The function \(f(x)=\cos x\) is strictly decreasing in :

If A is a skew-symmetric matrix, then which of the following statements is NOT true?
(A) A is singular if order of A is odd
(B) A is non-singular
(C) \(A^{2025}\) is a skew-symmetric matrix
(D) \(A^{2025}\) is a symmetric matrix
(E) all diagonal elements of A are zeros
Choose the correct answer from the option given below :

The following statements are made on the basis of given graph.
(A) OB represents the cost function.
(B) MA represents the cost function.
(C) Loss occurs at x = 5.
(D) Loss occurs at x = 15.
(E) Profit occurs at x = 10.

Let a relation \(R=\{(a, b): a\) is a factor of \(b, a, b \in N\}\). Then, \(R\) is __________.

Find the maximum value of the function sin x(1 + cos x) is:

The values of \(\lambda\) for which the following system of equations has unique solution:
\(\begin{array}{l}\lambda x+3 y-z=1 \\x+2 y+z=2 \\-\lambda x+y+2 z=-1\end{array}\)

The Greatest Integer Function \(f: R \rightarrow R\) given by \(f(x)=[x], x \in R\) and \([x]\) denotes the greatest integer less than or equal to \(x\) is :

A particle is dropped from height H. The de-Broglie wavelength of the particle as a function of height is proportional to:

A cell of emf 3 V and internal resistance 0.1 \(\Omega\) is connected to a 3.9 \(\Omega\) external resistance. What will be the potential difference across the terminals of the cell ?

A circular coil of 100 turns and area of cross-section \( 10^{-2} \text{ m}^2 \) is rotated about its vertical diameter at 60 rpm in a uniform horizontal magnetic field of \( 3.5 \times 10^{-2} \text{ T} \). The maximum emf induced in the coil is:

Read the passage carefully and answer the Questions
According to Valence Bond theory, the metal atom or ion under the influence of ligands can use its ( \(n-1\) )d, ns, np or \(n s, n p, n d\) orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on. These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding. While the VB theory, to a larger extent, explains the formation, structures and magnetic behaviour of coordination compounds, it suffers from the many shortcomings. The Crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. The five \(d\) orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands in a complex, it becomes asymmetrical and the degeneracy of the \(d\) orbitals is lifted. It results in splitting of the \(d\) orbitals. The pattern of splitting depends upon the nature of the crystal field.
Which of the following is not true about the limitations of VBT

The correct 4f sub-shell electronic configuration of Yb²⁺ion is

If \(x=t^{1 / 2}, y=t^{3 / 2}\), then \(\frac{d y}{d x}=\)