The order of the differential equation \(\left[1+\left(\frac{d y}{d x}\right)^2\right]^2=\left(\frac{d^3 y}{d x^3}\right)\) is:

The minimum value of \(a x+b y\), where \(x y=c^2\) and \(a, b, c\) are positive, is:

The value of \(\left|\begin{array}{ll}\sqrt{3} / 2 & 1 / 2 \\ \sqrt{3} / 2 & 1 / 2\end{array}\right|\)

The integral \(\int e^x\left(\frac{x-1}{2 x^2}\right) d x\) is equal to:

If matrix \(A=\left[a_{i j}\right]_{2 \times 2}\) where \(a_{i j}=\left\{\begin{array}{l}1, i \neq j \\ 0, i=j\end{array}\right.\) then \(A^3\) is equal to :

The interval(s), where the function \(f(x)=\left\{\begin{array}{l}\frac{1-e^x}{e^{2 x}-1}: x \neq 0 \\ -\frac{1}{2}: x=0\end{array}\right.\) is increasing, is/are:

The value of \(\int(5 x-2)^3 d x\) is:

Arrange the given steps of DNA fingerprinting in sequence.
(A) Transferring of separated DNA fragments on nitrocellulose membrane
(B) Isolation of DNA and digestion by restriction endonuclease
(C) Hybridisation using VNTR Probe
(D) Separation of isolated DNA fragments by Gel Electrophoresis
Choose the correct answer from the options given below :

p-block elements are placed in groups 13 to 18 of the periodic table. Group 15 is nitrogen family. Nitrogen makes various compounds like \(NH _3, HNO _3, N_2 O , NO _2\) etc. Phosphorus exists in the form of white and red phosphorus. White phosphorus glows in dark. \(PH _3\) gas is used as smoke screen. Group 16 is called oxygen family. Dry air contains \(21\% O_2\) gas by volume. Combined sulphur exists as sulphates such as gypsum, epsome salt, baryte etc. The allotropic forms of sulphur are Rhombic and monoclinic sulphur. \(S_2\) is paramagnetic like \(O_2\) and it stable at high temperature. Group 17 is Halogen family. \(F_2\) is highly reactive, \(C l_2\) is greenish yellow gas. Both \(S O_2\) and \(C l_2\) are used for bleaching. Group 18 is Noble gas family but some noble gases also form compounds.
Complete hydrolysis of \(XeF _6\) gives HF and \(XeO _3\) as main products.
The product of complete hydrolysis of \(XeF _6\) in the following reaction is
\(XeF _6+ H _2 O \rightarrow ?+ HF\)

Match List-I with List-II

List-I (Inverse Trigonometric Function)	List-II (Principal Value)
(A) \(\sin ^{-1}\left(-\frac{1}{2}\right)\)	(I) \(\pi / 6\)
(B) \(\cos ^{-1}\left(-\frac{1}{2}\right)\)	(II) \(-\pi / 6\)
(C) \(\tan ^{-1}(-\sqrt{3})\)	(III) \(2 \pi / 3\)
(D) \(\cot ^{-1}(\sqrt{3})\)	(IV) \(-\pi / 3\)

Choose the correct answer from the options given below :

If E and F are independent events associated with an experiment, then which one of the following statements is correct?

45 g of ethylene glycol (C₂H₆O₂) is mixed with 600 g of water. Calculate the depression in freezing point.
(K_f for water = 1.86 K kg mol^-1)

Which of the following is not the alien invasive species?