Let , 0 < x < 2 are integers m ≠ 0, n > 0 and let p be the left hand derivative of |x − 1| at x = 1. If , then
a) n = −1, m = 1
b) n = 1, m = −1
c) n = 2, m = 2
d) n > 2, n = m
Your Answer
A stone tablet 7 feet high is placed on a wall with base 9 feet above the level of an observer’s eye. How far from the wall should the observer stand that the angle of vision subtended by the tablet at the observer’s eye may be maximum?
The value of is
a) 2asina + a2cosa
b) 2asina - a2cosa
c) 2acosa + a2sina
d) None of these
If f ( x ) = sgn (x3) then
a) f is continuous but not differentiable at x = 0
b) f ʹ(0+) = 2
c) f ʹ(0-) = 1
d) f is not derivable at x = 0
If a + b + c = 0, then the equation 3ax2 + 2bx + c = 0 has
a) At least one root in [ 0, 1 ]
b) One positive and one negative root
c) No real root
d) None of the above
is equal to
a) 1
b) 1
c) 0
If the function f(x) = ax3 + bx2 + 11x – 6 satisfies the conditions of Rolle’s theorem in [1, 3] and = 0 then the values of a and b are respectively
a) -1, 6
b) -2, 1
c) 1, -6
d) -1,
If f(x) = cos(lnx) then f f
a) cos (x – y)
b) log (x – y)
c) cos (x + y)
The value of f(0), so that
f(x) =
is continuous everywhere is
a) 3(ln4)3
b) 4(ln4)3
c) 12(ln4)3
d) 15 (ln4)3
If where . Given F(5) = 5, then f(10) is equal to
a) 5
b) 10
d) 15
Multiple choices with one or more than one correct answers then
a) x = f(y)
b) f(1) = 3
c) y increases with x for x < 1
d) f is a rational function of x
Given and f(x) = cosx – x(x + 1). Find the range of f (A).
Subjective Problems Let f (x + y) = f (x) . f (y) for all x, y. Suppose f (5) = 2 and = 3. Find f (5).
The values of lies in the interval . . .
Let f(x) be a non constant differentiable function defined on (−∞, ∞) such that f(x) = f(1 – x) and then
a) vanishes at twice an (0, 1)
b)
c)
d)
The domain of the derivative of the function f (x) =
a) R { 0 }
b) R
c) R
d) R
Using the relation , or otherwise prove that
a) True
b) False
If A > 0, B > 0 and A + B = , then the maximum value of tan A tanB is ……….
a)
For all ,
Cosine of angle of intersection of curve y = 3x – 1lnx and y = xx – 1 is
If
then the value of is
a) 0
c) −1
d) 2
Let then for all x
a) f is not continuous
b) f is not differentiable for all x
c) f ʹ is continuous
Then f(x) is continuous and differentiable at x = 1, if
