 and P2, respectively
STATEMENT-1 :
At least two of the lines L1, L2 and L3 are non-parallel.
and
STATEMENT-2 :
The three planes do not nave a common point.
|
|
|
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
|
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| 13.
Consider the system of equations
x - 2y + 3z = -1
-x + y - 2z = k
x - 3y + 4z = 1
STATEMENT-1 :
The system of equations has no solution for k ≠ 3.
and
STATEMENT-2 :
The determinant
for k ≠ 3
|
|
|
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
|
|
| 14.
Consider the system of equations
ax + by = 0, cx + dy = 0, where a, b, c, d ∈ {0, 1}.
STATEMENT-1 :
The probability that the system of equations has a unique solution is 3/8.
and
STATEMENT-2 :
The probability that the system of equations has a solution is 1.
|
|
|
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
|
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| 15.
A circle C of radius 1 is inscribed in an equilateral triangle PQR.
The points of contact of C with the sides
PQ, QR, RP are D, E, F respectively. The line PQ is given by the equation
+ y - 6 = 0 and the
point D is (3/2, 3/2).
Further, it is given that the origin and the centre of C are on
the same side of the line PQ.
The equation of circle C is
|
|
|
A
)
|
(x - 2)2 + (y - 1)2 = 1
|
|
|
B
)
|
(x - 2)2 + (y + 1/2)2 = 1
|
|
|
C
)
|
(x - )2 + (y + 1)2 = 1
|
|
|
D
)
|
(x - )2 + (y - 1)2 = 1
|
|
| 16.
A circle C of radius 1 is inscribed in an equilateral triangle PQR.
The points of contact of C with the sides
PQ, QR, RP are D, E, F respectively. The line PQ is given by the equation
+ y - 6 = 0 and the
point D is (3/2, 3/2).
Further, it is given that the origin and the centre of C are on
the same side of the line PQ.
Points E and F are given by
|
|
|
A
)
|
|
(
|
|
,
|
3
|
) , ( , 0 )
|
|
2
|
2
|
|
|
|
B
)
|
|
(
|
|
,
|
1
|
) , ( , 0 )
|
|
2
|
2
|
|
|
|
C
)
|
|
(
|
|
,
|
3
|
) , (
|
|
,
|
1
|
)
|
|
2
|
2
|
2
|
2
|
|
|
|
D
)
|
|
(
|
3
|
,
|
|
) , (
|
|
,
|
1
|
)
|
|
2
|
2
|
2
|
2
|
|
|
| 17.
A circle C of radius 1 is inscribed in an equilateral triangle PQR.
The points of contact of C with the sides
PQ, QR, RP are D, E, F respectively. The line PQ is given by the equation
+ y - 6 = 0 and the
point D is (3/2, 3/2).
Further, it is given that the origin and the centre of C are on
the same side of the line PQ.
Equations of the sides QR, RP are
|
|
|
A
)
|
|
y =
|
2
|
x + 1 , y = -
|
2
|
x - 1
|
|
|
|
|
|
|
|
|
B
)
|
|
y =
|
2
|
x , y = 0
|
|
|
|
|
|
C
)
|
|
y =
|
|
x + 1 , y = -
|
|
x - 1
|
|
|
2
|
2
|
|
|
|
|
D
)
|
y = x , y = 0
|
|
| 18.
Consider the functions defined implicitly by the equation
y3 - 3y + x = 0 on various intervals in the real
line.
If x ∈ (-∞,-2) ∪ (2, ∞) , the equation implicitly defines a unique
real valued differentiable function y = f(x).
If x ∈ (2,2) , the equation implicitly defines a unique real valued
differentiable function y = g(x) satisfying g(0) = 0.
If f(-10) = 2,
then f''(-10,) =
|
|
|
A
)
|
|
4
|
|
7332
|
|
|
|
B
)
|
|
-
|
4
|
|
|
7332
|
|
|
|
|
C
)
|
|
4
|
|
733
|
|
|
|
D
)
|
|
-
|
4
|
|
|
733
|
|
|
|
| 19.
Consider the functions defined implicitly by the equation
y3 - 3y + x = 0 on various intervals in the real
line.
If x ∈ (-∞,-2) ∪ (2, ∞) , the equation implicitly defines a unique
real valued differentiable function y = f(x).
If x ∈ (2,2) , the equation implicitly defines a unique real valued
differentiable function y = g(x) satisfying g(0) = 0.
The area of the region bounded by the curve y = f(x), the x-axis,
and the lines x = a and x = b, where
-∞< a < b < -2, is
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 20.
Consider the functions defined implicitly by the equation
y3 - 3y + x = 0 on various intervals in the real
line.
If x ∈ (-∞,-2) ∪ (2, ∞) , the equation implicitly defines a unique
real valued differentiable function y = f(x).
If x ∈ (2,2) , the equation implicitly defines a unique real valued
differentiable function y = g(x) satisfying g(0) = 0.
|
|
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|
| 21.
Let A, B, C be three sets of complex numbers as defined below
A = { z:Imz ≥ 1 }
B = { z:|z-2-i|=3}
C = { z:Re((1-i)z) = }
The number of elements in the set A ∩ B ∩ C is
|
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| 22.
Let A, B, C be three sets of complex numbers as defined below
A = { z:Imz ≥ 1 }
B = { z:|z-2-i|=3}
C = { z:Re((1-i)z) = }
Let z be any point in A ∩ B ∩ C.
The |z+1-i|2 + |z-5-i|2 lies between
|
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|
|
| 23.
Let A, B, C be three sets of complex numbers as defined below
A = { z:Imz ≥ 1 }
B = { z:|z-2-i|=3}
C = { z:Re((1-i)z) = }
Let z be any point in A ∩ B ∩ C and let w be any
point satisfying
|w-2-i | < 3. Then, |z|-|w|+3 lies
between
|
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|
|
|
|
|
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|
|
| 24.
Student I, II and III perform an experiment for measuring
the acceleration due to gravity (g) using a simple
pendulum. They use different lengths of the pendulum and / or
record time for different number of oscillations.
The observations are shown in the table.
|
Student
|
Length of the Pendulum (cm)
|
Number of oscillations (n)
|
Total time for (n) oscillations(s)
|
Time period (s)
|
|
I
|
64.0
|
8
|
128.0
|
16.0
|
|
II
|
64.0
|
4
|
64.0
|
16.0
|
|
III
|
20.0
|
4
|
36.0
|
9.0
|
If EI, EII and EIII are percentage errors in g, i.e.,
(Δg/g x 100) for students I, II and III respectively,
|
|
|
|
|
|
|
|
|
|
| 25.
Figure shows three resistor configurations
R1, R2 and R3 connected to 3 V battery.
If the power dissipated
by the configuration R1, R2 and R3 is
P1, P2 and P3, respectively, then
Figure:
|
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|
|
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|
|
|
|
| 26.
Which one of the following statements is WRONG in the context
of X-rays generated from a X-ray tube?
|
|
|
A
)
|
Wavelength of characteristic X-rays decreases
when the atomic number of the target increases
|
|
|
B
)
|
Cut-off wavelength of the continuous X-rays
depends on the atomic number of the target
|
|
|
C
)
|
Intensity of the characteristic X-rays
depends on the electrical power given to the X-ray tube
|
|
|
D
)
|
Cut-off wavelength of the continuous X-rays
depends on the energy of the electrons in the X-ray tube
|
|
| 27.
Two beams of red and violet colours are made to pass separately
through a prism (angle of the prism is 60°).
In the position of minimum deviation, the angle of refraction will be
|
|
|
A
)
|
30° for both the colours
|
|
|
B
)
|
Greater for the violet colour
|
|
|
C
)
|
Greater for the red colour
|
|
|
D
)
|
Equal but not 30° for both the colours
|
|
| 28.
An ideal gas is expanding such that PT2 = constant.
The coefficient of volume expansion of the gas is
|
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|
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| 29.
A spherically symmetric gravitational system of particles has a mass density
Where ρ0 is a constant. A test mass can undergo
circular motion under the influence of the gravitational field
of particles. Its speed V as a function of distance
r (0 < r < ∞)
from the centre of the system is represented
by
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 30.
Two balls, having linear momenta
p1 = pi and
p2 = pi and
undergo a collision in free space. There is no external
force acting on the balls. Let
p'1 and p'2
be their final momenta. The following option(s) is (are) NOT
ALLOWED for any non-zero value of p, a1,
a2, b1, b2, c1
and c2.
|
|
|
A
)
|
p'1 =
a1i +
b1j +
c1k
p'2 =
a2i +
b2j
|
|
|
|
|
C
)
|
p'1 =
a1i +
b1j +
c1k
p'2 =
a2i +
b2j -
c1k
|
|
|
D
)
|
p'1 =
a1i +
b1j
p'2 =
a2i +
b1j
|
|
| 31.
Assume that the nuclear binding energy per nucleon (B/A)
versus mass number (A) is as shown in the figure.
Use this plot to choose the correct choice(s) given below.
Figure :
|
|
|
A
)
|
Fusion of two nuclei with mass numbers lying in the range of 1 < A < 50 will release en
|
|
|
B
)
|
Fusion of two nuclei with mass numbers lying in the range of 51 < A < 100 will release energy
|
|
|
C
)
|
Fission of a nucleus lying in the mass range of 100 < A < 200
will release energy when broken into two
equal fragments
|
|
|
D
)
|
Fission of a nucleus lying in the mass range of 200 < A < 260 will release energy when broken into two
equal fragments
|
|
| 32.
A particle of mass m and charge q, moving with velocity V
enters Region II normal to the boundary as shown
in the figure. Region II has a uniform magnetic field B
perpendicular to the plane of the paper. The length of
the Region II is l. Choose the correct choice(s).
Figure :
|
|
|
A
)
|
The particle enters Region III only if its velocity
|
|
|
B
)
|
The particle enters Region III only if its velocity
|
|
|
C
)
|
Path length of the particle in Region II is maximum when velocity
|
|
|
D
)
|
Time spend in Region II is same for any velocity V
as long as the particle returns to Region I
|
|
| 33.
In a Young's double slit experiment, the separation between the
two slits is d and the wavelength of the light
is λ . The intensity of light falling on slit 1 is four times the
intensity of light falling on slit 2. Choose the correct
choice(s).
|
|
|
A
)
|
If d = λ, the screen will contain only one maximum
|
|
|
B
)
|
If λ < d < 2λ, at least one more maximum
(besides the central maximum) will be observed on the screen
|
|
|
C
)
|
If the intensity of light falling on slit 1 is reduced
so that it becomes equal to that of slit 2, the intensities
of the observed dark and bright fringes will increase
|
|
|
D
)
|
If the intensity of light falling on slit 2 is increased so
that it becomes equal to that of slit 1, the intensities
of the observed dark and bright fringes will increase
|
|
| 34.
STATEMENT-1:
In a Meter Bridge experiment, null point for an unknown
resistance is measured. Now, the
unknown resistance is put inside an enclosure maintained
at a higher temperature. The null point can be
obtained at the same point as before by decreasing
the value of the standard resistance.
and
STATEMENT-2
Resistance of a metal increases with increase in temperature.
|
|
|
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.
|
|
| 35.
STATEMENT-1:
An astronaut in an orbiting space station above the
Earth experiences weightlessness.
and
STATEMENT-2
An object moving around the Earth under the influence
of Earth'\'s gravitational force is in a
state of 'free-fall'.
|
|
|
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.
|
|
| 36.
STATEMENT-1:
Two cylinders, one hollow (metal) and the other solid (wood)
with the same mass and identical
dimensions are simultaneously allowed to roll without
slipping down an inclined plane from the same height.
The hollow cylinder will reach the bottom of the inclined plane first.
and
STATEMENT-2
By the principle of conservation of energy, the
total kinetic energies of both the cylinders are
identical when they reach the bottom of the incline.
|
|
|
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.
|
|
| 37.
STATEMENT-1:
The stream of water flowing at high speed from a garden hose pipe tends to spread like a
fountain when held vertically up, but tends to narrow down when held vertically down.
and
STATEMENT-2
In any steady flow of an incompressible fluid, the
volume flow rate of the fluid remains constant.
|
|
|
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.
|
|
| 38.
A small spherical monoatomic ideal gas bubble (λ = 5/3) is
trapped inside a liquid of density ρl(see figure). Assume
that the bubble does not exchange any heat with the liquid.
The bubble contains n moles of gas. The temperature of the
gas when the bubble is at the bottom is T0, the height
of the liquid is H and the atmospheric pressure is P0
(Neglect surface tension).
As the bubble moves upwards, besides the buoyancy
force the following forces are acting on it
|
|
|
A
)
|
Only the force of gravity
|
|
|
B
)
|
The force due to gravity and the force due to the pressure of the liquid
|
|
|
C
)
|
The force due to gravity, the force due to the pressure of
the liquid and the force due to viscosity of the liquid
|
|
|
D
)
|
The force due to gravity and the force due to viscosity of the liquid
|
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| 39.
A small spherical monoatomic ideal gas bubble (λ = 5/3) is
trapped inside a liquid of density ρl(see figure). Assume
that the bubble does not exchange any heat with the liquid.
The bubble contains n moles of gas. The temperature of the
gas when the bubble is at the bottom is T0, the height
of the liquid is H and the atmospheric pressure is P0
(Neglect surface tension).
When the gas bubble is at height y from the bottom, its temperature is
|
|
|
A
)
|
| T0( |
P0 + ρlgH |
)2/5 |
|
P0 + ρlgy
|
|
|
|
B
)
|
| T0( |
P0 + ρlg(H-y) |
)2/5 |
|
P0 + ρlgH
|
|
|
|
C
)
|
| T0( |
P0 + ρlgH |
)3/5 |
|
P0 + ρlgy
|
|
|
|
D
)
|
| T0( |
P0 + ρlg(H-y) |
)3/5 |
|
P0 + ρlgH
|
|
|
| 40.
A small spherical monoatomic ideal gas bubble (λ = 5/3) is
trapped inside a liquid of density ρl(see figure). Assume
that the bubble does not exchange any heat with the liquid.
The bubble contains n moles of gas. The temperature of the
gas when the bubble is at the bottom is T0, the height
of the liquid is H and the atmospheric pressure is P0
(Neglect surface tension).
The buoyancy force acting on the gas bubble is
(Assume R is the universal gas constant)
|
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|
A
)
|
|
ρlnRgT0
|
( P0 + ρlgH )2/5
|
|
( P0 + ρlgy )7/5
|
|
|
|
B
)
|
|
ρlnRgT0
|
|
( P0 + ρlgH )2/5
[P0 + ρlg(H-y) ]3/5
|
|
|
|
C
)
|
|
ρlnRgT0
|
( P0 + ρlgH )3/5
|
|
( P0 + ρlgy )8/5
|
|
|
|
D
)
|
|
ρlnRgT0
|
|
( P0 + ρlgH )2/5
[P0 + ρlg(H-y) ]2/5
|
|
|
| 41.
In a mixture of H-He+ gas (He+ is singly ionized He atom),
H atoms and He+ ions are excited to their respective
first excited states. Subsequently, H atoms transfer their total
excitation energy to He+ ions (by collisions).
Assume that the Bohr Model of atom is exactly valid
The quantum number of n of the state finally populated in He+ ions is
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|
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| 42.
In a mixture of H-He+ gas (He+ is singly ionized He atom),
H atoms and He+ ions are excited to their respective
first excited states. Subsequently, H atoms transfer their total
excitation energy to He+ ions (by collisions).
Assume that the Bohr Model of atom is exactly valid
The wavelength of light emitted in the visible region by
He+ ions after collisions with H atoms is
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| 43.
In a mixture of H-He+ gas (He+ is singly ionized He atom),
H atoms and He+ ions are excited to their respective
first excited states. Subsequently, H atoms transfer their total
excitation energy to He+ ions (by collisions).
