Consider the function \(f(x)=\sin x\) in the interval \([\pi, 2 \pi]\), then which of the following statements are correct?
(A) \(x=\frac{3 \pi}{2}\) is its stationary point.
(B) Its maximum value is 1
(C) Its minimum value is -1
(D) It attains its maximum value at \(\pi\) and \(2 \pi\)
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The equation of the tangent to the curve \(y=\frac{x-5}{(x-3)(x+2)}\) at the point where it cuts the \(x\)-axis is :

The slope of normal to the curve \(y=3 x^2-6 x\) at \(x=0\) is:

A metal wire under constant potential difference, when heated, shows that the drift velocity of the electron :

For the system \(\left[\begin{array}{cc}2 & -3 \\ -4 & 6\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}5 \\ -10\end{array}\right]\), which of the following statements are correct?
(A) The system has no solution.
(B) The system is consistent.
(C) It has infinitely many solutions.
(D) It has a unique solution.
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If \(n\) is the sample size of the population, then degree of freedom in t-distribution is

If \(\tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}\), then the value of \(x\) is:

Arrange the following compounds in the increasing order of their acidic strength :
(A) 3,5-dinitrophenol
(B) Propan-1-ol
(C) 2,4,6-trinitrophenol
(D) 3-nitrophenol
(E) 4-methyl phenol
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When a current of 5 A flows through an ammeter, it gives full deflection. The resistance of ammeter is 20 \(\Omega\). If the same ammeter is to be used for measuring a maximum current of 10 A, then the ammeter must be connected to a resistance of :

Match List-I with List-II

List-I (Drugs)	List-II (Sources/features)
(A) Alcohol	(I) Sedative and painkiller
(B) Crack	(II) Diacetylmorphine
(C) Morphine	(III) Liver cirrhosis
(D) Smack	(IV) Erythroxylum coca

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In species-area relationships equation - log S = log C + Z log A
'Z' denotes the -

Read the passage carefully and answer the questions
The chemical reactions proceed at different rates which depend on various factors like concentration, temperature, etc. Rate law is an expression which relates the rate of reaction with concentration of various reacting species in the reaction. For a first order reaction, the concentration of the reactant after time \(t\) is related with its initial concentration by the relation, \(C=C_0 e^{-k t}\). The rate constants for different orders have different expressions. For a first order reaction, \(k=\frac{2.303}{t} \log \frac{a}{a-x}\), where \(a\) is the initial concentration and \(x\) is the extent of reaction.
The quantity k in a rate law expression is

Let A and B be two events. Then which of the following statements are TRUE?
(A) \(P(B \mid A)=\frac{P(A \cap B)}{P(A)}\), provided \(P(A) \neq 0\)
(B) \(P\left(B^{\prime}\right)=1+P(B)\)
(C) \(P(A \cup B)=P(A)+P(B)+P(A \cap B)\)
(D) \(P(A \cap B)=P(A) \cdot P(B)\) if A and B are independent events
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