Which of the following pairs of solutions are isotonic?

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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 pK_a values:
(A) CF₃-COOH
(B) O₂N-CH₂-COOH
(C) NC-CH₂-COOH
(D) H-COOH
Choose the correct answer from the options given below :

Number of hydrogen bond formed between adenine and thymine to connect each other is /are

The decomposition of \(H _2 O _2\) in alkaline medium, in presence of \(I ^{-}\)ions occurs as follows :
\(2 H_2 O_2 \xrightarrow{I^{-}, \text {allaline medium }} 2 H_2 O+O_2\)
If the reaction occurs in the following two steps:
Step 1: \(H _2 O _2+ I ^{-} \xrightarrow{\text { Slow }} H _2 O + IO ^{-}\)
Step 2 : \(H _2 O _2+ IO ^{-} \xrightarrow{\text { Fast }} H _2 O + I ^{-}+ O _2\)
The correct rate law expression for the reaction is :

Insulin keeps glucose level within the narrow limit. It is released in response to the rapid rise in blood glucose level. The hormone that tends to increase glucose level in the blood is :

What is Lucas Reagent?

Match List I with List II

LIST 1	LIST 2
A. \(Cr ^{3+}\)	I. \(d^3\) configuration
B. \(Mn ^{2+}\)	II. \(d^{10}\) configuration
C. \(Cu ^{+}\)	III. Paramagnetic
D. \(Ti ^{4+}\)	IV. Diamagnetic

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A dietician wishes to mix two types of food in such a way that the vitamin contents of the mixture contains atleast 8 units of Vitamin A and 10 units of Vitamin C. Food 'I' contains 2 units/kg of Vitamin A and 1 unit/kg of Vitamin C while food 'II' contains 1 unit/kg of Vitamin A and 2 units/kg of Vitamin C. It costs ₹5 per kg to purchase food I and ₹7 per kg to purchase food II. If 'x' kg of food I is mixed with 'y' kg of food II, then the constraint pertaining to vitamin C contents will be:

Area of the region bounded by \(y=x^2\) and the line \(y=16\) is

Three capacitors each of capacitance 9 pF are connected in series. The capacitance of the combination would be :

Consider the differential equation, \(x \frac{d y}{d x}=y\left(\log _e y-\log _e x+1\right)\), then which of the following are true?
(A) It is a linear differential equation
(B) It is a homogenous differential equation
(C) Its general solution is \(\log _e\left(\frac{y}{x}\right)=C x\), where \(C\) is constant of integration
(D) Its general solution is \(\log _e\left(\frac{x}{y}\right)=C_y\), where \(C\) is constant of integration
(E) If \(y(1)=1\), then its particular solution is \(y=x\)
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\(\int \frac{\left(x^4-x\right)^{1 / 4}}{x^5} d x\) is equal to

Every year the price of a motorcycle depreciates by Rs. 15,000. After 12 years its price has become Rs. 50,000. Then its original cost was: