The least positive integer \(x\) satisfying \(29 \equiv x(\bmod 5)\) is

If A is a square matrix of order \(3 \times 3\) such that \(A^2 = A\) and I is the unit matrix of order \(3 \times 3\), then the value of \((I - A)^3 + A^2 + I\) is:

If \(f(x) = \begin{cases} \frac{\sqrt{4+x}-2}{x}, & \text{if } x \neq 0 \\ k, & \text{if } x = 0 \end{cases}\) is continuous at \(x = 0\), then the value of k is:

Which of the following statements are correct?
(A) A fund which is created to accumulate money over the years to discharge a future obligation is called a sinking fund.
(B) The amount or future value of perpetuity is well-defined.
(C) The sinking fund be used in any emergency.
(D) An equated monthly installment is a fixed payment made by a borrower to a lender at a specific date every : month to clear off the loan.
Choose the correct answer from the options given below :

A pipe A can fill a tank in 4 hours. There are two outlet pipes, B and C, from the tank which can empty it in 8 and 10 hours respectively. If all the three pipes are opened simultaneously, how long will it take to fill the tank?

The area enclosed between the curves \(y^2=x\) and \(y=|x|\) is :

The interval in which where the function \(f(x)=x^3-3 x^2+4 x+1, x \in R\) is increasing, is:

The value of \(\lambda\) so that the lines \(\frac{1-x}{3}=\frac{7 y-14}{2 \lambda}=\frac{z-3}{2}\) and \(\frac{7-7 x}{3 \lambda}=\frac{y-5}{1}=\frac{6-z}{5}\) are at right angle, is :

A galvanometer has a resistance of 8 \( \Omega \). It is shunted by a wire of resistance 2 \( \Omega \). If the total current is 2 A, the current passing through the shunt is

The electric field and magnetic field of a plane electromagnetic wave propagating in vacuum are expressed as
\(E_x=E_0 \sin (k z-\omega t)\)
\(B_y=B_0 \sin (k z-\omega t)\)
Which of the following statements are correct?
(A). The wave is propagating along the z- direction.
(B). The electric field Ex and magnetic field By are perpendicular to each other and perpendicular to the z direction.
(C) The electric and magnetic fields Ex and By are perpendicular to each other, and parallel to the direction of propagation.
(D) k is related to the wave length À of the wave by the usual equation \(k = A / 2 Tt\)
Choose the correct answer from the options given below:

Read the passage carefully and answer:
Organic compounds derived from NH3 by replacing one or more H-atoms with alkyl or aryl groups will form primary, secondary and tertiary amines. The common methods which include their preparations are reduction of nitro group, amide group and nitrile group, Gabriel phthalimide synthesis and ammonolysis of alkyl halides. Amines are basic in nature due to the presence of a lone pair of electrons on the nitrogen atom. Important chemical properties of amines include acylation, alkylation and their interaction with nitrous acid. There are various tests which can distinguish different types of amines from each other, for e.g. carbylamine test, Hinsberg's test, coupling reaction etc. Another important class of compounds which can be derived from primary amines is azo compounds. These compounds are intensely colored and widely used as dyes in textile, leather and food industries.
Conversion of nitro group into primary amine is preferred using

Domain of function \(f(x)=\cos ^{-1} \sqrt{2 x-1}\) is:

Observe the figure and answer the following:

Match List I with List II

LIST I	LIST II
A. VI	I. Antipodals
B. III	II. Egg cell
C. IV	III. Filliform apparatus
D. I	IV. Central cell

Choose the correct answer from the options given below: