Solution of differential equation \(x d y-y d x=0\) represents :

Let \(A=\left[\begin{array}{ccc}2 & -1 & 3 \\ 1 & 2 & -1 \\ 4 & 1 & 2\end{array}\right]\). \(M_{i j}\) and \(A_{i j}\) respectively denote the minor and cofactor of an element \(a_{i j}\) of matrix \(A=\left[a_{i j}\right]\).
(A) \(M_{23}=6\)
(B) \(A_{22}=-8\)
(C) \(A_{13}=7\)
(D) \(M_{32}=-5\)
Choose the correct answer from the options given below:

The solution set of \(6 \leq-3(2 x-4)<12, x \in R\) is :

The value of the integral \(I=\int_{-1}^1|x| d x\) is:

Consider the relation R in the set Z of integers which is given by \(R=\{(a, b): 2\) divides \(a-b\}\).
Choose the correct option for the relation \(R\) :

If A is any \(m \times n\) matrix and B is a matrix such that AB and BA are both defined, then B is a matrix of order :

The value of \(\int \frac{x^5}{\sqrt{1+x^3}}\)dx is

Read the passage carefully and answer the Questions
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
A reaction is first order in A and second order in B. If the concentration of B is doubled its initial concentration and A is reduced to 3/4th of its initial concentration, the new rate of the reaction is

The reaction shown above is known as

If \(D_1=\left|\begin{array}{ccc}\frac{1}{2} & \frac{1}{\sqrt{2}} & 0 \\ -\frac{1}{\sqrt{2}} & \frac{1}{2} & 0 \\ 0 & 0 & 1\end{array}\right|\) and \(D_2=\left|\begin{array}{ccc}\frac{1}{\sqrt{2}} & \frac{1}{2} & 0 \\ -\frac{1}{2} & \frac{1}{\sqrt{2}} & 0 \\ 0 & 0 & 1\end{array}\right|\), then \(D_1 D_2\) is equal to :

The critical points of \(f(x)=x^3+x^2+x+1\) are

Transfer of pollen grains from anther of one flower to the stigma of a flower of different plant is called as:

Two nuclei have mass numbers in the ratio \(3:5\). The ratio of their nucleus densities would be :