\(\int_0^8\left(x^{\frac{2}{3}}+1\right) d x\) is equal to

Match list-I with List -II

List-I	List-II
(A) An observed set of population selected for analysis	(I) Parameter
(B) A specific characteristic of the population	(II) Hypothesis
(C) A specific characteristic of the sample	(III) Statistic
(D) A statement made about a population parameter for testing	(IV) Sample

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Probabilities to solve a specific problem by A, B and C are \(\frac{1}{2}, \frac{1}{3}\) and \(\frac{1}{4}\ respectively. Probability that at least one will solve the problem is:

A die is rolled in such a way that an even number is twice likely to occur as an odd number.
If the die is rolled twice, then the mean of the number of perfect squares in two tosses is :

Match List-l with List-ll
Where \(R\) is set of real numbers

List-l	List-ll
(A) \(f: R \rightarrow R\) s.t \(f(x)=x^4\) is	(I) one-one, Into
(B) \(f: R \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is	(II) many-one, into
(C) \(f:[0, \infty) \rightarrow R\) s.t \(f(x)=x^4\) is	(III) one-one, onto
(D) \(f:[0, \infty) \rightarrow[0, \infty)\) s.t \(f(x)=x^4\) is	(IV) many-one, onto

Choose the correct answer from the options given below :

Which one of the following set of constraints represents the shaded region given below?

If \(f(x)=\left\{\begin{array}{cl}\frac{k \cos x}{\pi-2 x}, & x \neq \frac{\pi}{2} \\ 3, & x=\frac{\pi}{2}\end{array}\right.\) is continuous at \(x=\frac{\pi}{2}\), then \(k\) is :

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.
Which type of ether is anisole ?

A circular loop of conducting wire is placed near a current carrying wire as shown in the figure. Both are in the same plane. If the current flowing through the wire is suddenly increased.

Considering the following statements; identify the correct statements:
(A) Scandium is regarded as a transition element, but zinc is not.
(B) \(V _2 O _3\) is amphoteric and \(V _2 O _5\) is basic oxide.
(C) The similar radii of Zr and Hf is a consequence of the lanthanoid contraction.
(D) The oxidation state of chromium in chromate and dichromate ion is same.
Choose the correct answer from the options given below:

Choose the correct statement about molar conductivity, \(\Lambda_{m}\)

Match List - I with List - II.

List - I	List - II
(A) RNA	(I) Adenosine
(B) Nucleoside	(II) Adenosine monophosphate
(C) Nucleotide	(III) Deoxyribose
(D) Sugar	(IV) Uracil

Choose the correct answer from the options given below:

The hormone releasing IUDs function by: