The function given by \(f(x)=|x-1|+|x-2|+|x-3|\) is:

The area enclosed by the curves \(x y=4, y=x, x=e^2\) and the \(x\)-axis, is :

If \(A=\left[\begin{array}{ll}1 & 2 \\ 0 & 3\end{array}\right]\), then \(|A \operatorname{adj} A|\) is

Match List - I with List - II.

LIST - I	LIST - II
(A) \(x^x\) has a stationary point at \(x\) equal to	(I) \(e\)
(B) For \(x>0\), minimum value of \(x^x\)	(II) \(1 / e\)
(C) The greatest value of \(\left(\frac{1}{x}\right)^x\)	(III) \(e^{1 / e}\)
(D) The stationary point of \(\frac{\log x}{x}\) for \(x\), where \(x>0\), is	(IV) \(e^{-1 / e}\)

Choose the correct answer from the otions given below:

The maximum value of \(Z=3 x+4 y\) subject to constraint \(x+y \leq 6, x, y \geq 0\) is:

A person creates a sinking fund to accumulate 60,000 in 5 years to buy a bike.
The amount to be deposited at the end of every quarter with a 12\% rate of interest compounded quarterly is :
Use \(\frac{0.03}{(1.03)^{20}-1}=0.0372\)

Which of the following are similarities between the sinking fund and the savings account?
(A) The sinking fund and the savings account are both financial tools.
(B) Both can be used in any emergency.
(C) They both involve setting aside an amount of money for the future.
(D) Both are long-term accounts which can be closed any time.
Choose the correct answer from the options given below

The osmotic pressure of a solution at 0°C is 2 atm. What will be its osmotic pressure at 819 K ?

If 50000 J energy available to primary producer, then energy available to tertiary consumer will be:

Read the passage and answer the following
Microbes are organisms that cannot be seen with the naked eye. They include bacteria, archaea, protists, viruses, prions, and fungi. They account for most of the diversity of life on earth. Far more microbes inhabit a single person's body than there are people on the entire planet. Microbes also dominate in terms of their ability to live and thrive in extreme environments, including clouds, deep-sea volcanoes, springs, ice caps, and animal intestines. Most animals, including humans, exhibit numerous associations with microbes. Our "human microbiome" includes our skin, hair, mouth, and gut.
Which of the following microbe is harmful?

Match List - I with List - II.

List - I	List - II
(A) Range of \(y=\operatorname{cosec}^{-1} x\)	(I) \(\quad R-(-1,1)\)
(B) Domain of \(\sec ^{-1} x\)	(II) \(\quad(0, \pi)\)
(C) Domain of \(\sin ^{-1} x\)	(III) \(\quad[-1,1]\)
(D) Range of \(y=\cot ^{-1} x\)	(IV) \(\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]-\{0\}\)

Choose the correct answer from the options given below :

Answer the question on the basis of passage given below:
Second period elements of p-Block differs from the rest of their group members due to their small atomic size, high electronegativity, high ionization enthalpy and absence of d-orbitals. The elements from the second period like C, N, O have unique property of forming \(p \pi-p \pi\) multiple bonds whereas other heavier elements of p-block form \(d \pi-p \pi\) multiple bonds. This changes the properties of second period elements to great extent. Also the single bond strength of the p-block elements with their own atoms gets affected by their atomic size and presence of lone pairs.
Inert pair effect also affects the properties of the p-Block elements especially for those elements which are present from 4th period onward and this happens due to poor screening effect of inner (n-1)d subshell electrons.
Catenation tendency of Nitrogen is weaker than Phosphorus, because

Identify the reagent which can be used to convert benzamide into aniline in a single step: