\(\int \sin^3 x dx\) is equal to:

If \(A\) is a square matrix of order 3 and \(|A|=-2\), then the value of \(\left|-A^{-1}\right|\) 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) \(f(2 a-x)=f(x)\)

Choose the correct answer from the options given below :

For \(|x|<1\), if \(x=\cos \left(\frac{1}{a} \log y\right)\), then

If two vectors \(\vec{a}\) and \(\vec{b}\) are such that \(|\vec{a}|=2,|\vec{b}|=3\) and \(\vec{a} \cdot \vec{b}=4\), then \(|\vec{a}-2 \vec{b}|\) is :

Which one of the following statement is incorrect about sinking fund?

For the given values 27, 35, 42, 45, 51, 34, 43; the five yearly moving averages are:

Antibiotic resistance gene in a vector helps in the selection of:

Read the passage carefully and answer the questions
Replacement of a hydrogen atom in a hydrocarbon by an alkoxy or carboxyl group yields a class of compounds known as ethers. Ethers are classified as symmetrical or unsymmetrical on the basis of groups attached to the oxygen atoms. Diethyl ether, a symmetrical ether, has been widely used as an inhalation anesthetic. Ethers can be prepared by acid catalyzed intermolecular dehydration of alcohols and Williamson's synthesis. Acid catalyzed dehydration of alcohols is not generally preferred as it gives a mixture of elimination and substitution products. In Williamson's synthesis, an alkyl halide is allowed to react with sodium alkoxide. Ethers containing substituted Alkyl groups may also be prepared by this method. The C-O bond in ether is weakly polar and is cleaved under drastic conditions with excess of hydrogen halides. In electrophilic substitution, the alkoxy group deactivates the aromatic ring and directs the incoming group to ortho and para positions.
The major product in the reaction of anisole with bromine in ethanoic acid, is :

Converting milk to curd improves its nutritional quality by increasing which of the following vitamins in it:

Decreasing \(Pk_b\) value of following in solution :
(A) \(CH_3CH_2NH_2\)
(B) \((CH_3CH_2)_2NH\)
(C) \((CH_3CH_2)_3N\)
(D) Aniline (Structure shown)
(E) 4-Methoxyaniline (Structure shown)
Choose the correct answer from the options given below :

Arrange the following step of PCR in correct sequence.
(A) Extension of Primer
(B) Annealing
(C) Denaturation of ds DNA
(D) Amplification
(E) Use of DNA polymerase and deoxynucleotides
Choose the correct answer from the options given below:

A integrating factor of the differential equation \(\frac{d y}{d x}+\frac{y}{x}=\frac{1}{x^2}(x>0)\) is equal to