The differential equation of the family of straight lines whose slope is equal to \(y\)-intercept is
A. \(\frac{d y}{d x}=\frac{x-y}{y-1}\)
B. \(\frac{d y}{d x}=\frac{x+1}{y+1}\)
C. \(\quad(x+1) \frac{d y}{d x}-y=0\)
D. \((x+1) \frac{d y}{d x}+y=0\)
E. \(\quad \frac{d y}{d x}-\frac{x+1}{y+1}=0\)
Choose the correct answer from the given below:

The order and degree of differential equation \(\sqrt[3]{2 y+\frac{d y}{d x}}=\left(x+\frac{d^3 y}{d x^3}\right)\) respectively are :

A and B are two students. Their chances of solving a problem correctly are \(\frac{1}{3}\) and \(\frac{1}{4}\) respectively.
If the probability of their making a common error is \(\frac{1}{20}\) and they obtain the same answer, then the probability that their answer is correct is:

Area bounded by \(y=|x-5|\) and the \(x\)-axis between \(x=2\) and \(x=4\) is:

A black and a red die are rolled simultaneously. The probability of obtaining a sum greater than \(9\) , given that the black resulted in a \(5\) is:

Match List-I with List-II

List-I	List-II
(A) \(f(x)=|x|+1\)	(I) Not differentiable at \(x=3\) only
(B) \(f(x)=|x-3|\)	(II) Not differentiable at \(x=-3\) only
(C) \(f(x)=|x+3|\)	(III) Not differentiable at \(x=3\), \(-3\) only
(D) \(f(x)=\left|x^2-9\right|\)	(IV) Not differentiable at \(x=0\) only

Choose the correct answer from the options given below:

The number of equivalence relation on the set {1, 2, 3} containing (1, 2) and (2, 1) is

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Carbohydrates are essential for both plants and animals. Some common examples of carbohydrates are glucose, fructose, sucrose, glycogen, cellulose and starch. They form a major portion of our food. Honey has been used for a long time as an instant source of energy in Ayurvedic medicine. Carbohydrates are used as storage molecules in both plants and animals. The cell wall of bacteria and plants is made of cellulose. We use cellulose in the form of wood for making furniture and as cotton fiber for clothing. They also provide raw material for textiles,
paper, lacquers, and breweries. Carbohydrates are classified as Monosaccharides, Oligosaccharides and Polysaccharides on the basis of their behavior towards hydrolysis. Monosaccharides cannot be hydrolyzed further to simpler units whereas oligosaccharides can yield 2-10 units of monosaccharides on hydrolysis. Polysaccharides, which are non-sugars yield a large number of monosaccharide units on hydrolysis.
Answer the following questions about carbohydrates:
Hydrolytic products of maltose are?

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Our immune system plays the major role in preventing diseases when we are exposed to disease-causing agents. Immunity is of two types: (i) Innate immunity and (ii) Acquired immunity. The human immune system consists of lymphoid organs, tissues, cells and soluble molecules like antibodies. The immune system also plays an important role in allergic reactions, auto-immune diseases and organ transplantation. The primary lymphoid organs are bone marrow and thymus. The secondary lymphoid organs are spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. There is lymphoid tissue also located within the lining of the major tracts (respiratory, digestive and urogenital tracts) called mucosa associated lymphoid tissue (MALT). It is important to note that HIV/AIDS is not spread by mere touch or physical contact; it spreads only through body fluids. AIDS has no cure, prevention is the best option. Adolescence is accompanied by several biological and behavioural changes and surveys and statistics show that use of drugs and alcohol has been on the rise especially among the youth. Factors associated with drug and alcohol abuse among adolescents are a child's natural curiosity, stress, the perception among youth that it is 'cool' or progressive to smoke, media exposure and an unstable or unsupportive family structures and peer pressure. It is best to identify the situations that may push an adolescent towards use of drugs or alcohol, and to take remedial measures well in time.
Which one of the following structures is not an example of a cellular barrier in innate immunity?

A magnetic field B exists in a direction perpendicular to the plane of a square loop made of metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field B changes at a steady rate of \( 0.032 \text{ T s}^{-1} \). The induced current in the closed loop is\n(Given: Resistivity of the metal wire is \( \rho = 1.57 \times 10^{-8} \Omega \text{ m} \))

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 short bar magnet of magnetic moment \(m =0.45 J / T\) is placed in a uniform magnetic field of 0.22 T . If the bar is free to rotate in the plane of the field, what is the potential energy of the magnet in stable and unstable equilibrium respectively?

A parallelogram is constructed on the vectors \(\vec{a}=3 \vec{\alpha}-\vec{\beta}, \vec{b}=\vec{\alpha}+3 \vec{\beta}\). If \(|\vec{\alpha}|=|\vec{\beta}|=2\) and the angle between \(\vec{\alpha}\) and \[\vec{\beta}\] is \(\frac{\pi}{3}\), then length of the diagonal of the parallelogram is: