Wbjee

If f : R → R be defined by f(x) = ex and g : R → R be defined by g(x) = x². The mapping gof : R → R be defined by (gof)(x) = g[f(x)] ∀ x ∈ R, Then 

(A) gof is bijective but f is not injective 

(B) gof is injective and g is injective 

(C) gof is injective but g is not bijective 

(D) gof is surjective and g is surjective

A proton of mass ‘m’ moving with a speed v (<< c, velocity of light in vacuum) completes a circular orbit in time ‘T’ in a uniform magnetic field. If the speed of the proton is increased to 2v, what will be time needed to complete the circular orbit?

(A) √2T

(B) T

(C) T/√2

(D) T/2

The intensity of a sound appears to an observer to be periodic. Which of the following can be the cause of it? 

(A) The intensity of the source is periodic. 

(B) The source is moving towards the observer. 

(C) The observer is moving away from the source. 

(D) The source is producing a sound composed of two nearby frequencies.

If Young’s double slit experiment is done with white light, which of the following statements will be true? 

(A) All the bright fringes will be coloured. 

(B) All the bright fringes will be white. 

(C) The central fringe will be white. 

(D) No stable interference pattern will be white.

There is a small air bubble at the centre of a solid glass sphere of radius ‘r’ and refractive index ‘Ω‘. What will be the apparent distance of the bubble from the centre of the sphere, when viewed from outside?

(A) r

(B) r/μ

(C) r(1 – 1/μ)

(D) Zero

Out of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one?

(A) (n –1)d⁸ns² 

(B) (n –1)d⁵ns² 

(C) (n –1)d³ns² 

(D) (n –1)d⁵ns¹

A compound formed by elements X and Y crystallizes in the cubic structure, where X atoms are at the corners of a cube and Y atoms are at the centres of the body. The formula of the compound is : 

(A) XY 

(B) XY₂ 

(C) X₂Y₃ 

(D) XY₃

Which of the set of oxides are arranged in the proper order of basic, amphoteric, acidic?

(A) SO₂, P₂O₅, CO 

(B) BaO, Al₂O₃, SO₂ 

(C) CaO, SiO₂, Al₂O₃ 

(D) CO₂, Al₂O₃, CO

Without changing the direction of the axes, the origin is transferred to the point (2, 3). Then the equation x² + y² – 4x – 6y + 9 = 0 changes to 

(A) x² + y² + 4 = 0 

(B) x² + y² = 4 

(C) x² + y² – 8x – 12y + 48 = 0 

(D) x² + y² = 9

Which one of the following is a condensation polymer? 

(A) PVC 

(B) Teflon 

(C) Dacron 

(D) Polystyrene