The equation of a curve passing through the point \((-1,3)\), given that the slope of the tangent to the curve at any point \((x, y)\) is \(\frac{2 x}{y^2}\), is :

The relation \(R\) on the set \(N \times N\) defined by \((a, b) R(c, d) \Longleftrightarrow a+d=b+c\), \(\forall(a, b),(c, d) \in N \times N\), where N is the set of natural numbers, is:

A company is shut down due to unavailability of electricity due to non payment of electricity Bill because of some unavoidable circumstances. Under which component of time series does this situation fall?

If the minimum value of the objective function \(Z=a x+b y\) of an LPP occurs at two points \((3,5)\) and \((5,3)\), then

The minimum value of the function f(x) = 3sinx - 4cosx, x ∈ [- 4π, 4π] is equal to

If \(y=\frac{1}{2} x \sqrt{a^2-x^2}+\frac{a^2}{2} \sin ^{-1}\left(\frac{x}{a}\right)\), then \(\frac{d y}{d x}=\)

Let \(A=\left[a_{i j}\right]\) be a square matrix of order 2 with elements either 0 or 1 . Then the difference between the possible number of singular and non-singular matrices is

\(V_{ p } < V_{ n }\)
\(V_{ p }>V_{ n }\)
\(V_{ p }>V_{ n }\)
\(V_{ p }>V_{ n }\)
A ray of light incident on an equilateral glass prism of refractive index \( \mu = \sqrt{3} \), travels parallel to the base of the prism inside it. What is the angle of incidence for this ray ?

Arrange the following in decreasing order of the basic character in aqueous phase
(A) Ethanamine
(B) Benzeneamine
(C) Phenylmethanamine
(D) N-methylaniline
Choose the correct answer from the Options given below:

A line through the points \(A(3,4,1)\) and \(B(5,1,6)\) is drawn.
The coordinates of the points where the line through the points \(A \backslash \& B\) crosses the \(X Y\) plane is:

If \(\int e^x\left(\frac{x-1}{(x+1)^3}\right) d x=\frac{A e^x}{(x+1)^B}+C\), where \(C\) is constant of integration, then which of the following are correct?
(A) \(A=-1\)
(B) \(A=1\)
(C) \(B=3\)
(D) \(B=2\)
Choose the correct answer from the options given below :

Read the passage carefully and answer the Questions
In the formation of coordination complexes, if the inner \(d\) orbital \((n-1) d\) is used in hybridisation, the complex, is called an inner orbital or low spin or spin paired complex. And if it uses outer \(d\) orbital ( \(n d\) ) in hybridisation (like \(s p^3 d^2\) ), it is called outer orbital or high spin or spin free complex. The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the complex. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting. For coordination complexes, the magnetic moment is determined by the number of unpaired electrons and is calculated by using the 'spin-only' formula, \(\mu=\sqrt{n(n+2)}\) where \(n\) is the number of unpaired electrons and \(\mu\) is the magnetic moment in units of Bohr magneton (BM). The coordination compounds are of great importance. These compounds are widely present in the mineral, plant and animal worlds and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine.
Fe(II) octahedral complexes can show different 'spin only' magnetic moments for arrangements in the presence of weak and strong ligands. The 'spin only' magnetic moments of these complexes with weak and strong ligands, respectively, are

A can solve \(90 \%\) problems and B can solve \(70 \%\) problems of the book. A problem is selected at random from the book. The probability that the problem is solved, is equal to