If A and B are two matrices of order \(4 \times m\) and \(4 \times n\), respectively and \(m=n\),
then the order of matrix \((5 A-2 B)\) is:

If \(A\) is a square matrix such that \(A^2=A\) and \(I\) is the identity matrix of the same order as \(A\), then \((I+2 A)^2-5 A\) is equal to :

The integral \(\int e^x\left(\log x+\frac{1}{x^2}\right) d x\) equals for some arbitrary constant k

The value of \(\lambda\), so that the vector \(\vec{a}=2 \hat{i}+\lambda \hat{j}+\hat{k}\) and \(\vec{b}=\hat{i}-2 \hat{j}+3 \hat{k}\) are perpendicular to each other, is :

A person invested ₹ \(2,50,000\) in a fund.
At the end of the year, the value of the fund is ₹ \(3,00,000\).
If the market price is the same at the end of the year, then the nominal rate of return is :

If \(y=(\log x)^{\log x}, x>1\) then \(\frac{d y}{d x}\) is equal to

A card is drawn from a well-shuffled pack of 52 cards. Its outcome is noted and then another card is drawn without replacing the first card. The probability that the first card is a heart and the second card is a red ace is:

If \(A, B\) are symmetric matrices of the same order, then \(A B-B A\) is a :

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 certain amount of \(N _2 O _5\) decomposes to half of its initial amount in 50 minutes.
If the decomposition is a first order reaction, the rate constant of the reaction is.

If \(A=\left[\begin{array}{ll}x & 3 \\ 2 & y\end{array}\right], \quad B=\left[\begin{array}{cc}2 y & 1 \\ 3 & x\end{array}\right]\) and \(A+2 B=\left[\begin{array}{cc}6 & 5 \\ 8 & -2\end{array}\right]\), then the value of \((x, y)\) is:

Addition of HCN to carbonyl group results in formation of:

If \(E _{ p }\) and \(E _{ k }\) represents the potential and kinetic energy respectively of an orbital electron, then according to Bohr's theory.

The relation \(R\) on the set of real numbers defined by \(R=\left\{(a, b): a \leq b^2\right\}\) is