Cr is reducing but Mn is oxidising in nature although both have \(\text{d}^1\) configuration. It is due to the reason that Cr configuration changes from

\(100 \text{ cm}^3\) of \(1\text{M } \text{CH}_3\text{COOH}\) and \(100 \text{cm}^3\) of \(2\text{M } \text{CH}_3\text{OH}\) were mixed to form an ester, which follows Ist order kinetics with respect to both \(\text{CH}_3\text{COOH}\) and \(\text{CH}_3\text{OH}\). The change in their initial rate, if each solution is mixed with equal number of volume of water would be :

A first order reaction is found to have a rate constant, k = 5.5 × 10^-14 s^-1. The half life of the reaction will be :

Identify the major product in the following reaction :
\(CH_3-CH\left(CH_3\right)-CH_2 Br \xrightarrow{\text { aq. } OH^{-}} \text {? }\)

Match List - I with List - II.

List - I	List - II
A. Simple and face centred cubic	I. \(\text{a} = \text{b} = \text{c}\)
B. Cubic and rhombohedral	II. \(\alpha = \beta = \gamma = 90°\)
C. Cubic and tetragonal	III. have only two crystallographic angle of \(90°\)
D. Hexagonal and monoclinic	IV. belong to the same crystalline system

Choose the correct answer from the options given below :

In \(\left[ Ni ( en )_3\right] Cl _2\), the geometry of Ni is:

Match the complex given in List - I with the number of unpaired electrons given in List - II

List-I (Complex)	List-II (Number of unpaired electrons (n))
(A) \(\left[ NiCl _4\right]^{2-}\)	(I) 5
(B) \(\left[ Co \left( NH _3\right)_6\right]^{3 +}\)	(II) 1
(C) \(\left[ FeF _6\right]^{3-}\)	(III) 2
(D) \(\left[ Fe ( CN )_6\right]^{3-}\)	(IV) \(0\)

Choose the correct answer from the options given below:

Read the passage carefully and answer
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. Ligands are treated as point charges in case of anions or dipoles in case of neutral molecules. 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 (either anions or the negative ends of dipolar molecules like NH3 and H2O) 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.
If the fourth electron in d subshell enters one of the eg orbitals in octahedral complexes, it indicates that

The domain of the function \(f(x)=\sin ^{-1}(2 x-3)\) is :

On which of the following components, the pattern and behavior of the data in any time series is based?
(A). Secular trend component
(B). Seasonal component
(C). Cyclical component
(D). Regular component
Choose the correct answer from the options given below :

The genetically identical plants grown by the process of micropropagation are called

The value of \(\lim _{x \rightarrow 0} \frac{1-\cos x}{2 x^2}\) is:

The area bounded by the curve \(y=x^2|x|, x\)-axis and the ordinates \(x=-1\) and \(x=0\) is given by :