Arrange the following acids in increasing order of their acidic strengths: \(HCOOH , FCH _2 COOH , NO _2 CH _2 COOH , ClCH _2 COOH\)

Read the passage carefully and answer the following questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms. They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O-H bond along with the reactions involving the complete - COOH group.
Arrange the following in the increasing order of their \(p K_{ a }\) values :
(A) \(CF _3- COOH\)
(B) \(O _2 N- CH _2- COOH\)
(C) \(NC - CH _2- COOH\)
(D) \(H - COOH\)
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Out of the following compounds, which will give iodoform test:
A. Isopropyl alcohol
B. Isobutyl alcohol
C. Secondary butyl alcohol
D. Ethyl alcohol
E. Acetic Acid
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In the electrochemical series written in the increasing order of reduction potential
(A) The elements which are placed above the hydrogen in the electrochemical series are stronger oxidizing agents.
(B) The elements which are placed above the hydrogen in the electrochemical series are stronger reducing agents.
(C) The elements with the positive electrode potential values lie below the hydrogen in the electrochemical series.
(D) The activity of both the metals and non-metals in the electrochemical series decreases from top to bottom.
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On heating, \(\left[ Ti \left( H _2 O \right)_6\right] Cl _3\) becomes colorless because \(\backslash\) ldots \(\backslash\) ldots \(\backslash\) ldots

Products not possible from given reaction is :
\(R - CH _2- C ( O )- CH _2- R ^{\prime} \xrightarrow{[ O ]}\)
(A) RCOOH
(B) \(R ^{\prime} CH _2 COOH\)
(C) \(R - CH _2- COOH\)
(D) \(R ^{\prime}- C ( O )- OCH _3\)
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An alkyl halide with molecular formula \(\text{C}_5\text{H}_{11}\text{Br}\) on dehydrohalogenation give two isomeric alkenes X and Y with formula \(\text{C}_5\text{H}_{10}\). On reductive ozonolysis X and Y gave four compounds: \(\text{CH}_3\text{CHO}\) (ethanal), \(\text{CH}_3\text{COCH}_3\) (propanone), \((\text{CH}_3)_2\text{CHCHO}\) (3-methylbutanal), and \(\text{HCHO}\) (methanal). The alkyl halide is:

Aravalli Hills of Rajasthan and Khasi and Jaintia Hills in Meghalaya are the examples of:

What is the product of the following reaction?
\[R-CN \frac{H_2 / Ni}{Na(Hg) / C_2 H_5 OH}\]
The options are:

The angle between the line \(\vec{r}=(\hat{i}+2 \hat{j}-\hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})\) and the plane \(\vec{r} \cdot(2 \hat{i}-\hat{j}+\hat{k})=4\) is :

When a number of capacitors are connected in parallel between two points increases, the equivalent capacitance

Match List-I with List-II
Let \(\theta\) be the angle between the vector \(\vec{a}\) and \(\vec{b}\).

List-I	List-II
(A) \(\vec{a} \cdot \vec{b}\)	(I) \(\frac{1}{10} \log \left|\frac{5+x}{5-x}\right|+C\)
(B) \(\vec{a} \times \vec{b}\)	(II) \(\frac{\vec{a} \cdot \vec{b}}{|\vec{b}|^2} \vec{b}\)
(C) Projection vector of \(\vec{a}\) on \(\vec{b}(\neq 0)\)	(III) \(|\vec{a}||\vec{b}| \sin \theta \hat{n}\) where \(\hat{n}\) is a unit vector perpendicular to both \(\vec{a}\) and \(\vec{b}\)
(D) \(\vec{a}\) and \(\vec{b}\) are orthogonal vectors	(IV) \(|\vec{a}||\vec{b}| \cos \theta\)

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The \(K H\) values of \(HCOOH > CH _4> Ar\) and CO _2 > at \(2 9 8 K\) are \(1 . 8 3 \times 1 0 - 5 ~ k b a r\), \(0.413 kbar , 40 kbar\) and 1.67 kbar respectively. Arrange them in the order of their decreasing solubility at constant pressure :