The greatest possible value of \(a\) such that the function\(f(x)=x^2+a x+1\) is always decreasing in the interval \([1,2]\), is:

The window of the house is in the form of a rectangle surmounted by a semi-circular portion, having a perimeter of 10 m as shown in figure.

If \(x\) and \(y\) represent the length and breadth of rectangular region, then the area A of the window in terms of \(x\) is :

The level of production where the revenue from sales is equal to the cost of production and marketing is known as

If the points \(( a 1, b 1),( a 2, b 2)\) and \(( a 1+ a 2, b 1+ b 2)\) are collinear, then

\(y=a \cos x+b \sin x\) where \(a, b\) are arbitrary constants is a solution of the differential equation:

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

The maximum value of Z = 3x + y subject to the constraints
x + y \(\le\) 7,
x \(\le\) 5,
y \(\le\) 4,
x \(\ge\) 0, y \(\ge\) 0 is:

A catalyst increases the rate of reaction by:

The magnitude of induced emf in a coil depends on the :

A first order reaction requires 6.96 months for the concentration of reactant A to be reduced to 25% of its original value. The half-life of the reaction is:
(Given \(\text{log } 2 = 0.3010\))

The relation \(R=\{(a, b):\) both \(a\) and \(b\) are either odd or even \(\}\) on the set \(\{1,2,4,5,7,8\}\) is

If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots \infty}}}\) then \(\frac{d y}{d x}\) equals to

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: