The value of \(x\), for which the function \(f(x)=x(x-2)\) attains its minimum value, is:

A person invested ₹ \(10000\) in a stock of a company for \(6\) years.
The value of his investment at the end of each year is given below:

2018	2019	2020	2021	2022	2023
₹11000	₹11500	₹13000	₹11800	₹12200	₹14000

The compound annual growth rate (CAGR) of his investment is:
[Given (1.4) \({ }^{\frac{1}{8}}=1.058\) ]

If the matrix \(\left[\begin{array}{ccc}-1 & x-y & 4 \\ 2 & 0 & 5 \\ x+y & z & 6\end{array}\right]\) is symmetric, then \(x+3 y+2 z\) is equal to

The integral \(\int \frac{2 d x}{e^{2 x}-1}\) is equal to:

The value of derivative of the function \(\cot ^{-1}\left\{(\cos 2 x)^{1 / 2}\right\}\) at \(x=\frac{\pi}{6}\) is

If A and B are skew-symmetric matrices, then which of the following is not true?

The slope of the normal to the curve \(y^2=16 x\) at the point \((1,4)\) is :

Calculate the magnetic moment (spin-only) of a trivalent ion in aqueous solution if its atomic number is 22 .

Arrange the following cells in correct sequence of oogenesis:
(A) Secondary oocyte
(B) Oogonia
(C) Primary oocyte
(D) Ovum
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 role of a catalyst is to change

The conductivity of a 0.001 \(\mathrm{mol} \mathrm{L}^{-1}\) solution of a weak monobasic acid is \(4.0 \times 10^{-5} \mathrm{~S} \mathrm{~cm}^{-1}\). Calculate its dissociation constant if \(\Lambda_m^{\circ}\) for the weak acid is \(400.0 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\).

Somaclones can be defined as:

Arrange the following steps of sewage treatment in a sequential order.
(A) Primary effluent passed in aeration tank
(B) Activated sludge is formed
(C) Filtration and sedimentation of sewage
(D) Aerobic microbes grow into flocs
Choose the correct answer from the options given below: