The values of 'a' for which the vectors \(\vec{\alpha}=\hat{i}+2 \hat{j}+\hat{k}, \vec{\beta}=a \hat{i}+\hat{j}+2 \hat{k}\) and \(\vec{\gamma}=\hat{i}+2 \hat{j}+a \hat{k}\) are coplanar are:

In which of the following interval the function \(f(x)=x^x, x>0\) is strictly increasing?

The area of the region bounded by the curve \(y=\sin x\) and the \(x\)-axis between \(x=\pi / 2\) and \(x=3 \pi / 2\) is :

The effective rate that is equivalent to a nominal rate of 16 % compounded semi-annually is :

The value of \(\sin \left(2 \sin ^{-1} \frac{4}{5}\right)\) is given by :

Consider the LPP: Minimize \(Z=x+2 y\) subject to \(2 x+y \geq 3, x+2 y \geq 6, x, y \geq 0\). The optimal feasible solution occurs at:

For a full wave rectifier, if the input frequency is \(5 0 ~ H z\), the output frequency will be

Read the passage carefully and answer the Questions:
Amines are classified as primary \(\left(1^{\circ}\right)\), secondary \(\left(2^{\circ}\right)\) and tertiary \(\left(3^{\circ}\right)\) depending upon the number of hydrogen atoms replaced by alkyl or aryl groups in ammonia molecules. Aliphatic amines are a stronger bases due to \(+I\) effect of an alkyl groups. Intermolecular hydrogen bonding in primary and secondary amines affects the boiling points of amines. The intermolecular association is more in primary amines than in secondary amines as there are more number of hydrogen atoms available for hydrogen bond formation. Nitro compounds are reduced to amines by passing hydrogen gas in the presence of finely divided nickel, palladium or platinum and also by reduction with metals in an acidic medium. Gabriel synthesis is used for the preparation of primary amines. Primary amines react with nitrous acid to give unstable diazonium-salts which can be used to synthesize a variety of compounds.

The reaction is an example of:

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

List-I (Name)	List-II (Structure)
(A) Cinnamaldehyde	(I)
(B) Vanillin	(II)
(C) Salicylaldehyde	(III)
(D) Benzophenone	(IV)

Choose the correct answer from the options given below:

From the statements given below, choose the correct statement regarding the galvanic cell.

There exists a horizontal magnetic field in space of value \( B = 9 \times 10^{-4} \text{ T} \). A magnetic bar of magnetic moment \( M = 9 \times 10^3 \text{ J/T} \) is placed at an angle \( \theta_i = 60^\circ \) to the field and is free to rotate. Finally, it comes to a position parallel to the field. Work done by magnetic field on the magnetic bar will be

According to the Raoult's law, vapour pressure of a solution is directly proportional to:

Area of the region enclosed by the curves \(y=\sqrt{x}\) and \(y=x^2\) is :