For the function, \(f(x)=\frac{-3}{4} x^4-8 x^3-\frac{45}{2} x^2-350\), which of the following statements are correct?
(A) \(x=-3\) and \(x=-5\) are the only critical points of the given function.
\((B) x=-3\) is a point of local minimum.
(C) The local minimum value at \(x =-3\) is 231.
\((D) x=-5\) is a point of local maximum.
Choose the correct answer from the options given below:

If the points \(( a , b ),( c , d )\) and \(( a + c , b + d )\) are collinear, then

Match List-l with List-ll

List-l	List-ll
(A) \(\cos ^{-1} x+\cos ^{-1}(-x)\)	(I) \(\frac{\pi}{3}\)
(B) \(\operatorname{cosec}^{-1}(-x)+\sec ^{-1}(-x)\)	(II) \(-\frac{\pi}{3}\)
(C) \(\tan ^{-1} \sqrt{3}-\sec ^{-1}(-2)\)	(III) \(\pi\)
(D) \(\tan ^{-1}\left(\tan \frac{4 \pi}{3}\right)\)	(IV) \(\frac{\pi}{2}\)

Choose the correct answer from the options given below :

If \(\frac{1}{x^2}-\frac{1}{x}\) > 0, then \(x\) lies in the interval

For the linear programming problem,
Minimize (Z) =60x + 30y
subject to : \(2 x - y \geq-5 ; 3 x + y \geq 3 ; 2 x -3 y \leq 12; x , y \geq 0\)
the optimal value of \(z\) is

Consider two independent events A and B such that P(A) = 0.3, P(B) = 0.6.
match List - I with List - II

List - I	List - II
(A) P(A and B)	(I) 0.28
(B) P(A and not B)	(II) 0.18
(C) P(A or B)	(III) 0.12
(D) P(neither A nor B)	(IV) 0.72

Choose the correct answert from the option given below :

The area of the region enclosed between the two circles \(x^2+y^2=1\) and \((x-1)^2+y^2=1\) is

A bulb of \( 100 \text{ W} \) glows for \( 6 \text{ hours} \) a day. The units of energy consumed in \( 7 \text{ days} \) 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 cells are involved in phagocytosis and destruction of microbes?

Let \(f(x)=x^3-6 x^2+9 x-8\) be a function, then which of the following statements are TRUE?
(A) \(f^{\prime}(x)=3(x-1)(x-3)\)
(B) The critical points of the function are \(x=1\) and \(x=3\)
(C) \(x=1\) is the point of local minimum
(D) The local maximum value is -4
Choose the correct answer from the options below :

The area of the region bounded by \(y=|x-5|, x=0\) and \(x=1\) is :

For an endothermic reaction, energy of activation is \(E_a\) and enthalpy of reaction is \(\Delta H\)
(both of these are in \(kJ'\) mol\(^{-1}\)), minimum value of \(E_a\) will be :

The first isolated restriction endonuclease was: