(A) The degree of differential equation \(\frac{d^2 y}{d x^2}+\sin \left(\frac{d y}{d x}\right)=0\) is 2
(B) The degree of differential equation \(\frac{d}{d x}\left(\frac{d y}{d x}\right)+\left(\frac{d y}{d x}\right)^3+\sin x=0\) is 1
(C) The order of differential equation \(2 x^2 \frac{d^2 y}{d x^2}-3 \frac{d y}{d x}+y=0\) is 2
(D) The number of arbitrary constants in a particular solution of a differential equation of third order are 3
(E) The integrating factor of the differential equation \(\frac{d y}{d x}-y=\cos x\) is \(e^{-x}\)
Choose the correct answer from the options given below:

If a function \(f: R \rightarrow R\) is defined by \(f(x)=x^2+1\), then the pre-images of 17 and -3 respectively are:

The equation of motion of a missile is x = 3t, y = - 4t, z = t where time 't' is in seconds and the distance is measured in kilometres.
At what distance will the rocket be from the point (0, 0, 0) in 5 seconds?

If A is any \(m \times n\) matrix and B is a matrix such that AB and BA are both defined, then B is a matrix of order :

Let A = {1, 2, 3}. The number of equivalence relations containing (1, 3) is

Consider the Linear Programming Problem
Maximize \(z=x+y\)
Subject to the constraints \(x-y \leq-1, x \geq y, x \geq 0, y \geq 0\)
Then which one of the following is TRUE?

"The random variable \(X\) has a probability distribution \(P ( X )\) of the following form, where \(k\) is some number.
\(P(X=x)=\left\{\begin{array}{ll}k, & \text { if } x=0 \\2 k, & \text { if } x=1 \\3 k, & \text { if } x=2 \\0, & \text { otherwise }\end{array}\right.\)
Then \(P(x \leq 2)\) is :"

Read the following paragraph and answer the given questions.
Bio-fertilisers are organisms that enrich the nutrient quality of the soil like cyanobacteria, while there are organisms that help to control plant diseases and pests. The very familiar beetle, the ladybird and dragonflies are useful to get rid of aphids and mosquitoes, respectively. An example of microbial biocontrol agents that can be introduced to control butterfly caterpillars is certain bacteria, which are available in sachets in the form of dry spores. These spores are mixed with water and sprayed onto vulnerable plants. Trichoderma species that are very common in the root ecosystem, are very effective biocontrol agents of several plant pathogens.Baculoviruses attack insects and other arthropods. Usage of these viruses is desirable when an ecological sensitive area is being treated.
Find the odd one out of the given organisms?

Read the passage carefully and answer the questions
Biomolecules are the organic compounds present as an essential constituents of living organisms in different cells. molecules are generally termed as macromolecules, which are carbohydrates, enzymes, nucleic acids, amino acids and proteins The etc. Carbohydrates are classified as sugars and non-sugars include sucrose, glucose, fructose, starch and cellulose. Enzymes are coordinated with various chemical reactions in nucleic acid. Nucleic acids are found in living organisms made up of proteins and atural polymers. Two types that are generally found in biological systems are DNA and RNA nucleic acid. Amino acids bifunctional groups of carboxyl and amino groups. Proteins are a class of biologically important compounds. They are crucial are to virtually all processes in living systems. Some of them are hormones, which serve as chemical messengers that coordinate certain biochemical activities.
The zwitterionic form of amino acid is

A TV tower has a height of 20 m and the radius of earth is \(6.4 \times 10^6 m\). The range of the tower is:

In a pair of adjacent coils, if current in one coil changes from 0 A to 10 A in 0.25 s , causing a magnetic flux change of 15 Wb in the adjacent coil, the mutual inductance of the coils is :

Process of sone reflning is used in the purification of

Let \(f(x)=\left\{\begin{array}{ll}|x|+3 & \text { if } x \leq-3 \\ -2 x & \text { if }-3 < x < 3, \text { then which of the following is true? } \\ 6 x+2 & \text { if } x \geq 3\end{array}\right.\)