Assume that the Bohr Model of atom is exactly valid
The ratio of the kinetic energy of the n = 2 electron for
the H atom to that of He+ ion is
|
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| 44.
A small block of mass M moves on a frictionless surface of
an inclined plane, as shown in figure. The angle of the
incline suddenly changes from 60° to 30° at point B.
The block is initially at rest at A. Assume that collisions
between the block and the incline are totally inelastic (g = 10 m/s2)
Figure :
The speed of the block at point B immediately
after it strikes the second incline is
|
|
|
A
)
|
 m/s
|
|
|
B
)
|
 m/s
|
|
|
C
)
|
 m/s
|
|
|
D
)
|
 m/s
|
|
| 45.
A small block of mass M moves on a frictionless surface of
an inclined plane, as shown in figure. The angle of the
incline suddenly changes from 60° to 30° at point B.
The block is initially at rest at A. Assume that collisions
between the block and the incline are totally inelastic (g = 10 m/s2)
Figure :
The speed of the block at point C, immediately before it leaves the second incline is
|
|
|
A
)
|
 m/s
|
|
|
B
)
|
 m/s
|
|
|
C
)
|
 m/s
|
|
|
D
)
|
 m/s
|
|
| 46.
A small block of mass M moves on a frictionless surface of
an inclined plane, as shown in figure. The angle of the
incline suddenly changes from 60° to 30° at point B.
The block is initially at rest at A. Assume that collisions
between the block and the incline are totally inelastic (g = 10 m/s2)
Figure :
If collision between the block and the incline is completely elastic,
then the vertical (upward) component of the
velocity of the block at point B, immediately
after it strikes the second incline is
|
|
|
A
)
|
m/s
|
|
|
B
)
|
m/s
|
|
|
|
|
D
)
|
- m/s
|
|
| 47.
Hyperconjugation involves overlap of the following orbitals
|
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| 48.
The major product of the following reaction is
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 49.
Aqueous solution of Na2S2O3
on reaction with Cl2 gives
|
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|
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|
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| 50.
Native silver metal forms a water soluble complex with a
dilute aqueous solution of NaCN in the presence of
|
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| 51.
Under the same reaction conditions, initial concentration of
1.386 mol dm-3 of a substance becomes half in
40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio
(k1/k0)
of the rate
constants for first order (k1) and zero order (k0) of the reactions is
|
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| 52.
2.5 mL of 2/5 M weak monoacidic base (Kb = 1 x 10-12 at 25°C)
is titrated with 2/15 M HCl in water at 25°C.
The concentration of H+ at equivalence point is
( Kw = 1 x 10-14 at 25°C )
|
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| 53.
The correct statement(s) about the compound given below is (are)
|
|
|
A
)
|
The compound is optically active
|
|
|
B
)
|
The compound possesses centre of symmetry
|
|
|
C
)
|
The compound possesses plane of symmetry
|
|
|
D
)
|
The compound possesses axis of symmetry
|
|
| 54.
The correct statement(s) concerning the structures E, F and G is (are)
|
|
|
A
)
|
E, F and G are resonance structures
|
|
|
B
)
|
E, F and E, G are tautomers
|
|
|
C
)
|
F and G are geometrical isomers
|
|
|
D
)
|
F and G are diastereomers
|
|
| 55.
A solution of colourless salt H on boiling with excess NaOH
produces a non-flammable gas. The gas evolution
ceases after sometime. Upon addition of Zn dust to the same
solution, the gas evolution restarts. The
colourless salt(s) H is (are)
|
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|
| 56.
A gas described by van der Waals equation
|
|
|
A
)
|
Behaves similar to an ideal gas in the limit of large molar volumes
|
|
|
B
)
|
Behaves similar to an ideal gas in the limit of large pressures
|
|
|
C
)
|
Is characterised by van der Waals coefficients that are dependent on the identity of the gas but are
independent of the temperature
|
|
|
D
)
|
Has the pressure that is lower than the pressure exerted by the same gas behaving ideally
|
|
| 57.
STATEMENT-1 :
Bromobenzene upon reaction with Br2/Fe
gives 1,4-dibromobenzene as the major product.
and
STATEMENT-2 :
In bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric
effect in directing the incoming electrophile.
|
|
|
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
|
|
| 58.
STATEMENT-1 :
Pb4+ compounds are stronger oxidizing agents than Sn4+ compounds.
and
STATEMENT-2 :
The higher oxidation states for the group 14 elements are more stable for the heavier memberes
of the group due to 'inert pair effect'.
|
|
|
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
|
|
| 59.
STATEMENT-1 :
The plot of atomic number (y-axis versus number of neutrons (x-axis) for stable nuclei shows
a curvature towards x-axis from the line of 45° slope as the atomic number is increased.
and
STATEMENT-2 :
Proton-proton electrostatic repulsions begin to overcome
attractive forces involving protons and
neutrons in heavier nuclides.
|
|
|
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
|
|
| 60.
STATEMENT-1 :
For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.
and
STATEMENT-2 :
At constant temperature and pressure, chemical reactions are spontaneous in the direction
of decreasing Gibbs energy.
|
|
|
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
|
|
| 61.
In the following reaction sequence, products I, J and L are formed. K represents a reagent.
The structure of the product I is
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 62.
In the following reaction sequence, products I, J and L are formed. K represents a reagent.
The structures of compounds J and K, respectively, are
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 63.
In the following reaction sequence, products I, J and L are formed. K represents a reagent.
The structure of product L is
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 64.
There are some deposits of nitrates and phosphates
in earth's crust. Nitrates are more soluble in water. Nitrates
are difficult to reduce under the laboratory conditions
but microbes do it easily. Ammonia forms large number
of complexes with transition metal ions. Hybridization
easily explains the ease of sigma donation capability
of NH3 and PH3. Phosphine is a flammable
gas and is prepared from white phosphorus.
Among the following, the correct statement is
|
|
|
A
)
|
Phosphates have no biological significance in humans
|
|
|
B
)
|
Between nitrates and phosphates, are less abundant in earth's crust
|
|
|
C
)
|
Between nitrates and phosphates, nitrates are less abundant in earth's crust
|
|
|
D
)
|
Oxidation of nitrates is possible in soil
|
|
| 65.
There are some deposits of nitrates and phosphates
in earth's crust. Nitrates are more soluble in water. Nitrates
are difficult to reduce under the laboratory conditions
but microbes do it easily. Ammonia forms large number
of complexes with transition metal ions. Hybridization
easily explains the ease of sigma donation capability
of NH3 and PH3. Phosphine is a flammable
gas and is prepared from white phosphorus.
Among the following, the correct statement is
|
|
|
A
)
|
Between NH3 and PH3, NH3 is a better
electron donor because the lone pair of electrons occupies
spherical s orbital and is less directional
|
|
|
B
)
|
Between NH3 and PH3, PH3 is a better
electron donor because the lone pair of electrons occupies sp3
orbital and is more directional
|
|
|
C
)
|
Between NH3 and PH3, NH3 is a better electron donor
because the lone pair of electrons occupies sp3
orbital and is more directional
|
|
|
D
)
|
Between NH3 and PH3, PH3 is a better
electron donor because the lone pair of electrons occupies spherical
s orbital and is less directional
|
|
| 66.
There are some deposits of nitrates and phosphates
in earth's crust. Nitrates are more soluble in water. Nitrates
are difficult to reduce under the laboratory conditions
but microbes do it easily. Ammonia forms large number
of complexes with transition metal ions. Hybridization
easily explains the ease of sigma donation capability
of NH3 and PH3. Phosphine is a flammable
gas and is prepared from white phosphorus.
White phosphorus on reaction with NaOH gives PH3
as one of the products. This is a
|
|
|
A
)
|
Dimerization reaction
|
|
|
B
)
|
Disproportionation reaction
|
|
|
C
)
|
Condensation reaction
|
|
|
D
)
|
Precipitation reaction
|
|
| 67.
Properties such as boiling point, freezing point and vapour pressure
of a pure solvent change when solute
molecules are added to get homogeneous solution. These are called
colligative properties. Applications of
colligative properties are very useful in day-to-day life. One of
its examples is the use of ethylene glycol and
water mixture as anti-freezing liquid in the radiator of automobiles.
