The area of the region bounded by the curves \(y=x^2+2, y=x, x=0\) and \(x=2\) is

The integrating factor of the differential equation \(\frac{d y}{d x}+y \cot x=2 x+x^2 \cot x, x \neq 0\) is

If the matrix \(A=\left[\begin{array}{ccc}x & 2 & y \\ -2 & 0 & 3 \\ -1 & z & 0\end{array}\right]\) is skew-symmetric, then the value of \(2 x-3 y+5 z\) is equal to

For any real numbers x and y, we define x R y if and only if \(\operatorname{cosec}^2 x-\cot ^2 y=1\). The relation R is:

A T.V. panel costing Rs 18000 has a useful life of 12 years. If the annual depreciation is Rs 1000, then its scrap value by linear method is :

If A and B are two matrices of order \(4 \times m\) and \(4 \times n\), respectively and \(m=n\),
then the order of matrix \((5 A-2 B)\) is:

If \(e^y=\log x\), then which of the following is true?

The maximum value of the objective function \(Z=8 x+2 y\) of an L.P.P. subject to the constraints: \(2 x+y \leq 3,2 x+3 y \leq 6, x \geq 0, y \geq 0 \) is:

Which one of the following is not an example of narrowly utilitarian reason to conserve biodiversity?

Match List-l with List-II

List-l (Test)	List-II (Identification)
(A) Hinsberg's Test	(I) Primary, Secondary and tertiary Amines
(B) Isocyanide test	(II) Aliphatic and Aromatic primary amines
(C) Azo dye test	(III) Primary Aromatic amines
(D) Tollen's Test	(IV) Reducing sugars

Choose the correct answer from the options given below:

The mathematical expression that represents the logistic growth in a population is :

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?

A convex lens of glass (n = 1.5) has a focal length 18 cm in air. When it is immersed in water (n = 4/3) the focal length increases to: