The value of which of the following integrals is zero?
(A) \(\int_0^1 x d x\)
(B) \(\int_{-1}^1 x d x\)
(C) \(\int_{-1}^1 x^2 d x\)
(D) \(\int_0^1 \log \left(\frac{x}{1-x}\right) d x\)
Choose the correct answer from the options given below:

If the following data is obtained from a simple random sample : 6, 7, 9, 10, 11, 17
Then the point estimate of population standard deviation is :

The value of the determinant \(\left|\begin{array}{ccc}85 & 15 & 30 \\ 1 & 3 & 4 \\ 17 & 3 & 6\end{array}\right|\) is:

The value of the determinant \(\left|\begin{array}{lll}1 & x & y+z \\ 1 & y & z+x \\ 1 & z & x+y\end{array}\right|\) is :

If \(x = \sqrt{a^{\sin^{-1}t}}, y = \sqrt{a^{\cos^{-1}t}}\), then \(\frac{dy}{dx}\) is:

If \(\int_0^1\left(3 x^2+2 x+5 k\right) d x=0\), then the value of \(k\) is:

If \(P(A)=\frac{3}{5}, P(B)=\frac{1}{2}\) and \(P(A \cap B)=\frac{1}{4}\), then \(P(\bar{A} \mid \bar{B})\) is

Area (in sq. units) of the region bounded by the curve \(y^2=4 x, y\)-axis and the line \(y=3\) is

Read the passage carefully and answer the Questions
The concentration dependence of the rate of a reaction is called the differential rate equation. It is not always convenient to determine the instantaneous rate, as it is measured by calculating the slope of the tangent at point 't' in the concentration vs time plot. This makes it difficult to determine the rate and hence the order of the reaction. This difficulty is overcome by integrating the differential rate equation. This integrated rate equation gives a direct relation between concentrations at different times and the rate constant. The integrated rate equations are different for the reactions having different reaction orders.
Choose the correct statement regarding kinetics of a chemical reaction.

Answer the question on basis of passage given below :
Alcohols and phenol are formed when a hydrogen atom in a hydrocarbon, aliphatic and aromatic respectively, is replaced by \(\text{-OH}\) group. The substitution of a hydrogen atom in a hydrocarbon by an alkoxy or aryloxy group forms ethers. Alcohols and phenol consist of two part, an alkyl/aryl group and a hydroxyl group. The properties of alcohols and phenols are primarily due to the hydroxyl group. The nature of alkyl and aryl groups simply modify these properties. Alcohol react both as nucleophiles and electrophiles whereas in phenols, the reactions that take place on the aromatic ring are electrophilic subtitution reactions.
Aspirin is an acetylation product of :

Which one of the following statements is not true with reference to AIDS infection in human beings?

If \(\left|\begin{array}{ccc}-a^2 & a b & a c \\ b a & -b^2 & b c \\ a c & b c & -c^2\end{array}\right|=k \cdot a^l b^m c^n\), then
Match List-I with List-II

List-I	List-II
(A) \(l=m=n=\)	(I) 10
(B) \(k+l+m+n=\)	(II) 6
(C) \(k^2+l^2+(m-n)^2\)	(III) 2
(D) \(l^2+m^2+(n-k)=\)	(IV) 20

Choose the correct answer from the options given below :

Match List-I with List-II

List-I (Type of cell/Batteries)	List-II (Reaction)
(A) Daniell cell	(I) \(2 H _2(g)+ O _2(g) \rightarrow 2 H _2 O ( l )\)
(B) Fuel Cell	(II) \(Pb ( s )+ PbO _2(s)+2 H _2 SO _4( aq ) \rightarrow 2 PbSO _4(s)+2 H _2 O ( l )\)
(C) Primary Batteries	(III) \(Zn ( s )+ Cu ^{2+}( aq ) \rightarrow Zn ^{2+}( aq )+ Cu ( s )\)
(D) Secondary Batteries	(IV) \(Zn ( Hg )+ HgO ( s ) \rightarrow ZnO ( s )+ Hg ( l )\)

Choose the correct answer from the options given below: