The differential equation that represents the family of lines parallel to x + y = 2 is:

If \(y^{\frac{1}{m}}+y^{-\frac{1}{m}}=2 x\), then the value of \(\left(x^2-1\right) \frac{d^2 y}{d x^2}+x \frac{d y}{d x}\) is :

In a 900 meters race, Ram gives Shyam a start of 150 meters and defeats him by 50 seconds. If the speed of Ram is 4.5 m/sec, then the speed of Shyam is

Which of the following statements is incorrect?

If the minimum value of \(a\) is \(-\frac{k}{2}\), such that the function \(f(x)=x^2+a x+5\) is increasing in \([1,2]\). Then value of \(k\) is

The annual depreciation of an asset is independent of:-

The critical points of \(f(x)=x^3+x^2+x+1\) are

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. 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. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- 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. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused.
Which one of the following drugs is not used as medicine to help patients cope with mental illnesses like depression and insomnia?

Which of the following properties are desired in materials for permanent magnets ?
(A) High retentivity
(B) High coercivity
(C) High permeability
(D) low permeability
Choose the correct answer from the options given below:

Which of the following will exhibit only +3 oxidation state?

The speed of light in a medium whose critical angle is \(60^{\circ}\) will be:

Match List-I with List-II

List-I (EM waves)	List-II (Application)
(A) Infrared	(I) diagnostic tool in medicine
(B) X-rays	(II) water purification
(C) UV rays	(III) communication radar
(D) Microwaves	(IV) improving visibility in foggy days

Choose the correct answer from the options given below:

For the given linear programming problem \(z=a x+b y, a, b>0\) subject to the constraint
\(2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0\). If the corner points are \((0,0),(5,0),(3,4)\) and \((0,5)\) and \(z\) is maximum at both \((3,4)\) and \((0,5)\), then the relationship between \(a\) and \(b\) is