The least non-negative remainder, when \(5^{61}\) is divided by 7 , is

The function \(f(x)=\left\{\begin{array}{ll}\frac{x^2+2 x-3}{x-1} & x \neq 1 \\ 2 & x=1\end{array}\right.\) is :

If \(y=\sin ^{-1} \sqrt{\frac{x}{x+1}}+\sec ^{-1} \sqrt{\frac{x+1}{x}}\), then \(\frac{d y}{d x}\) is

Two pipes P and Q can fill a tank in 26 minutes and 52 minutes respectively.
Both the pipes are opened together for some time and then pipe P is closed.
If the tank is filled in 26 minutes, then after how many minutes pipe P is closed?

If \(\mathbb{Z}\) and \(\mathbb{R}\) set of integers and set of real numbers respectively, then match List I with List II.

List - I	List - II
(A) \(5 x-3<3 x+1, x \in \mathbb{Z}\)	(I) \(x \in(-\infty,-3)\)
(B) \(3 x+17 \leq 2(1-x), x \in \mathbb{R}\)	(II) \(x \in(-\infty,-1)\)
(C) \(13 x+17<2(1-x), x \in \mathbb{R}\)	(III) \(\{\ldots,-4,-3, \ldots, 0,1\}\)
(D) \(\frac{2 x+3}{5}-2>\frac{3(x-2)}{5}, x \in \mathbb{Z}\)	(IV) \(\{\ldots,-4,-3,-2\}\)

Choose the correct answer from the options given below:

Area of the bounded region between the curve \(y=|x-2|\) and the line \(y=2\) is :

If \(A\) is a square matrix of order 3 and \(|A|=-2\), then the value of \(\left|-A^{-1}\right|\) is :

The number of electrons in one coulomb of electric charge is :

Read the passage carefully and answer the questions based on the passage:
Species diversity on earth is not uniformly distributed. It is generally highest in the tropics and decreases towards the poles. Earth's fossil history reveals the incidences of mass extinctions in the past. Earth's rich biodiversity is vital for the very survival of mankind. It is believed that communities with high diversity tend to be less variable and more productive. The reasons of conserving biodiversity are narrowly utilitarian, broadly utilitarian and ethical. Biodiversity conservation may be in-situ as well as ex-situ.
Which one of the following does not exhibit narrowly utilitarian argument for conserving biodiversity?

The karyotype of a person with Turner's syndrome is:

Which of the following compounds will show highest acidic strength?

Match List-I with List-II

List-I	List-II
(A) \(S _{ N } 2\)	(I) Racemization
(B) Iodoform	(II) Ozone depletion
(C) \(S _{ N } 1\)	(III) Antiseptic
(D) Carbon tetrachloride	(IV) Inversion

Choose the correct answer from the options given below:

Observe the figure and answer the following:


What is represented by figure D?