Multiple Choice QuestionsLet f : R → R be a continuous function defined
by f(x) = 1/ex + 2e-x
Statement - 1: f(c) = 1/3, for some c ∈ R.
Statement-2: 0 < f(x)≤ 
, for all x ∈ R.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Statement-1 is true, Statement-2 is true; statement-2 is not a correct explanation for Statement-1.
Statement-1 is true, Statement-2 is false.
Statement-1 is true, Statement-2 is false.
The equation of the tangent to the curve
, that is parallel to the x-axis, is
y = 0
y = 1
y = 3
y = 3
The differential equation whose solution is Ax2 + By2 = 1, where A and B are arbitrary constants is of
second order and second degree
first order and second degree
first order and first degree
first order and first degree
The differential equation representing the family of curves 
, where c > 0, is a parameter, is of order and degree as follows:
order 1, degree 2
order 1, degree 1
order 1, degree 3
order 1, degree 3
Let f be differentiable for all x. If f(1) = - 2 and f′(x) ≥ 2 for x ∈ [1, 6] , then
f(6) ≥ 8
f(6) < 8
f(6) < 5
f(6) < 5
If f is a real-valued differentiable function satisfying |f(x) – f(y)| ≤ (x – y)2 , x, y ∈ R and f(0) = 0, then f(1) equals
-1
0
2
2
A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness than melts at a rate of 50 cm3 /min. When the thickness of ice is 5 cm, then the rate at which the thickness of ice decreases, is
A function y = f(x) has a second order derivative f″(x) = 6(x – 1). If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x – 5, then the function is
(x-1)2
(x-1)3
(x+1)3
(x+1)3
then the solution of the equation is
. If f(x) is continuous in 
then f (π/4) is
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