Let f (x)=(x+1) (x+2) (x+3)…..(x+100) an...

Let `f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f'(x) ^(2).` Let n be the numbers of real roots of `g(x) =0,` then:

`n lt 2`

`n gt 2`

`n lt 100`

`n gt 100`

Text Solution

Verified by Experts

The correct Answer is:

A, C

Topper's Solved these Questions

CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|30 Videos
CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATHCING TYPE PROBLEMS)|3 Videos
CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|24 Videos
COMPOUND ANGLES
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|31 Videos
DETERMINANTS
VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE-4 : SUBJECTIVE TYPE PROBLEMS|12 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

Let f (x)= signum (x) and g (x) =x (x ^(2) -10x+21), then the number of points of discontinuity of f [g (x)] is

Let f(x)={x+1,x >0 \n 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

Let f and g be two differentiable functins such that: f (x)=g '(1) sin x+ (g'' (2) -1) x g (x) = x^(2) -f'((pi)/(2)) x+ f'(-(pi)/(2)) The number of solution (s) of the equation f (x) = g (x) is/are :

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Let f(x)=x^(2)+bx+c and g(x)=x^(2)+b_(1)x+c_(1) Let the real roots of f(x)=0 be alpha, beta and real roots of g(x)=0 be alpha +k, beta+k fro same constant k . The least value fo f(x) is -1/4 and least value of g(x) occurs at x=7/2 The roots of g(x)=0 are

Let f(x)=x^2+xg^2(1)+g^''(2) and g(x)=f(1).x^2+xf'(x)+f''(x), then find f(x) and g(x).

Let g(x) =f(x)-2{f(x)}^2+9{f(x)}^3 for all x in R Then

Let g (x )=f ( x- sqrt( 1-x ^(2))) and f ' (x) =1-x ^(2) then g'(x) equal to:

Let f(x) = tan x, x in (-pi/2,pi/2)and g(x) = sqrt(1-x^2) then g(f(x)) is

VIKAS GUPTA (BLACK BOOK) ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA, x...
Text Solution
|
Let f(x) =(x^(2)-3x+ 2) (x ^(2) + 3x +2) and alpha, beta, gamma satisf...
Text Solution
|
Let f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} t...
Text Solution
|
Let y=e^x s in x^3+(t a n x)^xdotF in d(dy)/(dx)dot
Text Solution
|
Let f(x)=x +(1-x) x ^(2) +[1- x) (1- x^(2)) +…..+ (1-x) …….(1-x ^(n-1)...
Text Solution
|
Let f (x)= [{:(x ^(2)+a,0 le x lt 1),( 2x+b,1le x le 2):}and g (x)=[{:...
Text Solution
|
If f(x) = {{:((sin[x^(2)]pi)/(x^(2)-3x - 18)+ax^(2)+b",","for",0 le x ...
Text Solution
|
Let f (x) [ {:(1+x"," , 0 le x le 2),( 3-x"," ,2 lt x le 3):}: g(x...
Text Solution
|
Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f'(x) ...
Text Solution
|
Let f(x)={{:(,|x|-3,x lt 1),(,|x-2|+a,x ge 1):} g(x)={{:(,2-|x|,x lt...
Text Solution
|
Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln...
Text Solution
|
f (x) is differentiable function satisfying the relationship f ^(2) (x...
Text Solution
|
The function f (x)=[sqrt(1-sqrt(1-x ^(2)))],(where [.] denotes greates...
Text Solution
|
A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y),...
Text Solution
|
The points of discontinuities of f (x)= [(6x)/(pi)]cos [(3x)/(pi)]"in"...
Text Solution
|
Check the continuity of f(x) = {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+...
Text Solution
|
If x=phi(t),y=Psi(t)," then "(d^(2)y)/(dx^(2)) is equal to
Text Solution
|
f (x)=[x] and g (x)= {{:( 0"," , x in I ),( x ^(2)"," , cancel(in)I)...
Text Solution
|
Let f : R ^(+) to R defined as f (x)= e ^(x) + ln x and g = f ^(-1) th...
Text Solution
|
Let f (x)=[{:((3x-x ^(2))/(2),,, x lt 2),([x-1],,, 2 le x lt 3),( x ^(...
Text Solution
|