The function \(f(x)=\left\{\begin{array}{ll}\frac{x^2+2 x-3}{x-1}, & \text { if } x \neq 1 \\ 0, & \text { if } x=1\end{array}\right.\) is

For the LPP :
Maximise \(z=4 x+y\)
subject to constraints
\(x+y \leq 50, \quad 3 x+y \leq 90, \quad x \geq 0, y \geq 0\) the maximum value of \(z\) is :

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 man is known to speak truth 3 out of 4 times. He throws a die and reports that it is four. The probability that it is actually four is :

If \(\vec{a}=2 \hat{i}-\hat{j}+\hat{k}, \vec{b}=\hat{i}+\hat{j}-2 \hat{k}, \vec{c}=\hat{i}+3 \hat{j}-\hat{k}\), such that \(\vec{a}\) is perpendicular to \((\lambda \vec{b}+\vec{c})\), then the value of \(\lambda\) is :

If \(f(x) = \begin{vmatrix} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{vmatrix}\), then \(f(0)\) is:

Match List-I with List-II

List-I	List-II
(A) Angle between \(\hat{i}-2 \hat{j}+3 \hat{k}\) and \(2 \hat{i}+\hat{j}\)	(I) \(\cos ^{-1}\left(\frac{2}{\sqrt{18}}\right)\)
(B) Angle between \(\hat{i}+\hat{j}+2 \hat{k}\) and \(2 \hat{i}+2 \hat{j}+4 \hat{k}\)	(II) 0
(C) Angle between \(2 \hat{i}-\hat{j}+\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\)	(III) \(90^{\circ}\)
(D) Angle between \(\hat{i}+\hat{j}-\hat{k}\) and \(\hat{i}+\hat{j}+\hat{k}\)	(IV) \(\cos ^{-1}\left(\frac{1}{3}\right)\)

Choose the correct answer from the options given below:

A swimmer's speed in still water is \(6 km / hr\). He swims between two points in a river and returns back to the starting point. He took 24 minutes more to cover the distance

Read the following paragraph carefully and answer the given questions.
Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. For determining the cause of allergy, the patient is exposed to or injected with very small doses of possible allergens, and the reactions studied. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Heroin, commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine. Techniques like radiography (use of X-rays), CT (computed tomography) and MRI (magnetic resonance imaging) are very useful to detect cancers of the internal organs. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal.
Malignant malaria is caused by -

The corner points of the LPP Minimize \(z=5 x+7 y\) subject to the constraints
\(
\begin{array}{l}
2 x+y \geq 8 \\
x+2 y \geq 10 \\
x, y \geq 0 \\
\text { are } A(10,0), B(2,4), C(0,8)
\end{array}
\)
The minimum value of the objective function is :

The value of \(\left|\begin{array}{ccc}1 & 1+p & 1+p+q \\ 2 & 3+2 p & 1+3 p+2 q \\ 3 & 6+3 p & 1+6 p+3 q\end{array}\right|\) is:

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 disaccharide present in milk is known as

Match List-l with List-II

List-l (Pathogens)	List-ll (Diseases)
(A) Wuchereria bancrofti	(I) Ringworms
(B) Rhino Virus	(II) Elephantiasis
(C) Haemophilus influenzae	(III) Common Cold
(D) Epidermophyton	(IV) Pneumonia

Choose the correct answer from the options given below: