| 1.
A particle P starts from the point
z0 = 1 + 2i
where i = 
It moves first horizontally away from origin by
5 units and then vertically away from origin by 3 units to
reach a point z1. From z1 the particle moves
 units in the direction of the
vector
 + 
and then it moves through an angle π/2
in anticlockwise direction on a circle with centre at origin,
to reach a point z2. The point z2 is given by
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| 2.
Let the function
g:(-∞, ∞) → (-π/2, π/2) be given by
g(u) = 2tan-1(eu-&pi/2.
Then, g is
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A
)
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Even and is strictly increasing in (0, ∞)
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B
)
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Odd and is strictly decreasing in (-∞, ∞)
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C
)
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Odd and is strictly increasing in (-∞, ∞)
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D
)
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Neither even nor odd, but is strictly increasing in (-∞, ∞)
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| 3.
Consider a branch of the hyperbola
x2 - 2y2 -
2x -
4y - 6 = 0
with vertex at the point A. Let B be one of the end
points of its latus rectum. If C is the focus of the hyperbola
nearest to the point A, then the area of the triangle ABC is
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A
)
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B
)
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C
)
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D
)
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| 4.
The area of the region between the curves
and
bounded by the lines x = 0 and x = &pi/4 is
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A
)
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B
)
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C
)
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D
)
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| 5.
Consider three points
P = (-sin(β-α), -cosβ) ,
Q = (cos(β-α), sinβ) and
R = (cos(β-α + θ), sin(β-θ)) ,
where
0 < α,β,θ < π/4 . Then
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A
)
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P lies on the line segment RQ
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B
)
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Q lies on the line segment PR
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C
)
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R lies on the line segment QP
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D
)
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P, Q, R are non-collinear
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| 6.
An experiment has 10 equally likely outcomes.
Let A and B be two non-empty events of the experiment. If A
consists of 4 outcomes, the number of outcomes that B
must have so that A and B are independent, is
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| 7.
Let two non-collinear unit vectors a and b form
an acute angle. A point P moves so that at any time t the
position vector OP (where O is the origin)
is given by
acost + bsint.
When P is farthest from origin O, let
M be the length of OP and u be the unit vector along OP . Then,
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A
)
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u=
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a + b
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and M = (1 + a.b)1/2
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|a + b|
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B
)
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u=
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a - b
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and M = (1 + a.b)1/2
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|a - b|
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C
)
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u=
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a + b
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and M = (1 + 2a.b)1/2
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|a + b|
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D
)
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u=
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a - b
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and M = (1 + 2a.b)1/2
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|a - b|
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| 8.
Let
Then, for an arbitrary constant C, the value of J - I equals
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A
)
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1
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log(
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e4x-e2x+1
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) + C
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2
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e4x+e2x+1
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B
)
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1
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log(
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e2x+ex+1
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) + C
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2
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e2x-ex+1
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C
)
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1
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log(
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e2x-ex+1
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) + C
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2
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e2x+ex+1
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D
)
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1
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log(
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e4x+e2x+1
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) + C
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2
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e4x-e2x+1
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| 9.
Let g(x) = log f(x) where f(x) is a twice differentiable positive function on
(0, ∞) such that f(x+1) = xf(x)
Then, for N = 1, 2, 3,....,
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g"(N +
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1
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) - g"(
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1
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) =
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2
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2
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A
)
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-4{1 +
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1
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+
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1
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+ ..... +
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1
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}
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9
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25
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(2N-1)2
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B
)
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4{1 +
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1
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+
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1
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+ ..... +
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1
|
}
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9
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25
|
(2N-1)2
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C
)
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-4{1 +
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1
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+
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1
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+ ..... +
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1
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}
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9
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25
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(2N+1)2
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D
)
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4{1 +
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1
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+
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1
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+ ..... +
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1
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}
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9
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25
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(2N+1)2
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| 10.
