Which of the following are the properties of Normal Distribution function f(x) and Normal probability curve:
(A) The probability of success remains the same in each trial and the number of trials is small in number.
(B) The curve is bell shaped and is symmetrical about the mean.
(C) If set of n trials are repeated N times, then frequency f(r) of r successes is given by
f(r) = N.P(r) = \(N e^{-m} \frac{m^r}{r!}\), r = 0, 1, 2...
(D) As x increases numerically, f(x) decreases rapidly and the maximum value of f(x) occurs at x = μ(mean).
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Consider the following hypothesis test.
\(H _0: \mu \leq 12\)
\(H _a: \mu>12\)
If a sample of 25 is taken with sample mean 15 and a sample standard deviation of 6, then the value of t-test statistic is:

Match List-l with List-ll

List-l Differential Equation	List-ll Integrating Factor
(A) \(y d x+\left(x-y^3\right) d y=0\)	(I) \(e^{-x}\)
(B) \(x \frac{d y}{d x}+y=x^2\)	(II) \(\frac{1}{x}\)
(C) \(\frac{d y}{d x}-y=e^x\)	(III) \(y\)
(D) \(x d y-y d x=x^3 d x\)	(IV) \(x\)

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A cone, whose height is always equal to its diameter, is increasing in volume at the rate of \(40 cm^3 / sec\). The rate at which radius is increasing when circular base area is \(1 m^2\) is :

If \(\sin ^{-1}\left(\frac{x}{5}\right)+\operatorname{cosec}^{-1}\left(\frac{5}{4}\right)=\frac{\pi}{2}\), then the value of x is:

The feasible region associated with the inequality \(2 x+3 y>4\) is

If the objective function \(z = 4x + 3y\) has maximum value on a line joining points (3, a) and (b, 2) where \(a > 0, b > 0\) such that \(a - b = 2\) then the maximum value of z is:

The de-Broglie wavelength associated with a ball of mass \( m = 150 \, g \) traveling at \( v = 30.0 \, m/s \) would be

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.
Which of the following technique is not very useful to detect the cancers of internal organs?

Scientific term for a situation where a single gene can exhibit multiple
phenotypic expressio is:

What is the structure of anionic coordination sphere in \(\left[ Cr \left( NH _3\right)_6\right]\left[ CuCl _5\right]\) complex?

Observe the given figure and answer the following questions:

What is essential before undertaking any organ transplant?

Which of the following statements are not correct?
(A) The milk produced during the initial few days of lactation is called colostrum which contain several antibodies
(B) The signals for the parturition originate from the pituitary gland of the mother
(C) Parturition is induced by a complex neuroendocrine mechanism
(D) Oxytocin is released from the ovary of mother and acts on the uterine muscles
Choose the correct answer from the options given below: