If corner points of the bounded feasible region are \((0,0),(3,0)\) and \((0,3)\) and objective function is \(Z=4 x+7 y\), then the maximum value of \(Z\) is

The value of integral \(\int \sqrt{4 x^2+9} d x\) is

The following data are from a random sample : \(5,8,10,7,10,14\), then the point estimate of the population standard deviation is

If the system of equations \(2 x+5 y=7,6 x+\lambda y=28\) is inconsistent, then

If A and B are two square symmetric matrices of same order, then AB-BA is

The unit vector in the direction of sum of vectors \(\vec{a}=2 \hat{i}-\hat{j}+\hat{k}\) and \(\vec{b}=2 \hat{j}+\hat{k}\) is:

Two pipes can fill a cistern in 8 and 12 hours respectively. The pipes are opened simultaneously, and it takes 12 minutes more to fill the cistern due to leakage. If the cistern is full, what will be the time taken by the leakage to empty it?

\(\frac{d}{d x}\left(e^{2 \log _e x^3}\right)\) equals

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.

The refractive index of a glass prism is minimum for

Let a relation \(R=\{(a, b): a\) is a factor of \(b, a, b \in N\}\). Then, \(R\) is __________.

Which of the following are not involved in intra uterine devices?
(A) Lippes Loop
(B) LNG-20
(C) Saheli
(D) Implants
Choose the correct answer from the options given below:

A proton accelerated through a potential difference of V volts has a de-Broglie wavelength \( \lambda \) associated with it. In order to get the same wavelength with an \( \alpha \)-particle, the required accelerating potential is