Questions fo 28-9-=2007

1. A solid cylinder of mass m and radius r is rolling on a rough inclined plane of inclination θ. The coefficient of friction between the cylinder and incline is μ. Then


(A)frictional force is always μmg cos θ
(B)friction is a dissipative force
(C)by decreasing θ, frictional force decreases
(D)friction opposes translation and supports
rotation.

Note: Multiple alternatives possible.

2.
The coordination number of Ni(2+) ion is 4.

NiCl-2 + KCN (excess) → A (cyano complex)
NiCl-2 + Conc. HCl (excess) → B (chloro complex)


The IUPAC name of A and B are
(A) Potassium tetracyanonickelate (II), potassium tetrachloronickelate (II)
(B) Tetracyanopotassiumnickelate (II), teterachlorpotassiumnickelate (II)
(C) Tetracyanornickel (II), tetrachloronickel (II)
(D) Potassium tetracyanonickel (II), potassium tetrachloronickel (II)

3. Let a, b, c be the sides of a triangle. No two of them are equal and λ ∈ R. If the roots of the equation x^2 + 2(a + b+ c) x
+ 3λ (ab + bc + ca) = 0 are real, then
(A) λ < 4/3
(B) λ > 5/3
(C)λ can be any value between 1/3 and 5/3
(D)λ is higher than 4/3 but less than 5/3