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If are respectively the sets of local minimum and local maximum points of the function, then :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1) Option 2) Option 3)   Option 4)

The tangents to the curve  at its points

of intersection with the line  , intersect at the point :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Clearly,   and   Tangent to Parabola at B : To find slope, differentiate the given curve  Equation of tangent at B :                                       => ................(1) Equation of tangent at A : .........................(2) Clearly,(1) and (2) intersect at  .   Option 1) Option 2) Option 3) Option 4)

Let    and   ,

. If   attains maximum value at  and  attains minimum

value at  , then

is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Maxima  of  occured at   i.e.  Minima  of     occured at   i.e.     Option 1) Option 2) Option 3) Option 4)

is:

• Option 1)

6

• Option 2)

2

• Option 3)

3

• Option 4)

1

Option 1) 6 Option 2) 2 Option 3) 3 Option 4) 1

The derivative of ,

with respect to , where  is :

• Option 1)

1

• Option 2)

• Option 3)

• Option 4)

2

Derivation of             Now,  Option 1) 1     Option 2) Option 3) Option 4) 2

If m is the minimum value of k for which the function  is increasing in the interval  and M is the maximum value of  in  when  then the ordered pair  is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

For                                                                so  &                                                   minimum value of  minimum value of k is                          Option 1)   Option 2)          Option 3)               Option 4)

Let  be a continuously differentiable function such that  and . If , then  is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

and                                                                                              Option 1)Option 2)Option 3)Option 4)

ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate , then the rate  at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is  above the ground is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1)   Option 2)    Option 3)    Option 4)

If  the ordered pair  at  is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Again differentiate w.r.t.   x Option 1) Option 2)   Option 3)      Option 4)

Let  be an A.P. with  . Then the

common difference of this A.P., which maximises the product

, is :

• Option 1)

• Option 2) • Option 3)

• Option 4)

Assuming the first term of A.P. is a and difference is d. Then, Let  =>  So,  will be maximum at  So, option (2) is correct. Option 1) Option 2) Option 3) Option 4)

If  , then a+b is equal to :

• Option 1)

-4

• Option 2)

5

• Option 3)

-7

• Option 4)

1

As  denominator will become 0 => for finite limit numerator must also approach to zero as . So, L' Hospital Law will be applicable. 1-a+b=0........................(1) Now,    and    So, option(3) is correct.Option 1)-4Option 2)5Option 3)-7Option 4)1

A spherical iron ball of rdius 10cm is coated with a layer of ice of uniform

thickness that melts at a rate of  . When the thickness of

the ice is 5 cm , then the rate at which the thickness ( in cm / min ) of the ice

decreases, is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Volume of ice ,                                                                         at x = 5,                           So, option (1) is correct.                         Option 1) Option 2) Option 3) Option 4)

If the tangent to the curve  ,

at a point  on it is parallel to the line 2x+6y-11=0, then :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

the curve  ,point  parallel  line 2x+6y-11=0 Slope of given line =>  For tangent at   =>  =>  =>  =>  =>   as its given  So, for ,  and  Now,  for  ,  So, option (1)    is correct answer.     Option 1) Option 2) Option 3) Option 4)

Let  and

If  is a positive real number such that

and , then:

• Option 1)

• Option 2)

• Option 3)

• Option 4)

and                                                                                  Now, and   at    is   Now, lets check every option (1)  put the value in LHS (2)  put the value in LHS (3)   put the value in LHS (4)   put the value in LHS   So, option (2) is correct as  is true. Option 1)   Option 2) Option 3) Option 4)

The tangent and normal to the ellipse  at the point P(2,2)

meet the x-axis at Q and R, respectively, The the area(in sq. units) of the

triangle PQR is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

=> Equation of tangent at point (2,2)  => Equation of normal at point (2,2)  Area of  =  So, option (4) is correct. Option 1) Option 2) Option 3) Option 4)

If

is continuous at x = 0 , then the oredered pair ( p , q) is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

f(x) is continuous at x = 0 then LHL, for continuity LHL = RHL correct option is (3)      Option 1)Option 2)Option 3)Option 4)

Let  and  .

Then the set of all  , where the function

is increasing , is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Case 1 :                  Case 2 :                =>    correct option (2)     Option 1) Option 2) Option 3) Option 4)

If  , then k is:

• Option 1)

• Option 2)

• Option 3)

• Option 4)

So, option (1) is correct.   Option 1) Option 2) Option 3) Option 4)

Let  be differentiable at  and f(c) = 0.

If , then at x=c , g is :

• Option 1)

not differentiable if

• Option 2)

differentiable if

• Option 3)

differentiable if

• Option 4)

not differentiable

Given g(x) = | f(x) | and also given f(c)=0                                             For  g(x)  to be differentiable at C     correct option is (3) Option 1) not differentiable if  Option 2) differentiable if  Option 3) differentiable if  Option 4) not differentiable

If    is a differentiable function and    , then    is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1) Option 2) Option 3) Option 4)
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