Suppose four distinct positive numbers
a1, a2, a3, a4 are in G.P.
Let b1 = a1, b2 = b1 + a2,
b3 = b2 + a3 and
b4 = b3 + a4.
STATEMENT-1:
The numbers b1, b2, b3, b4 are neither in A.P. nor in G.P.
and
STATEMENT-2:
The numbers b1, b2, b3, b4 are in H.P.
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A
)
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Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
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B
)
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Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
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C
)
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Statement-1 is True, Statement-2 is False
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D
)
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Statement-1 is False, Statement-2 is True
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| 11.
Let a, b, c, p, q be real numbers. Suppose α , β
are the roots of the equation
x2 + 2px + q = 0 and
α , 1/β are the roots of the equation
ax2 + 2bx + c = 0,
where
β2 ∉ {-1, 0, 1}
STATEMENT-1:
(p2 - q)(b2 - ac) ≥ 0
and
STATEMENT-2:
b ≠ pa or c ≠ qa
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A
)
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Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
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B
)
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Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
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C
)
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Statement-1 is True, Statement-2 is False
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D
)
|
Statement-1 is False, Statement-2 is True
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| 12.
Consider
L1 : 2x + 3y + p - 3 = 0
L1 : 2x + 3y + p + 3 = 0
where p is a real number, and C : x2 + y2 + 6x - 10y + 30 = 0.
STATEMENT-1:
If line L1 is a chord of circle C, then line L2
is not always a diameter of circle C.
and
STATEMENT-2:
If line L1 is a diameter of circle C, then line L2
is not a chord of circle C.
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A
)
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Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
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B
)
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Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
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C
)
|
Statement-1 is True, Statement-2 is False
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D
)
|
Statement-1 is False, Statement-2 is True
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| 13.
Let a solution y = y(x) of the differential equation
x dy -
y dx = 0
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satisfy y(2) =
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2
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STATEMENT-1:
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y(x) = sec(sec-1x -
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π
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)
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6
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and
STATEMENT-2:
y(x) is given by
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A
)
|
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
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B
)
|
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
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C
)
|
Statement-1 is True, Statement-2 is False
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D
)
|
Statement-1 is False, Statement-2 is True
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| 14.
Consider the function f : (-∞, ∞) → (-∞, , ∞) defined by
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f(x) =
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x2-ax+1
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, 0 < a < 2
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x2+ax+1
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Which of the following is true?
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A
)
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(2 + a)2 f"(1) + (2-a)2 f"(-1) = 0
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B
)
|
(2 - a)2 f"(1) - (2+a)2 f"(-1) = 0
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C
)
|
f'(1) f'(-1) = (2-a)2
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D
)
|
f'(1) f'(-1) = -(2+a)2
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| 15.
Consider the function f : (-∞, ∞) → (-∞, , ∞) defined by
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f(x) =
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x2-ax+1
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, 0 < a < 2
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x2+ax+1
|
Which of the following is true?
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A
)
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f(x) is decreasing on (-1, 1) and has a local minimum at x = 1
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B
)
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f (x) is increasing on (-1, 1) and has a local maximum at x = 1
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C
)
|
f (x) is increasing on (-1, 1) but has neither a local maximum nor a local minimum at x = 1
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D
)
|
f (x) is decreasing on (-1, 1) but has neither a local maximum nor a local minimum at x = 1
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| 16.
Consider the function f : (-∞, ∞) → (-∞, , ∞) defined by
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f(x) =
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x2-ax+1
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, 0 < a < 2
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x2+ax+1
|
Let
Which of the following is true?
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A
)
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g'(x) is positive on (-∞, 0) and negative on (0, ∞)
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B
)
|
g'(x) is negative on (-∞, 0) and positive on (0, ∞)
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C
)
|
g'(x) changes sign on both (-∞, 0) and (∞, 0)
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D
)
|
g'(x) does not change sign on (-∞, ∞)
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| 17.
Consider the lines :
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L1 :
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x+1
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=
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y+2
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=
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z+1
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3
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1
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2
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L2 :
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x-2
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=
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y+2
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=
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z-3
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1
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2
|
3
|
|
The unit vector perpendicular to both L1 and L2 is
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A
)
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-i+7j+7k
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B
)
|
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-i-7j+5k
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5
|
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C
)
|
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-i+7j+5k
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5
|
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D
)
|
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7i-7j-k
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| 18.
Consider the lines :
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L1 :
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x+1
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=
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y+2
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=
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z+1
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3
|
1
|
2
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|
|
L2 :
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x-2
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=
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y+2
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=
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z-3
|
|
1
|
2
|
3
|
|
The shortest distance between L1 and L2 is
|
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B
)
|
|
17
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C
)
|
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41
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5
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D
)
|
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17
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5
|
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| 19.
Consider the lines :
|
L1 :
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x+1
|
=
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y+2
|
=
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z+1
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3
|
1
|
2
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|
|
L2 :
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x-2
|
=
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y+2
|
=
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z-3
|
|
1
|
2
|
3
|
|
The distance of the point (1, 1, 1) from the plane passing
through the
point (-1, -2, -1) and whose normal is
perpendicular to both the lines L1 and L2 is
|
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A
)
|
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2
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B
)
|
|
7
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C
)
|
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13
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D
)
|
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23
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| 20.
Consider the lines given by
L1: x + 3y - 5 = 0
L2: 3x - ky - 1 = 0
L3: 5x + 2y - 12
Match the Statements/Expressions in Column I with the
Statements/Expressions in Column II and indicate
your answer by darkening the appropriate bubbles in
the 4 x 4 matrix given in the ORS.
|
Column I
|
Column II
|
(A)
L1, L2, L3 are concurrent, if
|
(p)
k = -9
|
(B)
One of L1, L2, L3 is parallel to at least one
of the other two, if
|
(q)
k = -6/5
|
(C)
L1, L2, L3
of the other two, if
|
(r)
k = 5/6
|
(D)
L1, L2, L3 do not form a triangle, if
|
(s)
k = 5
|
Answer:
A → (s) , B → (p,q) , C → (r), D → (p,q,q)
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| 21.
Match the Statements/Expressions in Coilumn I with the
Statements/Expressions in Column II and indicate
your answer by darkening the appropriate bubbles in
the 4 x 4 matrix given in the ORS.
|
Column I
|
Column II
|
(A)
|
The minimum value of
|
x2+2x+4
|
is
|
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x+2
|
|
(p)
0
|
(B)
Let A and B be 3 x 3 matrices of real number,
where A is symmetric, B is skew-symmetric, and
(A + B) (A - B) = (A - B) (A + B). If (AB)t = (-1)k AB,
where (AB)t is the transpose of the matrix AB,
then the possible values of k are
|
(q)
1
|
(C)
Let a = log3 log32. An integer k satisfying
1 < 2-k+3a < 2 , must be less than
|
(r)
2
|
(D)
if sinθ = cosφ , then the possible values of
|
(s)
3
|
Answer:
A → (r) , B → (q,s), C → (r), D → (p,r)
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| 22.
Consider all possible permutations of the letters of the word ENDEANOEL.
Match the Statements/Expressions
in Column I with the Statements/Expressions in Column II and
indicate your answer by darkening the
appropriate bubbles in the 4 x 4 matrix given in the ORS.
|
Column I
|
Column II
|
(A)
The number of permutations containing the
word ENDEA is
|
(p)
5!
|
(B)
The number of permutations in which the
letter E occurs in the first and the last positions is
|
(q)
2 x 5!
|
(C)
The number of permutations in which none of the letters D, L, N occurs in the last five positions is
|
(r)
7 x 5!
|
(D)
The number of permutations in which the letters A, E, O occur only in odd positions is
|
(s)
21 x 5!
|
Answer:
A → (p) , B → (s), C → (q), D → (q)
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| 23.
Consider a system of three charges
q/3 , q/3 and -2q/3
placed at points A, B and C, respectively, as shown
in the figure. Take O to be the centre of the circle of radius R and angle CAB = 60°
Figure :
|
|
|
A
)
|
|
The electric field at point O is
|
q
|
directed along the negative x-axis
|
|
8πε0R2
|
|
|
|
B
)
|
The potential energy of the system is zero
|
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|
C
)
|
The magnitude of the force between the charges at C and B is
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D
)
|
|
The potential at point O is
|
q
|
|
12πε0R
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| 24.
A radioactive sample S1 having an activity of 5μCi has twice the
number of nuclei as another sample S2
which has an activity of 10μCi. The half lives of S1 and S2 can be
|
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|
A
)
|
20 years and 5 years, respectively
|
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|
B
)
|
20 years and 10 years, respectively
|
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| 25.
A transverse sinusoidal wave moves along a string in the
positive x-direction at a speed of 10 cm/s. The
wavelength of the wave is 0.5 m and its amplitude is 10 cm.
At a particular time t, the snap-shot of the wave
is shown in figure. The velocity of point P when its displacement is 5 cm is
Figure :
|
|
|
A
)
|
|
π
|
j m/s
|
|
50
|
|
|
|
B
)
|
|
-
|
π
|
j m/s
|
|
50
|
|
|
|
C
)
|
|
π
|
i m/s
|
|
50
|
|
|
|
D
)
|
|
-
|
π
|
i m/s
|
|
50
|
|
|
| 26.
A block (B) is attached to two unstretched springs S1 and S2
with spring constants k and 4k, respectively
(see figure I). The other ends are attached to identical
supports M1 and M2 not attached to the walls. The
springs and supports have negligible mass. There is no
friction anywhere. The block B is displaced towards
wall 1 by a small distance x (figure II) and released.
The block returns and moves a maximum distance y
towards wall 2. Displacements x and y are measured with
respect to the equilibrium position of the block B.
The ratio y/x is
Figure :
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| 27.
A bob of mass M is suspended by a massless string of length L.
The horizontal velocity V at position A is
just sufficient to make it reach the point B. The angle θ at
which the speed of the bob is half of that at A,
satisfies
Figure :
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| 28.
A glass tube of uniform internal radius (r) has a valve
separating the two identical ends. Initially, the valve is
in a tightly closed position. End 1 has a hemispherical soap
bubble of radius r. End 2 has sub-hemispherical
soap bubble as shown in figure. Just after opening the valve,
Figure :
|
|
|
A
)
|
Air from end 1 flows towards end 2. No change in the volume of the soap bubbles
|
|
|
B
)
|
Air from end 1 flows towards end 2. Volume of the soap bubble at end 1 decreases
|
|
|
|
|
D
)
|
Air from end 2 flows towards end 1. Volume of the soap bubble at end 1 increases
|
|
| 29.
A vibrating string of certain length l under a tension T resonates
with a mode corresponding to the first overtone
(third harmonic) of an air column of length 75 cm inside a tube closed
at one end. The string also generates
4 beats per second when excited along with a tuning fork of frequency n.
Now when the tension of the string
is slightly increased the number of beats reduces to 2 per second.
Assuming the velocity of sound in air to
be 340 m/s, the frequency n of the tuning fork in Hz is
|
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| 30.
A parallel plate capacitor C with plates of unit area and separation d
is filled with a liquid of dielectric constant
K = 2. The level of liquid is
d/3
initially. Suppose the liquid level decreases at a constant speed V, the time
constant as a function of time t is
Figure :
|
|
|
|
|
B
)
|
|
(15d+9Vt) ε0R
|
|
2d2-3dVt-9V2t2
|
|
|
|
|
|
D
)
|
|
(15d-9Vt) ε0R
|
|
2d2+3dVt-9V2t2
|
|
|
| 31.
A light beam is traveling from Region I to Region IV (Refer Figure).
The refractive index in Regions I, II, III and
IV are n0, n0/2 , n0/6 and n0/8 , respectively.
The angle of incidence θ for which the beam just misses entering
Region IV is
Figure :
|
Region I
|
Region II
|
Region III
|
Region IV
|
|
n0/2
|
n0/6
|
n0/8
|
|
|
|
|
|
|
|
|
|
|
| 32.
STATEMENT-1:
For an observer looking out through the window of a fast moving train, the nearby objects
appear to move in the opposite direction to the train, while the distant objects appear to be stationary.
and
STATEMENT-2:
If the observer and the object are moving at velocities V1
and V2 respectively with reference
to a laboratory frame, the velocity of the object with respect to the observer is
V2 - V1
|
|
|
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
|
|
| 33.
STATEMENT-1:
It is easier to pull a heavy object than to push it on a level ground.
and
STATEMENT-2:
The magnitude of frictional force depends on the nature of the two surfaces in contact.
|
|
|
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
|
|
| 34.
STATEMENT-1:
For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
and
STATEMENT-2:
The electrical potential of a sphere of radius R and with charge Q uniformly distributed on
the surface is given by
|
|
|
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:
The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic
material as a core inside the coil.
and
STATEMENT-2:
Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.
|
|
|
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.
The nuclear charge (Ze) is non-uniformly distributed within a
nucleus of radius R. The charge density ρ(r) [charge
per unit volume] is dependent only on the radial distance r
from the centre of the nucleus as shown in figure.
The electric field is only along the radial direction.
Figure :
The electric field at r = R is
|
|
|
|
|
B
)
|
Directly proportional to a
|
|
|
C
)
|
Directly proportional to a2
|
|
|
D
)
|
Inversely proportional to a
|
|
| 37.
The nuclear charge (Ze) is non-uniformly distributed within a
nucleus of radius R. The charge density ρ(r) [charge
per unit volume] is dependent only on the radial distance r
from the centre of the nucleus as shown in figure.
The electric field is only along the radial direction.
Figure :
For a = 0, the value of d (maximum value of ρ as shown in the figure) is
|
|
|
|
|
|
|
|
|
|
| 38.
The nuclear charge (Ze) is non-uniformly distributed within a
nucleus of radius R. The charge density ρ(r) [charge
per unit volume] is dependent only on the radial distance r
from the centre of the nucleus as shown in figure.
The electric field is only along the radial direction.
Figure :
The electric field within the nucleus is generally observed
to be linarly dependent on r. This implies
|
|
|
|
|
|
|
|
|
|
| 39.
A uniform thin cylindrical disk of mass M and radius R is attached to
two identical massless springs of spring
constant k which are fixed to the wall as shown in the figure. The
springs are attached to the axle of the disk
symmetrically on either side at a distance d from its centre.
The axle is massless and both the springs and
the axle are in a horizontal plane. The unstretched length of
each spring is L. The disk is initially at its
equilibrium position with its centre of mass (CM) at a distance L
from the wall. The disk rolls without slipping
with velocity
V0 = V0i
The coefficient of friction is μ
Figure :
The net external force acting on the disk when its
centre of mass is at displacement x with respect to its
equilibrium position is
|
|
|
|
|
|
|
|
|
|
| 40.
A uniform thin cylindrical disk of mass M and radius R is attached to
two identical massless springs of spring
constant k which are fixed to the wall as shown in the figure. The
springs are attached to the axle of the disk
symmetrically on either side at a distance d from its centre.
The axle is massless and both the springs and
the axle are in a horizontal plane. The unstretched length of
each spring is L. The disk is initially at its
equilibrium position with its centre of mass (CM) at a distance L
from the wall. The disk rolls without slipping
with velocity
V0 = V0i
The coefficient of friction is μ
Figure :
The centre of mass of the disk undergoes simple harmonic motion with angular frequency
ω
equal to
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 41.
A uniform thin cylindrical disk of mass M and radius R is attached to
two identical massless springs of spring
constant k which are fixed to the wall as shown in the figure. The
springs are attached to the axle of the disk
symmetrically on either side at a distance d from its centre.
The axle is massless and both the springs and
the axle are in a horizontal plane. The unstretched length of
each spring is L. The disk is initially at its
equilibrium position with its centre of mass (CM) at a distance L
from the wall. The disk rolls without slipping
with velocity
V0 = V0i
The coefficient of friction is μ
Figure :
The maximum value of V0 for which the disk will roll without slipping is
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 42.
Column I gives a list of possible set of parameters measured in
some experiments. The variations of the
parameters in the form of graphs are shown in Column II. Match
the set of parameters given in Column I with
the graphs given in Column II. Indicate your answer by darkening
the appropriate bubbles of the 4 x 4 matrix
given in the ORS.
|
Column I
|
Column II
|
(A)
Potential energy of a simple
pendulum (y axis) as a function
of displacement (x axis)
|
(p)
|
(B)
Displacement (y axis) as a function
of time (x-axis) for a one dimensional
motion at zero or constant acceleration
when the body is moving along the positive
x-direction
|
(q)
|
(C)
Range of a projectile (y axis) as
a function of its velocity (x axis)
when projected at a fixed angle
|
(r)
|
(D)
The square of the time period (y axis)
of a simple pendulum as a function
of its length (x axis)
|
(s)
|
Answer:
A → (p,s) , B → (q,r,s) , C → (s), D → (q)
|
|
|
|
|
|
|
|
|
|
| 43.
An optical component and an object S placed along its optic axis are
given in Column I. The distance between
the object and the component can be varied. The properties of images
are given in Column II. Match all the
properties of images from Column II with the appropriate components
given in Column I. Indicate your answer
by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS.
|
Column I
|
Column II
|
(A)
|
(p)
Real Image
|
(B)
|
(q)
Virtual image
|
(C)
|
(r)
Magnified image
|
(D)
|
(s)
Image at infinity
|
Answer:
A → (p,q,r,s) , B → (q) , C → (p,q,r,s), D → (p,q,r,s)
|
|
|
|
|
|
|
|
|
|
| 44.
Column I contains a list of processes involving expansion of an
ideal gas. Match this with Column II describing
the thermodynamic change during this process. Indicate your
answer by darkening the appropriate bubbles of
the 4 x 4 matrix given in the ORS.
|
Column I
|
Column II
|
(A)
An insulated container has two chambers
separated by a valve. Chamber I contains
an ideal gas and the Chamber II has vacuum.
The valve is opened.
|
(p)
The temperature of the gas decreases
|
(B)
An ideal monoatomic gas expands
to twice its original volume such or remains constant
that its pressure
|
P ∝
|
1
|
, is the volume of the gas
|
|
V2
|
|
(q)
The temperature of the gas increases or remains constant
|
(C)
An ideal monoatomic gas expands to
twice its original volume such that
its pressure
|
P ∝
|
1
|
, where V is its volume
|
|
V4/3
|
|
(r)
The gas loses heat
|
(D)
An ideal monoatomic gas expands such
that its pressure P and volume V follows
the behaviour shown in the graph
|
(s)
The gas gains heat
|
Answer:
A → (q) , B → (p,r) , C → (p,s), D → (q,s)
|
|
|
|
|
|
|
|
|
|
| 45.
The correct stability order for the following species is
|
|
|
A
)
|
(II) > (IV) > (I) > (III)
|
|
|
B
)
|
(I) > (II) > (III) > (IV)
|
|
|
C
)
|
(II) > (I) > (IV) > (III)
|
|
|
D
)
|
(I) > (III) > (II) > (IV)
|
|
| 46.
Cellulose upon acetylation with excess acetic
anhydride / H22SO4 (catalytic)
gives cellulose triacetate
whose structure is
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 47.
In the following reaction sequence, the correct structures of E, F and G are
*implies 13 C labelled carbon)
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 48.
Among the following, the coloured compound is
|
|
|
|
|
|
|
|
|
|
| 49.
Both [Ni(CO)4] and [Ni(CN)4]2- are diamagnetic.
The hybridisations of nickel in these complexes, respectively,
|
|
|
|
|
|
|
|
|
|
| 50.
The IUPAC name of [Ni(NH3)4][NiCl4] is
|
|
|
A
)
|
Tetrachloronickel (II)-tetraamminenickel (II)
|
|
|
B
)
|
Tetraamminenickel (II) - tetrachloronickel (II)
|
|
|
C
)
|
Tetraamminenickel (II) - tetrachloronickelate (II)
|
|
|
D
)
|
Tetrachloronickel(II) - tetraamminenickelate (0)
|
|
| 51.
Electrolysis of dilute aqueous NaCl solution was carried out by
passing 10 milli ampere current. The time
required to liberate 0.01 mol of H2 gas at
the cathode is
(1 Faraday = 96500 C mol-1)
|
|
|
|
|
|
|
|
|
|
| 52.
Among the following, the surfactant that will form micelles in aqueous solution
at the lowest molar concentration
at ambient conditions is
|
|
|
A
)
|
CH3(CH2)15N+(CH3)3Br-
|
|
|
|
|
|
|
D
)
|
CH3(CH2)11N+(CH3)3Br-
|
|
| 53.
Solubility product constants (Ksp) of salts of types MX,
MX3 and M3X at temperature 'T' are 4.0 x 10-8,
3.2 x 10-14 and 2.7 x 10-15, respectively.
Solubilities (mol dm-3) of the salts at temperature 'T' are in the order
|
|
|
|
|
|
|
|
|
|
| 54.
STATEMENT-1:
Aniline on reaciton with NaNO2/HCl at 0°C
followed by coupling with β-naphthol gives a dark
blue coloured precipitate.
and
STATEMENT-2:
The colour of the compound formed in the reaction of aniline with
NaNO2/HCl at 0°C followed
by coupling with β-naphthol is due to the extended conjugation.
|
|
|
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
|
|
| 55.
STATEMENT-1:
[Fe(H2O)5NO]SO4 is paramagnetic.
and
STATEMENT-2:
The Fe in [Fe(H2O)5NO]SO4 has three unpaired electrons.
|
|
|
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
|
|
| 56.
STATEMENT-1:
The geometrical isomers of the complex [M(NH3)4Cl2]
are optically inactive.
and
STATEMENT-2:
Both geometrical isomers of the complex [M(NH3)4Cl2]
possess axis of symmetry
|
|
|
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
|
|
| 57.
STATEMENT-1:
There is a natural asymmetry between converting work to heat and converting heat to work.
and
STATEMENT-2:
No process is possible in which the sole result is the absorption of heat from a reservoir and
its complete conversion into work.
|
|
|
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.
A tertiary alcohol H upon acid catalysed dehydration gives a product I.
Ozonolysis of I leads to compounds
J and K. Compound J upon reaction with KOH gives benzyl
alcohol and a compound L, whereas K on reaction
with KOH gives only M.
Compound H is formed by the reaction of
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 59.
A tertiary alcohol H upon acid catalysed dehydration gives a product I.
Ozonolysis of I leads to compounds
J and K. Compound J upon reaction with KOH gives benzyl
alcohol and a compound L, whereas K on reaction
with KOH gives only M.
The structure of compound I is
|
|
|
A
)
|
|
|
|
B
)
|
|
|
|
C
)
|
|
|
|
D
)
|
|
|
| 60.
A tertiary alcohol H upon acid catalysed dehydration gives a product I.