A solution M is prepared by mixing ethanol and water.
The mole fraction of ethanol in the mixture is 0.9.
Given :
Freezing point depression constant of water
(Kfwater) = 1.86 K kg mol-1
Freezing point depression constant of ethanol
(Kfethanol) = 2.0 K kg mol-1
Boiling point elevation constant of water
(Kbwater) = 0.52 K kg mol-1
Boiling point elevation constant of water
(Kbethanol) = 1.2 K kg mol-1
Standard freezing point of water = 273 K
Standard freezing point of ethanol = 155.7 K
Standard boiling point of water = 373 K
Standard boiling point of ethanol = 351.5 K
Vapour pressure of pure water = 32.8 mm Hg
Vapour pressure of pure ethanol = 40 mm Hg
Molecular weight of water = 18 g mol-1
Molecular weight of ethanol = 46 g mol-1
In answering the following questions, consider the
solutions to be ideal dilute solutions and solutes to be
non-volatile and non-dissociative.
The freezing point of the solution M is
|
|
|
|
|
|
|
|
|
|
| 68.
Properties such as boiling point, freezing point and vapour pressure
of a pure solvent change when solute
molecules are added to get homogeneous solution. These are called
colligative properties. Applications of
colligative properties are very useful in day-to-day life. One of
its examples is the use of ethylene glycol and
water mixture as anti-freezing liquid in the radiator of automobiles.
A solution M is prepared by mixing ethanol and water.
The mole fraction of ethanol in the mixture is 0.9.
Given :
Freezing point depression constant of water
(Kfwater) = 1.86 K kg mol-1
Freezing point depression constant of ethanol
(Kfethanol) = 2.0 K kg mol-1
Boiling point elevation constant of water
(Kbwater) = 0.52 K kg mol-1
Boiling point elevation constant of water
(Kbethanol) = 1.2 K kg mol-1
Standard freezing point of water = 273 K
Standard freezing point of ethanol = 155.7 K
Standard boiling point of water = 373 K
Standard boiling point of ethanol = 351.5 K
Vapour pressure of pure water = 32.8 mm Hg
Vapour pressure of pure ethanol = 40 mm Hg
Molecular weight of water = 18 g mol-1
Molecular weight of ethanol = 46 g mol-1
In answering the following questions, consider the
solutions to be ideal dilute solutions and solutes to be
non-volatile and non-dissociative.
The vapour pressure of the solution M is
|
|
|
|
|
|
|
|
|
|
| 69.
Properties such as boiling point, freezing point and vapour pressure
of a pure solvent change when solute
molecules are added to get homogeneous solution. These are called
colligative properties. Applications of
colligative properties are very useful in day-to-day life. One of
its examples is the use of ethylene glycol and
water mixture as anti-freezing liquid in the radiator of automobiles.
A solution M is prepared by mixing ethanol and water.
The mole fraction of ethanol in the mixture is 0.9.
Given :
Freezing point depression constant of water
(Kfwater) = 1.86 K kg mol-1
Freezing point depression constant of ethanol
(Kfethanol) = 2.0 K kg mol-1
Boiling point elevation constant of water
(Kbwater) = 0.52 K kg mol-1
Boiling point elevation constant of water
(Kbethanol) = 1.2 K kg mol-1
Standard freezing point of water = 273 K
Standard freezing point of ethanol = 155.7 K
Standard boiling point of water = 373 K
Standard boiling point of ethanol = 351.5 K
Vapour pressure of pure water = 32.8 mm Hg
Vapour pressure of pure ethanol = 40 mm Hg
Molecular weight of water = 18 g mol-1
Molecular weight of ethanol = 46 g mol-1
In answering the following questions, consider the
solutions to be ideal dilute solutions and solutes to be
non-volatile and non-dissociative.
Water is added to the solution M such that the mole
fraction of water in the solution becomes 0.9. The boiling
point of this solution is
|
|
|
|
|
|
|
|
|
|