The value of \(\int_{-3}^2 x^2|2 x| d x\) is:

\(\int \frac{d x}{e^x+e^{-x}}\) is equal to

Consider \(Z = x + y\) subject to the constraints \(2x + y \le 3, 2x - y \ge 0, x \ge 0, y \ge 0\). The maximum value of Z is:

If \(\vec{a}, \vec{b}, \vec{c}\) are three mutually perpendicular unit vectors, then \(|\vec{a}+\vec{b}+\vec{c}|\) is equal to:

If \(r_{e f f}=\) effective rate of interest, \(r=\) nominal rate of interest and \(m=\) number of conversion periods per year, the relationship between nominal rate and effective rate of interest is :

The order and degree of the differential equation \(\frac{d^2 y}{d x^2}+2 e^{-x}=0\), respectively are :

Which of the following statements are correct in reference to the linear programming problem (LPP):
Maximize \(Z =5 x +2 y, Z =5 x +2 y, Z =5 x +2 y\)
subject to the following constraints
\(3 x+5 y \leq 15,5 x+2 y \leq 10, x \geq 0, y \geq 0\)
(A) The LPP has a unique optimal solution at \((2,0)\) only.
(B) The feasible region is bounded with corner points \((0,0),(2,0),(20 / 19,45 / 19)\) and \((0,3)\).
(C) The optimal value is unique, but there are an infinite number of optimal solutions.
(D) The feasible region is unbounded.
Choose the correct answer from the options given below:

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 statements are correct about microbes ?
(A) All microbes are pathogenic
(B) Microbes can grow at 80°C temperature
(C) Microbes can be present at places where no other life-forms possibly exist
(D) All microbes are microscopic
Choose the correct answer from the options given below:

Arrange the following amines in increasing order of basic strength in gaseous phase
(A) \(\left(\mathrm{CH}_3\right)_3 \mathrm{~N}\)
(B) \(\mathrm{CH}_3 \mathrm{NH}_2\)
(C) \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{NH}_2\)
(D) \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{NH}_2\)
Choose the correct answer from the options given below:

Answer the question on basis of passage given below:
Chloroform is a very useful solvent for oils, fats and waxes and many organic compounds. It can also be used for preserving biological specimens. Chloroform was used as a general anaesthetic in surgery for a long time but because of its toxic nature, it is no longer used these days.
Why is chloroform stored in dark coloured air tight bottles ?

Isomerism shown by \(Co(NH_3)_3(NO_2)_3\) is

If A and B are symmetric matrices of the same order, then which of the following are true?
(A) AB - BA is a skew symmetric matrix
(B) AB is a symmetric matrix
(C) AB is a scalar matrix
(D) AB + BA is a symmetric matrix
Choose the correct answer from the options given below:

What product(s) is formed when an Alkyl halide undergoes ammonolysis ?
(A) Primary amine
(B) Secondary amine
(C) Quaternary ammonium salt
(D) Tertiary amine
Choose the correct answer from the options given below: