If \(A=\left[\begin{array}{lll}-1 & 2 & 3\end{array}\right], B=\left[\begin{array}{l}3 \\ 2 \\ 2\end{array}\right], C=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]\) and \(D=\left[\begin{array}{l}2 \\ 3 \\ 4\end{array}\right]\) then AB + CD is equal to :

The least non-negative remainder when \(2^{101}\) is divided by \(5\) is:

Approximate percentage increase in the volume of a sphere if its radius is increased by \(3 \%\) is:

The following system of equations \(2 x-y+3 z=5,3 x+2 y-z=7,4 x+5 y-\lambda z=\mu\) is consistent. Then

\(\int\left(\frac{1}{\log _e x}-\frac{1}{\left(\log _e x\right)^2}\right) d x\) is equal to

If \(x=a t^2, y=2 a t\); then \(\frac{d^2 y}{d x^2}\) is equal to

For fixed radii of curvature of a lens, power is proportional to :

Primary Alkyl halide \(C _4 H _9 Br (X)\) reacts with alcoholic KOH to give the compound \((Y)\). Compound \((Y)\) is reacted with HBr to give \((Z)\) which is an isomer of \((X)\). When \((X)\) is reacted with \(Na /\) dry ether, it gives a compound \((T), C _8 H _{18}\), which is different from the compound formed when \(n\)-butyl bromide is reacted with \(Na /\) dry ether. The correct IUPAC name of (T) is:

Werner was the first to describe the bonding features in coordination compounds. But his theory could not answer basic questions like :
(i) Why only certain elements possess the remarkable property of forming coordination compounds ?
(ii) Why the bonds in coordination compounds have directional properties ?
(iii) Why coordination compounds have characteristics magnetic and optical properties ?
Many approaches have been put forth to explain the nature of bonding in coordination compounds viz. Valence Bond Theory (VBT), Crystal Field Theory (CFT), Ligand Field Theory (LFT) and Molecular Orbital Theory (MOT).
We shall focus our attention on elementary treatment of the application of VBT and CFT to coordination compounds.
According to this theory, the metal atom or ion under the influence of ligands can use its ( \(n -1\) )d, ns np or ns, np, nd 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.
Which of the following pair of ions is colourless according to CFT ?

The magnetic field produced at the centre of circular loop of diameter 4 cm is \( 6.28 \times 10^{-5} \text{ T} \). The current required to flow in the loop is : (\( \mu_0 = 4\pi \times 10^{-7} \text{ N A}^{-2} \))

A coil \(C_1\) is connected to a galvanometer G. Second coil \(C_2\) is connected to a battery through a tapping key. The steady current in the coil \(C_2\) produces a steady magnetic field. As coil \(C_2\) is moved towards the coil \(C_1\), the galvanometer shows a deflection. To obtain a large deflection, one or more of the following steps can be taken:
(A) Use a rod made of soft iron inside the coil \(C_2\)
(B) Connect the coil \(C_2\) to a more powerful battery
(C) Move the arrangement of coil \(C_2\) rapidly towards the coil \(C_1\)
(D) hold the key pressed continuously
Choose the correct answer from the options given below:

Organs which differ in their origin and development but perform similar function are known as:

The maximum value of \(y=x^3-3 x\) is :