A man rows 15 km upstream in 5 hours and 25 km downstream in 5 hours each time, then the speed of the stream is

If \(f(x)=x^2-4 x+13, x \in R\), then which of the following are correct?
(A) \(x=2\) is a stationary point of \(f(x)\).
(B) \(f ( x )\) is increasing function on (2, \(\infty)\) .
(C) \(f ( x )\) have maxima at \(x =2\).
(D) \(f ( 2 )= 9\).
Choose the correct answer from the options given below :

Value of \(\int\left(\frac{1}{\log x}-\frac{1}{(\log x)^2}\right) d x\) is

If \(\left[\begin{array}{ll}x-y & 0 \\ x+y & 1\end{array}\right]\) is an identity matrix and \(\left[\begin{array}{ll}x & y \\ x & x\end{array}\right]\) is a singular matrix then :

The unit vector in the xy-plane, making an angle of \(60^{\circ}\) with the positive direction of x-axis is:

A letter is known to have come either from KOLKATA or TATANAGAR. On the envelope just two consecutive letters TA are visible. The probability that letter has come from TATANAGAR is

If \(A=\left[\begin{array}{ccc}2 & -1 & -2 \\ 0 & 2 & -1 \\ 3 & -5 & 0\end{array}\right]\), then the value of \(\operatorname{det}(\operatorname{adj}(2 A))\) is :

Answer the question on the basis of passage given below:
Second period elements of p-Block differs from the rest of their group members due to their small atomic size, high electronegativity, high ionization enthalpy and absence of d-orbitals. The elements from the second period like C, N, O have unique property of forming \(p \pi-p \pi\) multiple bonds whereas other heavier elements of p-block form \(d \pi-p \pi\) multiple bonds. This changes the properties of second period elements to great extent. Also the single bond strength of the p-block elements with their own atoms gets affected by their atomic size and presence of lone pairs.
Inert pair effect also affects the properties of the p-Block elements especially for those elements which are present from 4th period onward and this happens due to poor screening effect of inner (n-1)d subshell electrons.
Catenation tendency of Nitrogen is weaker than Phosphorus, because

\(\int(x-1) e^{-x} d x=\)

If \(x \cos (a+y)+\cos a \sin (a+y)=0\), then \(\frac{d y}{d x}\) is equal to

The number of years required for a sum of money to get tripple at the effective rate of \(4\%\) is : (Given \((1.04)^{28}=3\) )

Calculate Three yearly moving averages for the following data

Year	2016	2017	2018	2019	2020	2021
Production (thousand tonnes)	200	220	231	254	202	243

\(\int_{\sqrt{\log _e 2}}^{\sqrt{\log _e 4}} x e^{x^2} d x\) is equal to