If the sum and difference of squares of mean and variance of a Binomial distribution is \(\frac{225}{256}\) and \(\frac{63}{256}\) respectively, the \(P(X \geq 2)\) is :

The point at which the maximum value of \(x+y\), subject to constraints \(x+2 y \leq 70,2 x+y \leq 95, x \geq 0, y \geq 0\) is obtained, is :

The function f(x) = \(\log _e\)(sin x), x ∈ (0,π) is
(A) strictly increasing on \(\left(0, \frac{\pi}{2}\right)\)
(B) strictly decreasing on \(\left(0, \frac{\pi}{2}\right)\)
(C) strictly increasing on \(\left(\frac{\pi}{2}, \pi\right)\)
(D) strictly decreasing on \(\left(\frac{\pi}{2}, \pi\right)\)
(E) strictly increasing on \((0, \pi)\)
Choose the correct answert from the option given below :

The particular solution of the differential equation \(e^x \sqrt{1-y^2} d x+\frac{y}{x} d y=0\), given that \(y=1\), when \(x=0\), is:

If \(A=\left[\begin{array}{ccc}2 & -1 & 0 \\ 1 & 2 & 1 \\ -1 & 0 & 1\end{array}\right]\), then which of the following statement(s) is/are correct?
(A) A is singular matrix
(B) |3A |= 135
(C) |adj A| = 125
(D) \(\left|A^{-1}\right|=\frac{1}{5}\)
Choose the correct answer from the options given below:

If the matrix \(\begin{bmatrix} 3 & a+b & 4 \\ 2 & 0 & -1 \\ a-b & c & 5 \end{bmatrix}\) is symmetric, then the value of a, b and c is given by:

A pipe can fill a tank in 2 hours. Because of a leak in the tank, the pipe takes 2 hours 40 minutes to fill the tank. The time the leakage takes to empty the full tank is :

The correct structure representing N,N-dimethylethanamine is

For the given five values 15, 24, 18, 33, 42, the three-year moving averages are :

Read the passage carefully and answer the Questions
Werner in 1898, propounded his theory of coordination compounds. In coordination compounds metals show two types of linkages (valences)-primary and secondary. The primary valences are normally ionisable and are satisfied by negative ions. The secondary valences are non-ionisable. These are satisfied by neutral molecules or negative ions. The secondary valence is equal to the coordination number and is fixed for a metal. The ions or group bound by the secondary linkages to the metal have characteristic spatial arrangements corresponding to the different coordination numbers. Both double salts as well as complexes are formed by the combination of two or more stable compounds in stoichiometric ratio. However, they differ in the fact that double salts such as carnallite, Mohr's salt, potash alum etc. dissociate into simple ions completely when dissolved in water. But complex ions do not dissociate completely into simple ions.
Which of the following statement is correct as per Werner theory?

Health is a state of:

Two concentric coils, each of radius \( 2\pi \, \text{cm} \), are placed at right angles to each other. Currents of 3 A and 4 A respectively are flowing through the two coils. The magnetic induction at the center of the coils will be:

Select the correct relation of half life for a zero order reaction.