The function \(y=f(x)\) has extreme values at the points where ___________ .

If \(\vec{a}\) is any vector, then \(|\vec{a} \times \hat{i}|^2+|\vec{a} \times \hat{j}|^2+|\vec{a} \times \hat{k}|^2\) is equal to

A company has been producing steel tubes of mean inner diameter 2 cm.
A sample of 10 tubes gives a mean inner diameter of 2.01 cm and a variance of \(0.0004 cm^2\).
The value of the test statistic is :

The two curves \(x^3-3 x y^2+15=0\) and \(3 x^2 y-y^3+17=0\) :

If \(y=\sqrt{2024 x+2025}\), then which of the following is correct?

In reference to Inferential Statistics, if \(\bar{x}\) is a sample mean of random data \(\left\{x_i\right\}_{i=1}^n\) and n is the sample size, then the formula \(\frac{1}{n-1} \sum_{i=1}^n\left(x_i-\bar{x}\right)^2\) represents

The direction ratios of the line perpendicular to the lines \(\frac{x-5}{2}=\frac{y+11}{-3}=\frac{z+3}{1}\) and \(\frac{x-7}{1}=\frac{y+2}{2}=\frac{z-4}{-2}\) are proportional to :

A hollow metal sphere of radius 10 cm is uniformly charged such that the electric potential at a distance of 20 cm from the center is 10 V. The electric potential at a distance of 5 cm from the center of the sphere will be

What is the role of of the C peptide in insulin?

Read the passage carefully and answer
When a metal is placed in a solution of its ions, the metal can lose electron and can go in the solution as ion or the metal ion in the solution can take electron from the electrode and get deposited as metal. Thus, the electrode acquires either positive or negative charge with respect to the solution leading to the development of a potential difference between the metal electrode and the solution. This potential difference is called the electrode potential of the metal. The electrode potential of a metal is a measure of relative tendency to undergo oxidation (loss of electron) or reduction (gain of electron). When the concentration of the ions in the solution is unity, the electrode potential is called standard electrode potential. The magni of potential depends upon the nature of electrode, concentration of ions in solution and the temperature. In a galvanic cell, the electrode at which oxidation occurs is known as anodic half-cell and the electrode at which reduction occurs is known as cathodic half cell. The emf of the cell in terms of standard reduction potential is given by \(E_{\text {cell }}^{\circ}=E_{\text {cathode }}^{\circ}-E_{\text {anode. }}^{\circ}\).The standard free energy change of the redox reaction taking place in the cell is related to \(E_{\text {cell }}^{\circ}\) by \(\Delta G^{\circ}=-n F E^{\circ}\). A redox reaction would occur spontaneously if the free energy change is negative. The equilibrium constant of the reaction is related to the standard free energy change by \(\Delta G^{\circ}=-R T \ln K\).
The equillibrium constant of a feasible cell reaction is

An \( 80 \, \Omega \) resistor is connected to a 240 V, 50 Hz AC supply. The net power consumed over a full cycle is:

ELISA is based on the principle of -

The probability of not getting 53 Sundays in a leap year is :