In a box containing 100 bulbs, 10 are defective.
The probability that out of a sample of 5 bulbs none is defective is:

If \(\vec{a}+\vec{b}+\vec{c}=0,|\vec{a}|=3,|\vec{b}|=25,|\vec{c}|=7\), then the angle between \(\vec{a}\) and \(\vec{b}\) is:

The particular solution of the differential equation \(e^x \sqrt{1-y^2} d x+\frac{y}{x} d y=0\), given that \(y=1\), when \(x=0\), is:

In a LPP:
If two corner points yield the same maximum value of the objective function of an LPP then :
(A) the LPP has unique solution
(B) the LPP has 2 solutions
(C) the LPP has 3 solutions
(D) the LPP has infinite many solutions
Choose the correct answer from the options given below :

The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is \(\theta=60^{\circ}\), is :

The number of arbitrary constants in the particular solution of a differential equation of order 4 and degree 3 is

The solution of the differential equation \(\frac{d y}{d x}=1+x+y^2+x y^2\) is:

The function given by \(f(x)=|x-1|+|x-2|+|x-3|\) is:

The standard reduction potential \(\left(E^{\circ}\right)\) values of \(Ag ^{+}\left| Ag , K ^{+}\right| K , Mg ^{2+} \mid Mg\) and \(Cr ^{3+} \mid Cr\) are \(0.80 V,-2.93 V,-2.37 V\) and -0.74 V respectively. The decreasing order of reducing power of the following metals is:
(A)\(A g\)
(B)\(K\)
(C)\(Mg\)
(D)\(Cr\)
Choose the correct answer from the options given below:

Nitration of aniline with nitric acid and sulphuric acid gives major product as

Match List - I with List - II.

List - I (Molecule)	List - II (Application)
(A) Statin	(I) Immunosuppressive agent
(B) Streptokinase	(II) Detergent formulations
(C) Cyclosporin A	(III) Blood-cholesterol lowering agent
(D) Lipase	(IV) Clot buster

Choose the correct answer from the options given below:

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.
Heroin, commonly called smack is chemically ______ which is a white, odourless, bitter crystalline compound.

In the circuit diagram, the battery, diodes \( D_1 \) and \( D_2 \), bulbs \( B_1 \) and \( B_2 \) are connected as shown. Which of the following statements is true regarding bulbs \( B_1 \) and \( B_2 \)?