Ozonolysis of I leads to compounds
J and K. Compound J upon reaction with KOH gives benzyl
alcohol and a compound L, whereas K on reaction
with KOH gives only M.
The structures of compounds J, K and L respectively, are
|
|
|
A
)
|
PhCOCH3, PhCH2COCH3 and PhCH2COO-K+
|
|
|
B
)
|
PhCHO, PhCH2CHO and PhCOO-K+
|
|
|
C
)
|
PhCOCH3, PhCH2CHO and CH3COO-K+
|
|
|
D
)
|
PhCHO, PhCOCH3 and PhCOO-K+
|
|
| 61.
In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal
prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between
them. A space-filling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere
on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres
are then placed over the first layer so that they touch each other and represent the second layer. Each one
of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a
third layer that is identical to the bottom layer in relative position.
Assume radius of every sphere to be 'r'.
The number of atoms in this HCP unit cell is
|
|
|
|
|
|
|
|
|
|
| 62.
In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal
prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between
them. A space-filling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere
on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres
are then placed over the first layer so that they touch each other and represent the second layer. Each one
of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a
third layer that is identical to the bottom layer in relative position.
Assume radius of every sphere to be 'r'.
The volume of this HCP unit cell is
|
|
|
A
)
|
24r3
|
|
|
B
)
|
16r3
|
|
|
C
)
|
12r3
|
|
|
D
)
|
|
64
|
r3
|
|
3
|
|
|
| 63.
In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal
prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between
them. A space-filling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere
on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres
are then placed over the first layer so that they touch each other and represent the second layer. Each one
of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a
third layer that is identical to the bottom layer in relative position.
Assume radius of every sphere to be 'r'.
The empty space in this HCP unit cell is
|
|
|
|
|
|
|
|
|
|
| 64.
Match the compounds in Column I with their characteristic test(s)/reaction(s)
given in Column II. Indicate your
answer by darkening the appropriate bubbles of
the 4 x 4 matrix given in the ORS
|
Column I
|
Column II
|
(A)
|
(p)
Sodium fusion extract of the compound gives Prussian
blue colour with FeSO4
|
(B)
|
(q)
Gives positive FeCl3 test
|
(C)
|
(r)
Gives white precipitate with AgNO3
|
(D)
|
(s)
Reacts with aldehydes to form the corresponding
hydrazone derivative
|
Answer:
A → (r,s) , B → (p,q) , C → (p,q,r), D → (p)
|
|
|
|
|
|
|
|
|
|
| 65.
Match the conversions in Column I with the type(s) of reaction(s)
given in Column II. Indicate your answer
by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS
|
Column I
|
Column II
|
(A)
PbS → PbO
|
(p)
Roasting
|
(B)
CaCO3 → CaO
|
(q)
Calcination
|
(C)
ZnS → Zn
|
(r)
Carbon reduction
|
(D)
Cu2S → Cu
|
(s)
Self reduction
|
Answer:
A → (p) , B → (q) , C → (p,r), D → (p,s)
|
|
|
|
|
|
|
|
|
|
| 66.
Match the entries in Column I with the correctly related quantum
number(s) in Column II. Indicate your answer
by darkening the appropriate bubbles of the 4 x 4 matrix given in the ORS
|
Column I
|
Column II
|
(A)
Oribital angular momentum of the electron
in a hydrogen-like atomic orbital
|
(p)
Principal quantum number
|
(B)
A hydrogen-like one-electron wave function
obeying Pauli principle
|
(q)
Azimuthal quantum number
|
(C)
Shape, size and orientation of hydrogen-like
atomic orbitals
|
(r)
Magnetic quantum number
|
(D)
Probability density of electron at the nucleus
in hydrogen-like atom
|
(s)
Electron spin quantum number
|
Answer:
A → (q) , B → (s) , C → (p,q,r), D → (p,q,r)
|
|
|
|
|
|
|
|
|
|