Let `f(x)= 3/(x-2)+4/(x-3)+5/(x-4)`. Then `f(x)=0` has (A) exactly one real root in (2,3) (B) exactly one real root in (3,4) (C) at least one real root in (2,3) (D) none of these

[ 9.Let f(x)=ax+sin2x+b ,then f(x)=0 has (A) exactly one positive real root,if agt2 and blt0 (B) exactly one positive real root,if agt2 and bgt0 (C) Both(A)&(B) (D) None of these ]

If 3(a+2c)=4(b+3d), then the equation ax^(3)+bx^(2)+cx+d=0 will have no real solution at least one real root in (-1,0) at least one real root in (0,1) none of these

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]

If (a,0) is a point on a diameter of the circle x^(2)+y^(2)=4 then x^(2)-4x-a^(2)=0 has A ) Exactly one real root in (-1,0]B) Exactly one real root in [2,5]C) Distinct roots greater than -1D D Distinct roots less than 5

x^(3)+ax^(2)-bx-4=0 has (A) at least one negative root (C) one positive and one nell real roots 2 all real roots 2

Let a in R and f : R rarr R be given by f(x)=x^(5)-5x+a , then (a) f(x)=0 has three real roots if a gt 4 (b) f(x)=0 has only one real root if a gt 4 (c) f(x)=0 has three real roots if a lt -4 (d) f(x)=0 has three real roots if -4 lt a lt 4

If the equation x^(2)-2ax+a^(2)+a-3=0 has exactly one real root in (1,3) then largest integral value of a is

(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 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

Equation a/(x-1)+b/(x-2)+c/(x-3)=0(a,b,cgt0) has (A) two imaginary roots (B) one real roots in (1,2) and other in (2,3) (C) no real root in [1,4] (D) two real roots in (1,2)