If A and B are symmetric matrices of same order, then which of the following are correct?
(A) AB-BA is a skew-symmetric matrix.
(B) \(AB + BA\) is a skew-symmetric matrix.
(C) \(A B^T-B A^T\) is a skew-symmetric matrix.
(D) \(AB + BA\) is a symmetric matrix.
Choose the correct answer from the options given below :

The value of \(\int_0^{\pi / 2} \frac{\tan ^7 x}{\cot ^7 x+\tan ^7 x} d x\) is

The value(s) of \(x\) for which the matrix \(A=\left[\begin{array}{ccc}x-1 & 1 & 1 \\ 1 & x-1 & 1 \\ 1 & 1 & x-1\end{array}\right]\) is singular, is/are :

Let \(X\) denote the number of hours a student studies on a selected day. The probability distribution of \(X\) is given by (where \(k\) is some unknown constant)
\(P\left(X=x_i\right)=\left\{\begin{array}{ll}0.5, & \text { if } x_i=0 \\k x_i, & \text { if } x_i=1 \\k\left(4-x_i\right), & \text { if } x_i=2 \text { or } 3 \\0, & \text { otherwise }\end{array}\right.\)
Then the value of \(k\) is

In an influenza epidemic, the number of cases diagnosed in a week were as follows:

Day	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
Number of Cases	10	12	8	16	9	14	4

The 3-day moving averages are :

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

If \(|\vec{a}|=10,|\vec{b}|=2\) and \(\vec{a} \cdot \vec{b}=12\), then value of \(|\vec{a} \times \vec{b}|\) is :

Read the passage carefully and answer the questions
The coordination compounds are of great importance. These compounds are widely present in the mineral, plants and animal world and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine. For example, coordination compounds find use in many qualitative and quantitative chemical analysis. Some important metal extraction and purification make use of complex formation. Hardness of water can be estimated by stable complex formation of Ca\(^{2+}\) and Mg\(^{2+}\)
Wilkinson catalyst used for hydrogenation of alkenes is a complex of ___________.

Standard reduction potentials (\(\text{E}^{\circ}\)) of \(\text{Pb}^{2+}, \text{Ag}^+, \text{Cu}^{2+}\) and \(\text{Fe}^{2+}\) are \(-0.13 \text{ V}, +0.80 \text{ V}, +0.31 \text{ V},\) and \(-0.44 \text{ V}\) respectively. Which is the strongest reducing agent?

Area bounded by \(y=|x-5|\) and the \(x\)-axis between \(x=2\) and \(x=4\) is:

\(\text{C-Cl}\) bond in chlorobenzene in comparison to \(\text{C-Cl}\) bond in methyl chloride is :

In a hydrogen atom an electron makes a transition from \( n_1 \rightarrow n_2 \), where \( n_1 \) and \( n_2 \) are the principal quantum numbers of the two states. Assuming Bohr's model to be valid, if the time period of the electron in the initial state is eight times that in the final state, the possible values of \( n_1 \) and \( n_2 \) are:

Which of the following is caused due to substitution of glutamic acid to valine on 6th position of B-globin chain of Haemoglobin molecule ?