Time reversal test is satisfied by:

For \(x \in R -\{0\}\), the function \(f(x)=\frac{3}{x}+7\) is decreasing when

Match List-I with List-II

Differential equation	Degree
(A) \(\frac{d^2 y}{d x^2}+\sqrt{\frac{d y}{d x}}-y=0\)	(I) 6
(B) \(\sqrt{\frac{d^3 y}{d x^3}}-\sqrt[12]{\frac{d^2 y}{d x^2}}=0\)	(II) not defined
(C) \(\left(\frac{d^2 y}{d x^2}\right)^2+\frac{d y}{d x}+e^{\frac{d y}{d x}}=x^2\)	(III) 3
(D) \(\sqrt[3]{\frac{d y}{d x}}-\frac{d^2 y}{d x^2}=e^x\)	(IV) 2

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The sum of two positive numbers is 60. If the sum of their squares is minimum, then the absolute value of the difference of their cubes is

If \(A\) is an invertible matrix, then which of the following statement(s) is/are TRUE?
(A) \(\left|A^{-1}\right|=|A|\)
(B) \(\left(A^{-1}\right)^{-1}=A\)
(C) \(A^{-1}=\frac{\operatorname{adj} A}{|A|}\)
(D) \(\left(A^T\right)^{-1}=\left(A^{-1}\right)^T\)
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Let \(A=\left[a_{i j}\right]_{2 \times 3}\) and \(B=\left[b_{i j}\right]_{3 \times 2}\), then \(|5 A B|\) is equal to:

The value of \(\tan ^{-1}(2)+\tan ^{-1}(3)\) is equal to

When blood cells are placed in 1\(\%\) (w/v) \(\text{NaCl}\) aqueous solution :

In a typical microsporangium, the function of tapetum is -

In water hyacinth, pollination is carried out by -
(A) Wind
(B) Water
(C) Insects
(D) Animals
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Match List-l with List-ll

List - I (Reactions)	List - II (Products)
(A) CH3CH2Br + alc.KOH	(I) CH3CH2NO2
(B) CH3CH2Br + aq.KOH	(II) CH2 = CH2
(C) CH3CH2Br + KNO2	(III) CH3CH2ONO
(D) CH3CH2Br + AgNO2	(IV) CH3CH2OH

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Osmotic pressure is the pressure that stops the flow of a solvent and is related to the volume as:

Answer the question on basis of passage given below :
Alcohols and phenol are formed when a hydrogen atom in a hydrocarbon, aliphatic and aromatic respectively, is replaced by -OH group. The substitution of a hydrogen atom in a hydrocarbon by an alkoxy or aryloxy group forms ethers.
Alcohols and phenol consist of two part, an alkyl/aryl group and a hydroxyl group. The properties of alcohols and phenols are primarily due to the hydroxyl group. The nature of alkyl and aryl groups simply modify these properties. Alcohol react both as nucleophiles and electrophiles whereas in phenols, the reactions that take place on the aromatic ring are electrophilic subtitution reactions.
Few compounds are given below (A to D). Arrange them in the increasing
order of their boiling points.
(A) Pentan-1-ol
(B) n-Butane
(C) Pentan-1-al
(D) Ethoxyethane
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