If the area of the triangle with vertices A(x, 4), B(-2, 4) and C(2,-6) is 35 sq units, then the values of 2 are:

In a box containing 100 bulbs, 10 are defective.
The probability that out of a sample of 5 bulbs none is defective is:

If the matrix A = \(\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\), then \(A ^2\) is equal to:

If the matrix \(\left[\begin{array}{ccc}-3 & x-y & 5 \\ 1 & 0 & z \\ x+y & 4 & 7\end{array}\right]\) is symmetric, then the correct option of the following, is :

In the interval [-5, -3], the function f(x) = (x + 1)(x - 3) is:

"The random variable \(X\) has a probability distribution \(P ( X )\) of the following form, where \(k\) is some number.
\(P(X=x)=\left\{\begin{array}{ll}k, & \text { if } x=0 \\2 k, & \text { if } x=1 \\3 k, & \text { if } x=2 \\0, & \text { otherwise }\end{array}\right.\)
Then \(P(x \leq 2)\) is :"

In an electromagnetic wave, the ratio of energy densities of electric and magnetic fields is :

The semiconductor used for fabrication of visible LEDs must at least have a band gap of :

Read the passage carefully and answer the questions The resistance ( \(R\) ) of an object is given by the expression \(R=\rho \frac{l}{A}\).
The inverse of \(R\) is called conductance and the inverse of \(\rho\) is called conductivity or specific conductance represented by \(\kappa\).
The conductivity depends upon the nature of the material (insulator, semiconductor or conductor) and the temperature of the substance.
Similarly, the conductance due to the ions present in the solution (ionic conductance) depends upon the nature of the electrolyte, size of ions, the nature of the solvent and the temperature.
Molar conductivity ( \(\Lambda_m\) ) of a solution at a given concentration is the conductance of volume \(V\) containing one mole of electrolyte kept between two electrodes of area \(A\) and unit distance apart. It is given by the expression \(\Lambda_m=\kappa V .\)
Molar conductivity increases with decrease in concentration and when concentration approaches zero, it is called limiting molar conductivity.
The decrease is linear for a strong electrolyte. However, for a weak electrolyte the change is gradual at higher concentrations and sharp near zero concentration.
Using limiting molar conductivity values of strong electrolytes we can calculate the limiting molar conductivity of weak electrolytes using Kohlrausch law of independent migration of ions.
From molar conductivity and limiting molar conductivity we can determine the degree of dissociation \(\left(\frac{\Lambda_m}{\Lambda_m^0}\right)\) and the ionization constant of a weak acid.
For a weak acid like acetic acid, the correct expression for the ionisation constant at concentration \(c\) is

The largest open interval in which the function \(f(x)=4 x^3-5 x^2-8 x+12\) increases, is:

Answer the question on the basis of passage given below :
There are three kinds of amines which are primary, secondary and tertiary amines. These amines may have alkyl group or aryl group or both alkyl and aryl groups. These amines can be distinguished from one another by various chemical tests.
An amine A on treatment with \(\text{HNO}_2\) gives \(\text{N}_2\text{(g)}\) and an alcohol B. The molecular mass of alcohol B is 46.
The amine A is :

A parallel beam of monochromatic light of wavelength 489 nm passes through a single slit of width 0.3 mm. The angular width of the central maxima is

Identify the incorrect statements among the following.
(A) The two charges of an electric dipole will experience force in the same direction when placed in a uniform electric field,
(B) The dipole moment is a vector quantity,
(C) The direction of the dipole moment is from +q charge towards -q charge,
(D) The torque acting on the dipole in an electric field depends on the intensity of the field and the dipole moment.
Choose the correct answer from the options given below: