# If f and F be both continuous in [a,b] and are derivable in (a,b) and if f’(x)=F’(x) for all x in (a,b),then f(x) and F(x) differ

1.  By 1 in [a,b]

2.  By x in [a,b]

3.  By constant in [a,b]

4.  None of these

4

By constant in [a,b]

Explanation :
No Explanation available for this question

# x1/x is a decreasing function if

1.  x

2.  x>e

3.  x=e

4.  x>1/e

4

x>e

Explanation :
No Explanation available for this question

# is equal to

1.  Sin x

2.  Cos x

3.  Tan x

4.  Log x

4

Cos x

Explanation :
No Explanation available for this question

# Taylor’s expansion of the function f(x)=1/1+x2 is

1.   where -1where -1

2.   for all real x

3.  where -1

4.   where -1

4

for all real x

Explanation :
No Explanation available for this question

# If f(x),φ(x) and Ψ(x) have derivatives when a≤x≤b,thena value of c of x lying between a and b suchthat

1.

2.

3.

4.  None of these

4

Explanation :
No Explanation available for this question

# If f(x)=ax+b,x ε[-1,1],then the point cε(-1,1) Where f’(c)=f(1)-f(-1)/2

1.  Does not exist

2.  Can be any c ε (-1,1)

3.  Can be only 1/2

4.  Can be only -1/2

4

Can be any c ε (-1,1)

Explanation :
No Explanation available for this question

# Let f(x)=x(x-1)(x-2),a=0,b=1/2.The value of ‘c’ in the Lagrange’s mean value theorem is

1.  (6+√11)/6

2.  (6-√11)/6

3.  (6+√-12)/6

4.  (6-√21)/6

4

(6-√21)/6

Explanation :
No Explanation available for this question

# Maxima and Minima occur

1.  Simultaneously

2.  Once

3.  Alternately

4.  Rarely

4

Alternately

Explanation :
No Explanation available for this question

# The minimum value of |x2-5x+2| is

1.  -5

2.  0

3.  -1

4.  -2

4

0

Explanation :
No Explanation available for this question

1.  1

2.  √2

3.  1/√2

4.  3

4