Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively.
Both pipes A and B are opened together for some time and then pipe B is turned off.
If the tank is filled in 15 minutes, then after how many minutes is pipe B turned off?

Consider the Linear Programming Problem
Maximize \(z=x+y\)
Subject to the constraints \(x-y \leq-1, x \geq y, x \geq 0, y \geq 0\)
Then which one of the following is TRUE?

The maximum value of \(z=4 x+3 y\) subject to constraint \(x+y \leq 6, x, y \geq 0\) 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 \(R\) :

The value of \(\operatorname{cosec}^{-1}\left[\operatorname{cosec}\left(-\frac{\pi}{6}\right)\right]\) is :

The number of arbitrary constants in the general solution of a differential equation with degree 1 and order 3, is

The sum of order and degree of the differential equation \(y=x \frac{d y}{d x}+2 \sqrt{1+\left(\frac{d y}{d x}\right)^2}\) is

The least reactive aldehyde towards HCN would be :

Three charges \(+4 q, Q\) and \(q\) are placed along \(x\)-axis at points, \(x=0, I / 2\) and I respectively. The value of Q to make the net force on \(q\) to be zero :

In the given reaction \(CH_3CH_2OH + HCl \xrightarrow{Anhy ZnCl_2} X \xrightarrow{KCN(alc)} Y \xrightarrow{Na/Alcohol} Z\) \(Y\) and \(Z\) are:

Name the reaction when a mixture of acetaldehyde and propanal is treated with aqueous alkali solution.

If light of wavelength 412.5 nm is incident on each of the metals given below, which ones will show photoelectric emission ?

Metal	Work Function (eV)
Na	1.92
K	2.15
Ca	3.20
Mo	4.17

Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation r = k[A]^x[B]^y, where x and y are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is x + y. The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.
The rate law of a reaction is given by r = k[CH₃OCH₃]^3/2. If the pressure is measured in bar and time in minutes, then the unit of rate constant will be