`pi/3`
`pi/2`
`(3 pi)/2`
`pi`
`5`
`3`
`2`
`1`
`(3a^2)/4`
`a^2/2`
`(3 sqrt 3 a^2)/4`
`(sqrt 3 a^2)/4`
`f(x)` fluctuates in the interval
`f(x)` increases in the interval
`f(x) ` decreases in the interval
None of the above
`f(x)` is increasing in `(- oo , 1/2)` and decreasing in `(1/2 ,oo) `
`f(x)` is decreasing in `(- oo , 1/2)` and increasing in `(1/2 ,oo) `
`f(x)` is increasing in `(- oo, 1/2)` and dicreasing in `(1, oo)`
`f(x)` is decreasing in `(- oo, 1)` and increasing in `(1, oo)`
`f(x)` has local minima at more than one point in `(-oo , oo)`
`f(x)` has local maxima at more than one point in `(-oo , oo)`
`f(x)` has local minima at one point only in`(-oo , oo)`
`f(x)` has neither maxima nor minima in `(-oo , oo)`
None
One
Two
Three
None
One
Two
Three
`1`
`2`
`3`
`4`
`0`
`1`
`2`
`3`
It has local maximum at x = 0.
It has local minimum at x = 0.
It has neither maximum nor minimum at x= 0
It has maximum value 1.
1 only
2 only
Both 1 and 2
Neither 1 nor 2
1 and 2 only
2 and 3 only
1 and 3 only
1 , 2 and 3
`0`
`2x-1`
`4x-2`
`8x-4`
1 only
2 only
Both 1 and 2
Neither 1 nor 2
`0`
`2x-1`
`4x-2`
`8x-4`
`f(x)` is a strictly decreasing function in ( 0 , x)
`f(x)` is a strictly increasing function in ( 0 , x)
`f(x)` is neither increasing nor decreasing function in ( 0 , x)
`f(x)` is not decreasing in ( 0 , x)
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Only I
Only II
Both I and II
Neither I nor II
`-1`
`0`
`1`
`2`
`0`
`1/2`
`-1`
`2`
Only `1`
Only `2`
Both `1` and ` 2`
Neither `1` nor `2`
`x < 0` only
`x > 2` only
`0 < x < 2`
`x in (- oo,0) cup (2,oo)`
`1`
`3`
`7`
`9`
Only I
Only II
Both I and II
Neither I nor II
Only `1`
Only `2`
Both `1` and `2`
Neither `1` nor `2`
`e`
`sqrt(e)`
`1/sqrt(e)`
`1/e`
`e`
`e ^(2/e)`
`e ^(1/e)`
`1/e`
`(- 2, -1)`
`(-oo,- 2)`
`(- 1, 2)`
`(-1, oo)`
`(- 2,- 1)`
`(- oo,- 2)`
`(-1,oo)`
`(- oo,- 2) cup (- 1, oo)`
`1/2`
`1/3`
`2`
`3`
`1//2`
`1//3`
`2`
`3`
`0`
`1`
`2`
None of these
`0`
`1`
`2`
`4`
`(1, 0)`
`(2, 0)`
`(-1//2, 0)`
`(1//2, 0)`
` (2r)/sqrt(3)`
` 1/sqrt(3)`
`2r`
` sqrt(3)r`
` (2r)/sqrt(3)`
` sqrt(2r)/sqrt(3)`
`r`
`sqrt(3) r`
1 inch
1.5 inch
2 inch
2.5 inch
`x=0`
`x=2`
`x=4`
`x=-4`
`x=0`
`x=1`
`x=2`
`x=4`
`-1/e`
`1/e`
`-e`
`e`
Only I
Only II
Both I and II
Neither I nor II
`e^x` is an increasing function
`e^x` is a decreasing function
`e^x` is neither increasing nor decreasing function
`e^x` is a constant function
`-1`
`0`
`1`
`2`
`x=e^(-2)`
`x=e`
`x=e^(-1)`
`x=2e^(-1)`
square of radius
square root of radius
inversely proportional to radius
cube of the radius
`pi/4`
`pi/2`
`pi`
`(3 pi)/2`
`(0, 3)`
`(3, 6)`
`(6, 9)`
None of these
fog is always an increasing function
fog is always a decreasing function
fog is neither an increasing nor a decreasing function
None of the above
`(dy)/(dx)` must be zero
`(d^2y)/(dx^2)` must be zero
`(dy)/(dx)` must be non-zero
`(d^2y)/(dx^2)` must be non-zero
`(- 2, -1)`
`(-oo,- 2)`
`(- 1, 2)`
`(-1, oo)`
`(- 2,- 1)`
`(- oo,- 2)`
`(-1,oo)`
`(- oo,- 2) cup (- 1, oo)`
`1/2`
`1/3`
`2`
`3`
`1//2`
`1//3`
`2`
`3`
`0`
`1`
`2`
None of these
`0`
`1`
`2`
`4`
`(1, 0)`
`(2, 0)`
`(-1//2, 0)`
`(1//2, 0)`
` (2r)/sqrt(3)`
` 1/sqrt(3)`
`2r`
` sqrt(3)r`
` (2r)/sqrt(3)`
` sqrt(2r)/sqrt(3)`
`r`
`sqrt(3) r`
1 inch
1.5 inch
2 inch
2.5 inch
`x=0`
`x=2`
`x=4`
`x=-4`
`x=0`
`x=1`
`x=2`
`x=4`
`-1/e`
`1/e`
`-e`
`e`
Only I
Only II
Both I and II
Neither I nor II
`e^x` is an increasing function
`e^x` is a decreasing function
`e^x` is neither increasing nor decreasing function
`e^x` is a constant function
`-1`
`0`
`1`
`2`
`x=e^(-2)`
`x=e`
`x=e^(-1)`
`x=2e^(-1)`
square of radius
square root of radius
inversely proportional to radius
cube of the radius
`pi/4`
`pi/2`
`pi`
`(3 pi)/2`
`(0, 3)`
`(3, 6)`
`(6, 9)`
None of these
fog is always an increasing function
fog is always a decreasing function
fog is neither an increasing nor a decreasing function
None of the above
`(dy)/(dx)` must be zero
`(d^2y)/(dx^2)` must be zero
`(dy)/(dx)` must be non-zero
`(d^2y)/(dx^2)` must be non-zero