The derivative of \(\sec (\tan \sqrt{x})\) with respect to \(x\) is :

Match List-l with List-ll

List-l	List-ll
(A) \(\int_{-a}^a f(x) d x=0\)	(I) \(0\)
(B) \(\int_0^{2 a} f(x) d x=2 \int_0^a f(x) d x\)	(II) 1
(C) \(\int_{-\pi}^\pi \cos x d x\)	(III) \(f\) is an odd function
(D) \(\int_{-1}^1 x^{101} d x+1\)	(IV) \(f(2 a-x)=f(x)\)

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In a kilometer race \(P\) runs at \(10 m / sec , Q\) runs at \(5 m / sec\) then which of the following statement \(( s )\) is \(/\) are correct?
(A) \(P\) wins the race in 100 sec
(B) Q wins the race in 100 sec
(C) P defeats Q by 500 m
(D) Q defeats P by 500 m
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The function \(f(x)=[x]\), where \([x]\) denotes the greatest integer function, is continuous at \(x=\)
(A) 2.9
(B) 5
(C) -3
(D) 6.5
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Match List-I with List-II

List-I	List-II
(A) The minimum value of \(f(x)=(2 x-1)^2+3\)	(I) 4
(B) The maximum value of \(f(x)=-|x+1|+4\)	(II) 10
(C) The minimum value of \(f(x)=\sin (2 x)+6\)	(III) 3
(D) The maximum value of \(f(x)=-(x-1)^2+10\)	(IV) 5

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If the random variable X has the following probability distribution :

X	0	1	2	Otherwise
P(X)	K	3K	5K	0

then \(K\) is equal to

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

Which enzyme is used as a 'clot buster'?

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.

What is not true regarding compound \(\text{[B]}\) ?
(A) They are higher boiling liquids than aldehydes and ketones due to extensive H Bonding
(B) They are soluble in Benzene
(C) They produce alkane when heated with soda lime
(D) Produces \(\text{CO}_2\) when treated with \(\text{NaHCO}_3\)
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Aqueous NaCl solution is electrolysed. The product formed at anode is :

Which of the following statements about the rate of a chemical reaction are correct?
(A) The rate of reaction is always proportional to the concentration of reactants
(B) An exponential time course is followed by the first order reaction
(C) The unit of rate of reaction in the gaseous state is atm/s
(D) The concentration of reactant decreases exponentially with time for a zero order reaction
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Which of the following statements are true?
(A) Decomposition of gaseous ammonia on a hot platinum surface is a zero order reaction.
(B) The rate of a reaction increases with the passage of time.
(C) A catalyst does not change the equillibrium of a reaction.
(D) The molecularity of a reaction can be zero, fraction and negative.
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