The point which lies in the half plane \(2 x-y \geq 6\) is:

If \(A=\left[\begin{array}{ccc}2 & 3 & 1 \\ 2 & -1 & 0\end{array}\right]\) and \(B^T=\left[\begin{array}{cc}4 & 4 \\ 6 & -2 \\ 2 & 0\end{array}\right]\) then \(4 A+B\) is

The value of the integral \(\int\left(x^6+x^4\right) d\left(x^2\right)\) is equal to:

The degree of the differential equation \(\left(\frac{d y}{d x}\right)^3+\left(\frac{d^2 y}{d x^2}\right)^2=0\) is:

The corner points of the bounded feasible region determined by the system of linear constraints are \((0,0), (5,0), (6,5)\), \((6,8),(4,10), (0,8)\). Let \(Z=3 x-4 y\) be the objective function. The minimum value of \(Z\) occurs at

The value of \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(x^3+x \cos x+\tan ^5 x+1\right) d x\) is:

If \(|\vec{a}|=1,|\vec{b}|=2,|2 \vec{a}+\vec{b}|=2 \sqrt{3}\) then \(|\vec{a}-\vec{b}|\) is :

Find the odd one out with reference to terrestrial ecosystem:

Read the passage carefully and answer the Questions
\(KMnO _4\) is prepared by the fusion of \(MnO _2\) with an alkali metal hydroxide and an oxidizing agent like \(KNO _3\) to give a dark-green manganate ion which disproportionate to give permanganate as follows.
\(\begin{array}{l}2 MnO _2+4 KOH + O _2 \rightarrow 2 K_2 MnO _4+2 H _2 O \\ 3 K_2 MnO _4+4 H ^{+} \rightarrow 2 KMnO _4+ MnO _2+2 H _2 O \end{array}\)
On heating \(K _2 MnO _4\) decomposes at 513 K to give \(K _2 MnO _4\). Permanganate ion is tetrahedral and diamagnetic
Acidified \(KMnO _4\) acts a strong oxidizing agent which oxidizes oxalic acid, ferrous ions, nitrite ion and iodides.
Oxidation states of Mn in \(MnO _2, KMnO _4\) and \(K _2 MnO _4\) are

Answer the question on the basis of passage given below:
In the periodic table, the d-block contains the elements of group \(3\) to \(12\). The d-orbitals are progressively filled in each of the four long periods. The elements of d block referred as transition metals have partly filled d orbitals and exhibit certain characteristic properties such as variety of oxidation states, formation of coloured ions, act as catalyst and show paramagnetic behaviour.
The two inner transition metals series \(4f\) and \(5f\) are known as Lanthanoids and Actinoids respectively. The lanthanoids resemble one another more closely as compared to ordinary transition elements in any series.
The catalytic activity of transition metals and their compounds is ascribed mainly to:

Arrange the following complexes in decreasing order of number of unpaired electrons on the metal ion
(A) \([Co(NH_{3})_{6}]^{3+}\)
(B) \([CoF_{6}]^{3-}\)
(C) \([FeF_{6}]^{3-}\)
(D) \([Fe(CN)_{6}]^{3-}\)
Choose the correct answer from the options given below:

Isomerism shown by the complex pair \(\left[ Cr \left( H _2 O \right)_6\right] Cl _3\) and \(\left[ Cr \left( H _2 O \right)_5 Cl ]Cl _2 \cdot H _2 O\right.\) is ___________

From the binding energy per nucleon versus mass number curve :
(A) B.E/nucleon is small for light nuclei like \( {}_{1}^{1}H, {}_{1}^{2}H, {}_{1}^{3}H \)
(B) B.E/nucleon decreases in heavy nuclei making them less stable stab.
(C) When two light nuclei combine to form heavy nucleus, energy is absorbed.
(D) Heavy nucleus splits into lighter nuclei which results in liberation of energy.
Choose the correct answer from the options given below :