The domain of the function \(\cos ^{-1}(2 x-3)\) is

If \(R=\left\{(x, y) \mid x, y \in Z , x^2+y^2 \leq 4\right\}\) is a relation in \(Z\), then domain of \(R\) is :

If three points \(A \left(a_1, b_1\right), B \left(a_2, b_2\right)\) and \(C \left(a_3, b_3\right)\) are collinear and D is the determinant of their coordinates with a column of 1s, then:

If A = \(\left[\begin{array}{ccc}0 & 1 & -3 \\ -1 & 0 & 5 \\ 3 & -5 & 0\end{array}\right]\), then the value of \(\left|A^{2025}\right|\) is

The direction cosines of a line equally inclined with the co-ordinate axes are :

The area (in sq. units) of the region bounded by the curve \(y=\sin x,-2 \pi \leq x \leq 2 \pi\) and the \(x\)-axis is :

Which one of the following set of constraints represents the shaded region given below?

If A is a matrix of order \(m \times n\) and B is a matrix such that \(A B^T\) and \(B^T A\) are both well-defined matrices, then order of matrix B is

Read the following passage carefully and answer the given questions
The earthworm is referred to as the farmer's friend. This is because they help in the breakdown of complex organic matter as well as in loosening of soil. Similarly, decomposers break down complex organic matter into inorganic substances like carbon dioxide, water and nutrients and the process is called decomposition. Dead plant remains such as leaves, bark, flowers and dead remains of animals, including fecal matter, constitute detritus, which is the raw material for decomposition. Some of the steps in the process of decomposition are fragmentation, catabolism, leaching, humification etc.
The process of decomposition largely requires -

The pattern and behavior of the data in any time series are based on which of the following components:
(A) Secular trend component
(B) Seasonal component
(C) Cyclical component
(D) Irregular component
Choose the correct answer from the options given below :

The electrostatic potential at a point on the surface of a charged spherical conducting shell of radius 10 cm is 120 V. The electric potential at a distance of 5 cm from the centre of the shell is:

Choose the correct statement from the following:

Which of the following hormone is also known as flight or fight hormone?