The order and degree of the differential equation \(\left(\frac{d^2 y}{d x^2}\right)^2+x^2\left(\frac{d y}{d x}\right)^3+y=\sin x\) respectively are:

The area of the parallelogram determined by the vectors \(\hat{i}+2 \hat{j}+3 \hat{k}\) and \(3 \hat{i}-2 \hat{j}+\hat{k}\) is

The corner points of the bounded feasible region determined by the system of linear constraints are (15,0), (40,0), (4, 18) and (6, 12). If objective function is Z = 30x + 20y then the sum of the maximum and the minimum values of Z is

The differential equation of the family of curves \(y=A e^{3 x}+B e^{-3 x}\) where A and B are arbitrary constants, is

The area (in sq. units) of the region bounded by the curve \(y=2 x^3, x\)-axis and ordinates \(x=-1\) and \(x=1\) is.

Let \(f(x)\) satisfies the requirements of Lagrange's mean value theorem in \([0,2]\).
If \(f(0)=0\) and \(f^{\prime}(x) \leq \frac{1}{2}\) for all \(x \in[0,2]\), then :

The straight line \(\frac{x+3}{3}=\frac{y+2}{4}=\frac{z+1}{0}\) is

A metal conductor of length 1m rotates in vertical plane about an axis passing through one of its ends at angular velocity 4 rad s-¹. What is the emf developed between the two ends of the conductor, if the horizontal component of the earth's magnetic field is 0.2 G?

Benzenediazonium chloride is a colourless solid that decomposes in

Match List-I (Name) with List-II (Solution)

List-I (Name)	List-II (Solution)
(A) Isotonic solution	(I) A solution with lower osmotic pressure than that of other solution
(B) Hypotonic solution	(II) A solution with higher osmotic pressure than that of other solution
(C) Ideal solution	(III) Different solutions with equal osmotic pressure
(D) Hypertonic solution	(IV) A solution that obeys Raoult's law at all temperatures and concentration

Choose the correct answer from the options given below:

Read the passage carefully and answer the questions
Amines are considered as derivatives of ammonia obtained by replacement of hydrogen atoms with alkyl or aryl groups. In nature they occur among proteins, vitamins, alkaloids and hormones. These can be primary, secondary or tertiary depending on the number of hydrogen groups replaced. They can be prepared from nitro compounds, alkyl halides, nitriles, amides etc. Due to unshared pair of electrons they behave as Lewis bases. Influence of the number of hydrogen atoms at nitrogen atom is displayed in physical properties such as solubility, boiling point and chemical reactions including basicity. Basic character of amines is expressed in terms of their \(K_b\) and \(p K_b\) values. Three classes of amines can be distinguished with p-toluene sulphonyl chloride which reacts with primary and secondary ddu amines. Amino group when attached to benzene ring behaves as an activating and ortho para directing group.
Which of the following reaction is not given by aniline?

When white light consisting of wavelengths ranging from 400 nm to 700 nm passes through water (u = 4/3), then the wavelength range in water will be :

Acetaldehyde and benzaldehyde can be best distinguished by: