If (2,-1,3) is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is
If the electrical potential at a point on the surface of a hollow conducting sphere of radius R is V, then the electric potential at a point which is at a distance R/3 from the centre of the sphere is:
If f(x) = ex, h(x) = (fof) (x), then \(\frac{h'(x)}{h'(x)}\) =
The displacement of a particle executing simple harmonic motion is given by x = 2cos(t) where t is the time in seconds then the time period of the particle is:
A copper disc of radius 0.1 m rotates about an axis passing through its center and perpendicular to its plane with 10 revolutions per second in a uniform transverse magnetic field of 0.1 T. The emf induced across the radius of the disc is:
Let y = t2 - 4t -10 and ax + by + c = 0 be the equation of the normal L. If G.C.D of (a,b,c) is 1, then m(a+b+c) =
Identify the correct statement about the oxidation states of group 14 elements
If A(1,2,3) B(3,7,-2) and D(-1,0,-1) are points in a plane, then the vector equation of the line passing through the centroids of △ABD and △ACD is
Among the following the incorrect statement about transition metals is
At 50 °C, the vapour pressure of pure benzene is 268 torr. The number of moles of non-volatile solute per mole of benzene required to prepare a solution having a vapour pressure of 167 torr at the same temperature is
The variance of 50 observations is 7. Suppose that each observation in this data is multiplied by 6 and then 5 is subtracted from it. Then the variance of that new data is
If \(\frac{3x+2}{(x+1)(2x^2+3)} = \frac{A}{x+1}+ \frac{Bx+C}{2x^2+3}\), then A - B + C=
If sin 2θ and cos 2θ are solutions of x2 + ax - c = 0, then
If the function f(x) = xe -x , x ∈ R attains its maximum value β at x = α then (α, β) =
The roots of the equation x4 + x3 - 4x2 + x + 1 = 0 are diminished by h so that the transformed equation does not contain x2 term. If the values of such h are α and β, then 12(α - β)2 =
If a point P moves so that the distance from (0,2) to P is \(\frac{1}{√2 }\) times the distance of P from (-1,0), then the locus of the point P is
Electromagnetic radiation of intensity 0.6 Wn-2 is falling on a blank surface. The radiation pressure on the surface is:
The velocity of a particle having a magnitude of 10 ms-1 in the direction of 60° with positive X-axis is
If γ is the susceptibility and μr is the relative permeability of a ferromagnetic substance, then
A point source of light is placed at the focus of a concave mirror. Consider only paraxial rays. The shapes of the wavefronts of incident and reflected lights respectively are:
If a man of mass 50 kg is in a lift moving down with a acceleration equal to acceleration due to gravity, then the apparent weight of the man is:
If x2 + 2px - 2p + 8 > 0 for all real values of x, then the set of all possible values of p is
The rate law for the decomposition of hydrogen iodide is - = d[HI]/dt = k[HI]2. The units of rate constant k are: