If  then  is

a) 0

b) 1

c)

d)

The function defined by     is

a) Continuous at x = 1

b) Continuous at x= 3

c) Differentiable at x = 1

d) All of the above

The two curves  and

a) cut at right angle

b) touch each other

c) cut at an angle of

d) cut at an angle of

The derivative of f(tanx) with respect to g(secx) at  where  and  is

a)

b)

c) 1

d) None of these

Let
and

where a and b are non–negative real numbers
The value of a, if (gof)x is continuous for all values of all real x, is

a) – 1

b) 0

c) 1

d) 2

Let

And

Where a and b are non – negative real numbers
The value of b if (gof) (x) is continuous for all x, is

a) – 1

b) 0

c) 1

d) 2

If the function  satisfies the conditions of Rolle’s theorem in [1, 3] and  then the values of a and b are respectively

a)

b)

c)

d)

Let f(x) satisfies the requirements of Lagrange’s mean value theorem in [0, 2]. If  and  for all x in [0, 2], then

a)

b)

c)

d)

Let  for

a) h(x) is differentiable for all x

b)  for all

c) h(x) is differentiable at two values of x in (0, 1)

d) h is continuous

The value of f(0), so that  is continuous, is equal to

a)

b)

c)

d)

The equation of motion of two stones thrown vertically upwards are  and  respectively and the maximum height attained by the first one is h. When the height of the first stone is maximum, the height of the second stone will be

a)  

b)  

c)  h

d)  0

If  then atleast one root of the equation  lies in the interval

a) (1, 2)

b) (0, 1)

c) (2, 3)

d) None of these

Let  and   then  is equal to

a)  

b)  

c)  

d)  

The function  satisfies all the conditions of Rolle’s theorem in . The value of c is

a)  0

b)  –1

c)  –2

d)  –3

If  then  is equal to

a)  

b)  1

c)  0

d)  None of these

 is equal to

a)  

b)  

c)  

d)  

If the function   be continuous at , then k is equal to

a) 3

b) 6

c) 18

d) None of these

Statement 1 – If the ordinate of a point describing the circle  decreases at the rate of 1.5 cm/s, the rate of change of the abscissa of that point when ordinate equals 4cm is 2cm/s.
Statement 2 –
Then which one of the following codes is correct

a) Statement 1 is false. Statement 2 is true.

b) Statement 1 is true. Statement 2 is true. Statement 2 is correct explanation of statement 1.

c) Statement 1 is true. Statement 2 is true. Statement 2 is not a correct explanation of statement 1.

d) Statement 1 is true. Statement 2 is false.

If   be a differentiable function with  and . Let  then  is equal to

a) 4

b) –4

c) 0

d) –2

Let be a positive increasing function with  then

a)  1

b)  

c)  

d)  3

Let  f : ℝ  ℝ defined by  

If f has a local minimum at  then a possible value of k is

a) 1

b) 0

c)

d) 1