The maximum value of \(z=4 x+3 y\) subject to constraint \(x+y \leq 6, x, y \geq 0\) is:

Evaluate the determinant \(\begin{vmatrix} x-y & y-z & z-x \\ y-z & z-x & x-y \\ z-x & x-y & y-z \end{vmatrix}\)

If \(x\) is real, the minimum value of \(f(x)=x^2-8 x+20\) is :

The acute angle between the lines \(\vec{r}=(4 \hat{i}-\hat{j})+\lambda(2 \hat{i}+\hat{j}-3 \hat{k})\) and \(\frac{x-1}{1}=\frac{y+1}{-3}=\frac{z-2}{2}\) is

If \(\sin y=x \cos (a+y)\), then \(\frac{d y}{d x}\) is equal to

If the slope of the tangent to the curve \(y=y(x)\) at any point \((x, y)\) is \(\frac{2 x}{y^2}\) and the curve passes through the point \(\left(\frac{1}{\sqrt{3}}, 1\right)\), then the equation of the curve is :

If \(P(A)=\frac{3}{10}, P(B)=\frac{2}{5}\) and \(P(A \cup B)=\frac{3}{5}\), then the value of \(P(B \mid A)+P(A \mid B)\) is :

Read the Passage carefully and answer the questions
When a ligand is bound to a metal ion through a single donor atom, it is said to be a unidentate ligand but when it bind through two donor atoms, then it is said to be didentate ligand and when several donor atoms are present in a single ligand, it is said to be a polydentate ligand. When a di- or polydentate ligand uses its two or more donor atoms simultaneously to bind a single metal ion, it is said to be a chelate ligand. The number of such ligating groups is called the denticity of the ligand. ligand which has two different donor atoms and either of the two ligetes in the complex is called ambidentate ligands. The number of ligand donor atoms to which the metal is directly bonded, is called coordination number of the metal ion in the complex. Complexes in which a metal is bound to only one kind of donor groups are known as homoleptic and in which a metal is bound to more than one kind of donor groups are known as heteroleptic complexes.
Which of the following molecule/ion is not expected to behave as a ligand?

Three point charges +q, +q and -2q are placed at the corner of an equilateral triangle of side 'a'. The net dipole moment of the system is

In reference to Inferential Statistics, for 20 degrees of freedom, the least statistical t-value among the given below is:

Which of the following are not contraceptive methods?
(A) IUDs
(B) GIFT
(C) IUI
(D) Cervical caps
Choose the correct answer from the options given below :

If the corner points of bounded feasible region for an LPP are (0, 2), (3,0), (6,0), (6, 8) and (0,5) then the minimum value of the objective function \(f = 4x + 6y\) occur at

If the molar conductivities at infinite dilution for \(\mathrm{CH}_3 \mathrm{COOK}, \mathrm{K}_2 \mathrm{SO}_4\) and \(\mathrm{H}_2 \mathrm{SO}_4\) are respectively, \(\mathrm{z}, \mathrm{y}\) and \(\times\left(\mathrm{S} \mathrm{cm}^2 \mathrm{~mol}^{-1}\right)\), the molar conductivity of \(\mathrm{CH}_3 \mathrm{COOH}\) at infinite dilution will be: