Let `f(x)=x^3+x^2+10x+7sinx,` then the equation `1/(y-f(1))+2/(y-f(2))+3/(y-f(3))=0` has (A) no real root (B) one real roots (C) two real roots (D) more than two real roots

(x^(2)+1)^(2)-x^(2)=0 has (i) four real roots (ii) two real roots (iii) no real roots (iv) one real root

The quadratic equation 2x^(2)-sqrt5x+1=0 has (a) two distinct real roots (b) two equal real roots (c) no real roots (d) more than 2 real roots

If f(x)=x^(3)+3x^(2)+6x+2sin x, then the equation (1)/(x-f(1))+(2)/(x-f(2))+(3)/(x-f(3))=0 has number of real roots of the equation?

The equation e^(sin x)-e^(-sin x)-4=0 has (A) infinite number of real roots (B) no real roots (C) exactly one real root (D) exactly four real roots

If f(x) is continuous in [0,2] and f(0)=f(2) then the equation f(x)=f(x+1) has (A) one real root in [0,2](B) atleast one real root in [0,1](C) atmost one real root in [0,2](D) atmost one real root in [1,2]

The equation (x/(x+1))^2+(x/(x-1))^2=a(a-1) has a. Four real roots if a >2 b.Four real roots if a<-1 c Two real roots if 1

If f(x)=x has non real roots, then the equation f(f(x))=x (A) has all real and unequal roots (B) has some real and non real roots (C) has all real and equal roots (D) has all non real roots

If 0ltalphaltbetaltgammaltpi/2 then the equation 1/(x-sinalpha)+1/(x-sinbeta)+1/(x-singamma)=0 has (A) imaginary roots (B) real and equal roots (C) real and unequal roots (D) rational roots

On the domain [-pi,pi] the equation 4 sin^3 x+2 sin^2 x-2 sinx-1=0 possess (A) only one real root(C) four real roots= 0 possess(B) three real roots(D) six real roots

Suppose a, b, c are real numbers, and each of the equations x^(2)+2ax+b^(2)=0 and x^(2)+2bx+c^(2)=0 has two distinct real roots. Then the equation x^(2)+2cx+a^(2)=0 has - (A) Two distinct positive real roots (B) Two equal roots (C) One positive and one negative root (D) No real roots