If a + b + c = 0. |a| = 3, |b| = 5, |c| = 7, then the angle between a and b is
The quadratic equation whose roots are sin218° and cos2 36° is
The Fahrenheit and Kelvin scales of temperature will have the same reading at a temperature of:
If sin 2θ and cos 2θ are solutions of x2 + ax - c = 0, then
If x - 2y + k = 0 is a tangent to the parabola y2 - 4x - 4y + 8 = 0, then the value of k is
The perimeter of a △ABC is 6 times the arithmetic mean of the values of the sine of its angles. If the side BC is of the unit length, then ∠A =
In a hypothetical Bohr hydrogen atom, if the mass of the electron is double then the energy of the electron in the first orbit 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:
If γ is the susceptibility and μr is the relative permeability of a ferromagnetic substance, then
A random variable X has the following probability distribution
For the events E = {x/x is a prime number} and F = {x/x <4} then P(E ∪ F)
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:
The following molecule with the structure acts as
Aluminum reacts with dilute HCL and liberates a gas 'A' and with aqueous alkali liberates a gas 'B'. A and B respectively are
Photodiodes are mostly operated in reverse biased conditions because:
The dimensions of four wires if the same material are given below. The increase in length is maximum in the wire of :
N molecules each of mass m of gas A and 2N molecules each of mass 2m of gas B are contained in a vessel which is maintained at a temperature T. The mean square velocity of the molecules of gas B is denoted by V22 and the mean square of the x-component velocity of the molecules of gas B is denoted by V12, then V1\V2 is:
Let d be the distance between the parallel lines 3x - 2y + 5 = 0 and 3x - 2y + 5 + 2√13 = 0. Let L1 = 3x - 2y + k1 = 0 (k1 > 0) and L2 = 3x - 2y + k2 = 0 (k2 > 0) be two lines that are at the distance of \(\frac{4d}{√13}\) and \(\frac{3d}{√13}\) from the line 3x - 2y + 5y = 0. Then the combined equation of the lines L1 = 0 and L2 = 0 is:
If the parametric equations of the circle passing through the points (3,4), (3,2) and (1,4) is x = a + r cosθ, y = b + r sinθ then ba ra =
It is found that a non-zero current is unable to produce any magnetic field at a particular point. Then the angle between the current element and the position vector of that point with respect to the current element is:
The effective capacitance between points A and B shown in the circuit is:
Metal detector works on the principle of
Electromagnetic radiation of intensity 0.6 Wn-2 is falling on a blank surface. The radiation pressure on the surface is:
The rate law for the decomposition of hydrogen iodide is - = d[HI]/dt = k[HI]2. The units of rate constant k are: