\(\int \frac{x \sin ^{-1} x}{\sqrt{1-x^2}} d x=\)

If \(\left[\begin{array}{cc}2 x+1 & 5 x \\ 0 & y^2+1\end{array}\right]=\left[\begin{array}{cc}x+3 & 10 \\ 0 & 26\end{array}\right]\) , then the possible values of x + y are:

The function \(f: R \rightarrow R\) given by \(f(x)=-|x-1|\) is

A card is selected at random from a pack of 52 playing cards.The selected card is a queen.The probability that this card is a card of spade is :

If \(\left[\begin{array}{ll}x+y & 4 \\ 1+z & y\end{array}\right]=\left[\begin{array}{ll}2 & 4 \\ 5 & 6\end{array}\right]\), then

In a linear programming problem, the constraints on the decision variables \(x\) and \(y\) are \(x-3 y \geq 0, y \geq 0,0 \leq x\) \(\leq 3\). The feasible region :

If |\(\vec{a}\)| = 8, |\(\vec{b}\)| = 3, and |\(\vec{a} \times \vec{b}\)| = 12, then the value of \(\vec{a} \cdot \vec{b}\) is:

Work done in moving a charge q along a closed path of length l by an electric field \(\vec{E}\) is given by:

A coin is tossed 3 times. If \(X\) denotes the number of heads, then Match List I with List II

LIST I	LIST II
A. \(P(X=0)\)	I. \(\frac{1}{8}\)
B. \(P(X=1)\)	ㅍ. \(\frac{7}{8}\)
C. \(P(X \leq 2)\)	III. \(\frac{4}{8}\)
D. \(P(X \geq 2)\)	IV. \(\frac{3}{8}\)

Choose the correct answer from the options given below:

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 dior 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 is a chelate complex?

Let the degree and order of the differential equation \(2 x^3 \frac{d y}{d x}-5\left(\frac{d^2 y}{d x^2}\right)^2=6\left(\frac{d y}{d x}\right)^3\) be \(m\) and \(n\) respectively. Then
(A) \(m=2\)
(B) \(n=3\)
(C) \(m=3\)
(D) \(m n=4\)

"Answer the question on basis of passage given below:
\(G = \frac{\kappa A}{l}\)=k (both \(A\) and \(l\) are unity in their appropriate units in m or cm)
Molar conductivity of a solution at a given concentration is the conductance of the volume \(V\) of solution containing one mole of electrolyte kept between two electrodes with area of cross section \(A\) and distance of unit length (\(l\)). Therefore,
\(\Lambda_m = \frac{\kappa A}{l}\)
Since \(l = 1\) and \(A = V\) (volume containing 1 mole of electrolyte),
\(\Lambda_m = \kappa V\)
If the length \(l\) in the column of an electrolytic cell is halved and its area of cross-section is tripled, then conductance (\(G\)) would become:"

The electric potential at any point in space is given by \( V = 4x^2 \text{ volt} \). The electric field at the point (1 m, 0, 2 m) in SI unit is