The differential equation representing the family of curves \(y=A \cos (x+B)\), where \(A\) and \(B\) are arbitrary constants is :

A box contains 3 white and 2 red balls. If we draw one ball and without replacing the first ball, the probability of drawing red ball in the second draw is:

If \(|\vec{a}-\vec{r}|=|\vec{a}|=|\vec{r}|=1\), then angle between \(\vec{a}\) and \(\vec{r}\) is

When two independent small samples of sizes \(n_1\) and \(n_2\) with means \(\bar{x}_1\) and \(\bar{x}_2\) respectively are drawn from populations with identical population variances, the test-statistic is computed as :

If \(f(x)=\left\{\begin{array}{ll}a x-1 & \text { if } x \geq 1 \\ 2 x+1 & \text { if } x<1\end{array}\right.\) is continuous at x = 1, then a equals

Let \(f(x)=\left\{\begin{array}{ll}\frac{|x|}{x}, & x \neq 0 \\ 1, & x=0\end{array}\right.\), and \(g(x)=\left\{\begin{array}{ll}x \sin \frac{1}{x}, & x \neq 0 \\ 0, & x=0\end{array}\right.\). Then at the origin, which one is true?

Let L be the set of all lines in a plane and R be the relation in L defined as \(R = \{(L_1, L_2) : L_1 \text{ is perpendicular to } L_2\}\) then R is:A. Reflexive
B. Symmetric
C. neither reflexive nor transitive
D. Transitive
E. neither reflexive nor symmetric
Choose the correct answer from the options given below:

Match List-I with List-II

List-I (Evolutionary stages of human species)	List-II (Time of origin)
(A) Ramapithecus	(I) About 1.5 million years ago
(B) Neanderthal man	(II) About 2 million years ago
(C) Australopithecines	(III) 1,00,000-40,000 years ago
(D) Homo erectus	(IV) About 15 million years ago

Choose the correct answer from the options given below:

Transition metals form a large number of complexes or coordination compounds in which the metal atoms are bound to a number of anions or neutral molecules. The valence bond theory explain the formation, magnetic behaviour and geometrical shapes while the crystal field theory explains the effect of different crystal fields on the degeneracy of d-orbitals energies of the central metal atom/ion. This provides for the quantitative estimation of orbital separation energies, magnetic moments and spectral and stability parameters.
Two complexes of nickel have same geometry but different magnetic behaviour are:
(A) \(\text{[Ni(CN)}_4]^{2-}\)
(B) \(\text{[Ni(CO)}_4]\)
(C) \(\text{[NiCl}_4]^{2-}\)
(D) \(\text{[Ni(NH}_3)_6]^{2+}\)
Choose the correct answer from the options given below :

\(y=a \cos x+b \sin x\) where \(a, b\) are arbitrary constants is a solution of the differential equation:

The main cause of basicity of oxoacids of phosphorous is :

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.
Which of the following metals belongs to Wilkinson catalyst?

Residual and persistent nucellus present in some seeds is called: