Which of the following statements are true regarding Lanthanoid elements?
i. \(\text{La}(\text{OH})_3\) is the basic hydroxide of Lanthanoids.
ii. \(\text{Zr}^{4+}\) and \(\text{Hf}^{4+}\) ions have almost similar ionic sizes.
iii. \(\text{Ce}^{4+}\) acts as an oxidising agent.
iv. Trivalent Lanthanoid ions are not coloured.
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Arrange the following amines in increasing order of their basic strength in the gaseous phase
(A) \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{NH}_2\)
(B) C\(_6\)\(\mathrm{H}_5CH\)\(_2\)\(\mathrm{NH}_2\)
(C) (CH\(_3\))\(_3\)N
(D) CH\(_3\)\(\mathrm{NH}_2\)
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\(\Lambda_m^{\circ}\) for \(\mathrm{NaCl}, \mathrm{HCl}\), and \(\mathrm{CH}_3 \mathrm{COONa}\) are \(126.4,425.9\), and \(91.0 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}\), respectively. Calculate \(\Lambda_m^{\circ}\) for \(\mathrm{CH}_3 \mathrm{COOH}\).

Which one of the following will exhibit maximum paramagnetic character?

Identify the product C in the following sequence of reactions.
\(\text{CH}_3 - \text{CH} = \text{CH} - \text{CH}_3 \xrightarrow{\text{O}_3} \text{A} \xrightarrow{\text{Zn/H}_2\text{O}} \text{B} \xrightarrow{\text{LiAlH}_4} \text{C}\)

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The chemical reactions proceed at different rates which depend on various factors like concentration, temperature, etc. Rate law is an expression which relates the rate of reaction with concentration of various reacting species in the reaction. For a first order reaction, the concentration of the reactant after time \(t\) is related with its initial concentration by the relation, \(C=C_0 e^{-k t}\). The rate constants for different orders have different expressions. For a first order reaction, \(k=\frac{2.303}{t} \log \frac{a}{a-x}\), where \(a\) is the initial concentration and \(x\) is the extent of reaction.
The quantity k in a rate law expression is

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Aldehydes and ketones undergo nucleophilic addition reactions. A nucleophile attacks the electrophilic carbon atom of polar carbonyl group from perpendicular to plane of \(sp^2\) hybridised orbitals of carbonyl carbon. The hybridisation of carbon changes from \(sp^2\) to \(sp^3\) and a tetrahedral alkoxide intermediate is formed. This captures \(H^+\) to give neutral product. In carboxylic acids, carbonyl carbon is less electrophilic than carbonyl carbon in aldehydes and ketones.
An organic compound \(C_3H_6O\) does not give a precipitate with 2,4-dinitrophenylhydrazine and also does not react with metallic sodium. It could be :

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The term vitamin was coined from the word vital +amine since the earlier identified compounds had amino groups. Later work showed that most of them didn't contain amino groups. They are very essential for the body. They has to be taken various diet or in the form of medicines also.
Vitamins are classified into two groups depending upon their solubility in water or fat.
Fat soluble vitamins are soluble in fat and oils but insoluble in water. They are stored in liver and adipose (fat storing) tissues Water-soluble vitamins are soluble in water. These must be supplied regularly in diet because they are readily excreated in urine and cannot be stored in our body.
Deficiency of Scurvy disease leads to

Consider \(f(x)=\sin (3 x)+4, \forall x \in \mathbb{R}\)
(A) Maximum value of f(x) is 5
(B) Maximum value of f(x) is 3
(C) Maximum value of f(x) is attained at \(x=\frac{\pi}{3}\)
(D) Minimum value of f(x) is attained at x = 0
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If \(x, y, z\) are all distinct and \(\left|\begin{array}{lll}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0\), then the value of \(x y z\) is :

If white colour flower of Antirrhinum sp. successfully crossed with the pink
colour flower, what would be the proportion of white and pink color flowers
in the next generation?

The demand function (in Rs.) for a product is \(P=20-0.25 x\). where P is the price per unit and \(x\) is the number of units sold. Find the price of one unit when the revenue is maximized

A parallel beam of monochromatic light of wavelength \( 460 \text{ nm} \) passes through a long slit of width \( 0.1 \text{ mm} \). What is the angular divergence in which most of the light is diffracted ?