The area bounded by the curve \(y=x^2|x|, x\)-axis and the ordinates \(x=-1\) and \(x=0\) is given by :

The area of the region enclosed between the parabolas \(y^2 = x + 1\) and \(y^2 = -x + 1\) is:

If a fair coin is tossed 10 times, then the probability of obtaining at least one head is:

A machine costing Rs.50,000 has a useful life of 4 years .The estimated scrap value is Rs 10,000. The rate of depreciation per annum is :

Suppose that A, B and C are matrices of order \(m \times n, n \times 5\) and \(5 \times q\) respectively. The restriction on m, n and q so that AB - BC is defined are

The value of \(\tan ^{-1}(-\sqrt{3})+\cos ^{-1}\left(-\frac{1}{2}\right)\) is:

The integrating factor of differential equation \(\left[y(1-x \tan x)+x^2 \cos x\right] d x-x d y=0\) is :

The \(K H\) values of \(HCOOH > CH _4> Ar\) and CO _2 > at \(2 9 8 K\) are \(1 . 8 3 \times 1 0 - 5 ~ k b a r\), \(0.413 kbar , 40 kbar\) and 1.67 kbar respectively. Arrange them in the order of their decreasing solubility at constant pressure :

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 compound having the highest boiling point is:

Read the passage carefully and answer the Questions
\(KMnO _4\) is prepared by the fusion of \(MnO _2\) with an alkali metal hydroxide and an oxidizing agent like \(KNO _3\) to give a dark-green manganate ion which disproportionate to give permanganate as follows.
\(\begin{array}{l}2 MnO _2+4 KOH + O _2 \rightarrow 2 K_2 MnO _4+2 H _2 O \\ 3 K_2 MnO _4+4 H ^{+} \rightarrow 2 KMnO _4+ MnO _2+2 H _2 O \end{array}\)
On heating \(K _2 MnO _4\) decomposes at 513 K to give \(K _2 MnO _4\). Permanganate ion is tetrahedral and diamagnetic
Acidified \(KMnO _4\) acts a strong oxidizing agent which oxidizes oxalic acid, ferrous ions, nitrite ion and iodides.
HCl is not used to make the medium acidic in oxidation reaction of \(KMnO _4\) in acidic medium, because....

A cell supplies a current of 0.6 A through a 3 \( \Omega \) resistor and a current of 0.2 A through a 10 \( \Omega \) resistor. The internal resistance of the cell is :

A radioactive nucleus decays as given below:
\( {}_Z^A P \rightarrow {}_{Z+1}^A Q \rightarrow {}_{Z-1}^{A-4} R^* \rightarrow {}_{Z-1}^{A-4} R \)
Which particles are emitted in the sequence?

The value of \(\tan ^{-1}\left(\tan \frac{3 \pi}{4}\right)+2 \cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)\) is: