Consider the determinant `f(x)=|0x^2-a x^3-b x^2+a0x^2+c x^4+b x-c0|dot` Statement 1: `f(x)=0` has one root `x=0.` Statement 2: The value of skew symmetric determinant of odd order is always zero.

If a ,b ,c are different, then the value of |0x^2-a x^3-b x^2+a0x^2+c x^4+b x-c0|=0 is c b. c c. b d. 0

If f (x) = |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)| then

Consider the function f(x)=|x-2|+|x-5|,c inR. Statement 1: f'(4)=0 Statement 2: f is continuous in [2,5], differentiable in

Consider the real function f(x ) = ( x+2)/( x-2) prove that f(x) f(-x) +f(0) =0

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

If a ,b ,c are different, then the value of x for which |[0,x^2-a, x^3-b], [x^2+a,0,x^2+c ],[x^4+b, x-c,0]|=0 is

The polynomial f(x)=x^4+a x^3+b x^2+c x+d has real coefficients and f(2i)=f(2+i)=0. Find the value of (a+b+c+d)dot

The polynomial f(x)=x^4+a x^3+b x^2+c x+d has real coefficients and f(2i)=f(2+i)=0. Find the value of (a+b+c+d)dot

Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2c x+d=0 has at least one real root lying between (0,3)dot Statement 2: If f(x) is continuous in [a,b], derivable in (a , b) such that f(a)=f(b), then there exists at least one point c in (a , b) such that f^(prime)(c)=0.

Statement 1: If g(x) is a differentiable function, g(2)!=0,g(-2)!=0, and Rolles theorem is not applicable to f(x)=(x^2-4)/(g(x))in[-2,2],t h e ng(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b),t h e ng(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b), then Rolles theorem is applicable for x in (a , b)dot