If` f(x)=|x-3|+2|x-1|` and `g(x)=-2x^(2)+3x-1` On the basis of above information answer the following questions: Minimum value of f(x) is

Let there are two functions defined of f(x)="min"{|x|,|x-1|,|x+1+] and g(x)="min"{e^(x),e^(-x)} on the basis of above information answer the following question: Number of solutions of f(x)=g(x) in the interval [0,1] is

Let f(x)={x;x =0 and g(x)+{x^(2);x<-1 and 2x+3;-1<=x<=1 and x ; On the basis of above information,answer the following questions Range of f(x) is

If f(x) is a monic polynomial of degree '3' such that lim_(x to 0) (1+f(x))^(1/(x^(2)))=e^(-3), g(x)=(f(x))/(x^(3))dx and g(1)=1 then On the basis of above information, answer the following question: Value of g(e) is

Consider a polynomial f(x)=(a-1)x^(2)+ax+a+1. On the basis of above information,answer the following questions: If f(x)>0AA xi nR, then set of values of 'a'is-

Let there are two functions defined of f(x)="min"{|x|,|x-1|} on the basis of above information answer the following question: Points of non-differentiability of f(x) in (-1,1)

If f_r(x),g_r(x),h_r(x),r=1,2,3 are differentiable function and y=|(f_1(x), g_1(x), h_1(x)), (f_2(x), g_2(x), h_2(x)),(f_3(x), g_3(x), h_3(x))| then dy/dx= |(f\'_1(x), g\'_1(x), h\'_1(x)), (f_2(x), g_2(x), h_2(x)),(f_3(x), g_3(x), h_3(x))|+ |(f_1(x), g_1(x), h_1(x)), (f\'_2(x), g\'_2(x), h\'_2(x)),(f_3(x), g_3(x), h_3(x))|+|(f_1(x), g_1(x), h_1(x)), (f_2(x), g_2(x), h_2(x)),(f\'_3(x), g\'_3(x), h\'_3(x))| On the basis of above information, answer the following question: Let f(x)=|(x^4, cosx, sinx),(24, 0, 1),(a, a^2, a^3)| , where a is a constant Then at x= pi/2, d^4/dx^4{f(x)} is (A) 0 (B) a (C) a+a^3 (D) a+a^4

If f(x)=(x-2)|x-4| sgn(x)AA x in R (Where sgn( x ) denotes signum function) On the basis of above information answer the following questions: f(x) is monotonically increasing in interval-

If f(x)=(x-2)|x-4| sgn(x)AA x in R (Where sgn( x ) denotes signum function) On the basis of above information answer the following questions: f(x) is monotonically increasing in interval-

If 3sin^(2)x-7sin x +2=0, x in [0(pi)/(2)] and f_(n)(theta)=sin^(n) theta + cos^(n) theta . On the basis of above information , answer the questions The value of ( sin 5 x + sin 4 x)/( 1+ 2 cos 3 x) is