Consider the differential equation \(x d y=\left(y+2 x^3\right) d x\). Then which of the following are TRUE?
(A) It is a homogeneous differential equation.
(B) Product of the order and degree of the differential equation is one.
(C) Integrating factor is \(x\).
(D) General solution of the differential equation is \(y=x^3+C x\), where \(C\) is an arbitrary constant.
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Match List-I with List-II

List-I	List-II
(A) Degree of this differential equation \(\frac{d^4 y}{d x^4}+2 \log _e\left(\frac{d^3 y}{d x^3}\right)=0\)	(I) 1
(B) Order of this differential equation \(e^{\left(\frac{dy}{dx}\right)^3}+3 y\left(\frac{d^2 y}{d x^2}\right)^3=0\)	(II) 4
(C) Degree of \(\frac{d^4 y}{d x^4}+\left(\frac{d y}{d x}\right)^2=0\)	(III) not defined
(D) Order of the differential equation \(2 \frac{d^4 y}{d x^4}+\left(\frac{d^2 y}{d x^2}\right)^5=0\)	(IV) 2

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Evaluate \(\int_0^{\frac{\pi}{4}} \frac{\sin 2 x}{\cos ^4 x+\sin ^4 x} d x=\)

For \(x \in[-2,2]\), let \(f(x)=x^2+2\).
A. \(f(x)\) is continuous in \([-2,2]\)
B. \(f(x)\) is differentiable in \((-2,2)\)
C. \(f(-2)=f(2)=6\)
D. \(f^{\prime}(1)=0\)
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Solution of \(\frac{d y}{d x}+y=2\) is:

The solution of LPP :
Min. \(z=100 x+400 y\)
s.t. \(x+2 y \geq 8\)
\(2 x+5 y \leq 20\)
\(x \geq 0, y \geq 0\)
occurs at :

If \(A=\left[\begin{array}{ccc}5 & 1 & 0 \\ 6 & 2 & -1\end{array}\right], B^T=\left[\begin{array}{cc}2 & 1 \\ -2 & 0 \\ 1 & 3\end{array}\right]\), then \(B A^T\) is :

Which of the following is NOT a basic step in the genetic modification of an organism?

The point on the curve \(y^2=8 x\) for which the abscissa and ordinate change at the same rate, is

Read the Passage below and answer the question:
Aldehydes and Ketones, having atleast one methyl group linked to the carbonyl carbon atom (methyl Ketones), are oxidised by sodium hypohalite to sodium salts of corresponding carboxylic acids having one carbon atom less than that of carbonyl compound is converted to haloform. This oxidation does not affect a carbon - carbon double bond, if present in a molecule.
Which of the following statements are true?
A. \(CH_3CHO\) and \(CH_3CH_2CHO\) can be distinguished by Tollen's test.
B. \(CH_3CH_2CHO\) and \(CH_3COCH_3\) can be distinguished by Fehling's test.
C. \(CH_3CHO\) and \(C_6H_5CHO\) can be distinguished by Fehling's test.
D. \(HCHO, CH_3CHO\) can be distinguished by \(NaHCO_3\) test.
E. \(HCOOH, CH_3COOH\) can be distinguished by \(NaHCO_3\) test.
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Choose the correct statements :
(A) If two non ideal batteries are connected in series, then equivalent emf is larger than either of the two
(B) If two non ideal batteries are connected in series, then the equivalent internal resistance is smaller than either of the two.
(C) If two non ideal batteries are connected in parallel, then the equivalent emf is smaller than either of the two
(D) If two non ideal batteries are connected in parallel then the equivalent internal resistance is smaller than the two internal resistances
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Enzymes that cut the DNA at specific locations are known as :

A function \(f: R \rightarrow R\) defined by \(f(x)=\frac{x}{x^2+1}\) is (where \(R\) is the set of real numbers) :