A die is thrown 4 times and getting 3 is considered a success. The probability of 2 successes is :

If \(a , b , c\) are the lengths of the sides of a triangle and \(\left|\begin{array}{ccc}a^2 & b^2 & c^2 \\ (a+1)^2 & (b+1)^2 & (c+1)^2 \\ (a-1)^2 & (b-1)^2 & (c-1)^2\end{array}\right|=0\) then :

If E and F are independent events associated with an experiment, then which one of the following statements is correct?

For any square matrix \(A ;\left(A-A^{\prime}\right)\) is :

The value of a for which \(\int_1^a x^2 d x=\frac{7}{3}\) is:

If \(A=\left[a_{i j}\right]\) is a square matrix of order 3 such that \(a_{i j}=i+j\) for all \(i, j\), then which of the following are correct?
(A) A is a skew-symmetric matrix
(B) A is a non-singular matrix.
(C) The inverse of A does not exist.
(D) A is a symmetric matrix.
Choose the correct answer from the options given below :

When two independent small samples of sizes \(n_1\) and \(n_2\) with means \(\bar{x}_1\) and \(\bar{x}_2\) respectively are drawn from populations with identical population variances, the test-statistic is computed as :

Anshu takes a personal loan of ₹\(10,00,000\) at the rate of \(12\%\) per annum for 2 years, then the EMI by using flat rate method is

Minimum boiling azeotropes show __________ deviation from Raoult's Law at a specific composition.

The standard electrode potential for Daniell cell is 1.1 V , calculate the standard Gibb's energy for the reaction:
\(Z n(s)+C u^{2+}(a q) \rightarrow Z n^{2+}(a q)+C u(s)\)
It is found to be

A deutron and an \(\alpha\)-particle moving with the same velocity enter into a uniform magnetic field acting normal to the plane of their motion. The ratio of the circular paths described by the deutron and \(\alpha\)-particle 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 ?

Consider the following hypothesis test:
\( \begin{array}{l} H_0: \mu \leq 12 \\ H_a: \mu>12 \end{array} \)
A sample of 25 provided a sample mean \(\bar{x}=14\) and a sample standard deviation \(S=4.32\). If \(t_{0.05}=1.711\), then which of the following is correct?
(A) The test statistic is defined as \(t=\frac{\bar{x}-\mu}{S / \sqrt{n}}\).
(B) The value of the test statistic is 1.31 .
(C) At \(\alpha=0.05\), the null hypothesis is rejected.
(D) If the value of the \(t\)-statistic is less than \(t_\alpha\), then null hypothesis is accepted.
Choose the correct answer from the options given below: