If \(A\) is a square matrix of order 3 such that \(|A|=3\) then \(|\operatorname{adj}(\operatorname{adj} A)|\) is equal to:

The set of values of \(x\) satisfying \(26 \equiv 5(\bmod x)\) is __________ .

Area of a rectangle having vertices \(P, Q, R\) and \(S\) with position vectors \(-\hat{i}+\frac{1}{2} \hat{j}+4 \hat{k}, \hat{i}+\frac{1}{2} \hat{j}+4 \hat{k}, \hat{i}-\frac{1}{2} \hat{j}+4 \hat{k}\) and \(-\hat{i}-\frac{1}{2} \hat{j}+4 \hat{k}\) respectively is :

\(x\)-axis, \(y=\cos x\) and \(y=\sin x, 0 \leq x \leq \frac{\pi}{2}\) is:

The maximum value of the function f(x) = \(x^2\) (60 - x) in [20, 80] is:

The integrating factor of the differential equation \(\left(x \log _e x\right) \frac{d y}{d x}+y=2 \log _e x\) is:

The differential equation that represents the family of lines parallel to x + y = 2 is:

If \(A=\left[\begin{array}{cc}1 & 0 \\ \frac{1}{25} & 1\end{array}\right]\), then the value of \(A^{125}\) is :

Which of the following statement(s) is/are incorrect?
(A) A current carrying loop may act as a magnetic dipole whose magnetic moment may depend on its area and the number of turns.
(B) A linear solenoid carrying current, may act as a bar magnet.
(C) The magnetic lines of forces due to the current carrying solenoid makes closed curves like in a bar magnet.
(D) The magnetic field inside a solenoid is perpendicular to its axis.
Choose the correct answer from the given options:

Read the passage carefully and answer the Questions In the formation of coordination complexes, if the inner \(d\) orbital \((n-1) d\) is used in hybridisation, the complex, is called an inner orbital or low spin or spin paired complex. And if it uses outer \(d\) orbital ( \(n d\) ) in hybridisation (like \(s p^3 d^2\) ), it is called outer orbital or high spin or spin free complex. The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the complex. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting. For coordination complexes, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the 'spin-only' formula, \(\mu=\sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons and \(\mu\) is the magnetic moment in units of Bohr magneton (BM). The coordination compounds are of great importance. These compounds are widely present in the mineral, plant and animal worlds and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine.
\(\left[ Co \left( NH _3\right)_6\right]^{3+}\) and \(\left[ Ni \left( NH _3\right)_6\right]^{2+}\) respectively are

Termination of protein synthesis occurs by binding of release factors to

The area bounded by the curve y = sin x and x-axis between \(x=-\pi\) and \(x=\pi\) is:

The specific conductance of a decinormal KCl solution is \(0.0121 ohm ^{-1} cm^{-1}\) and the resistance was found to be 56 ohm . Cell constant for the reaction will be