Function \(f(x)=x^x, x>0\) decreases on the interval

The solution of the differential equation \(\frac{d y}{d x}=\frac{3 e^{2 x}+3 e^{4 x}}{e^x+e^{-x}}\) is:

The speed of water current is half the speed of a motor boat.
The motor boat travels 15 km downstream in 1 hour.
Then the time taken to return to the starting point is:

If \(x, y\) and \(z\) are non zero real numbers, the inverse of matrix \(A=\left[\begin{array}{lll}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{array}\right]\) is:

\(\int \frac{\sqrt{\tan x}}{\sin x \cos x} d x\) equals :

A man rows downstream 30 km and upstream 20 km. If he takes 5 hours to cover each distance, then the speed of stream is

The function \(f:[0, \infty) \rightarrow R\) defined by, \(f(x)=2 x^2+3\), is:

Choose the correct statement/statements:
(A) Denaturation of protein causes loss of secondary and tertiary structure
(B) Nucleotides are joined together by diester linkage
(C) DNA contains Adenine, Guanine, cytosine and Uracil
(D) Amino acids show amphoteric behaviour
Choose the correct answer from the options given below :

Identify the correct statements.
(A) The density of nuclear matter is independent of the size of the nucleus.
(B) Nuclear forces are charge independent and are non-central forces.
(C) The nuclides having the same mass number are called isotones.
(D) The mass of a nucleus can be less or more than the sum of the masses of nucleons present inside it.
Choose the correct answer from the options given below:

Equal currents are flowing in four infinitely long wires. The distance between each other is the same and directions of currents are as shown in the figure. The net force on wire 2 is

Choose the correct answer from the options given below:

Let the corner points of the bounded feasible region of the linear programming problem \(( LPP ) Z=a x+b y\) be \((0,0),(2,0),\left(\frac{20}{19}, \frac{45}{19}\right)\) and \((0,3)\).
If the optimal value of \(Z\) occurs at both points \((2,0)\) and \(\left(\frac{20}{19}, \frac{45}{19}\right)\), then the relation between \(a\) and \(b\) is:

Read the following passage carefully.
Restriction enzyme
Restriction enzymes cut the strand of DNA a little away from the center of the palindrome sites, but between the same two bases on the opposite strands. This leaves single stranded portions at the ends. There are overhanging stretches called sticky ends on each strand. These are named so because they form hydrogen bonds with their complementary cut counterparts. This stickiness of the ends facilitates the action of the enzyme DNA ligase. The word palindromes refer to group of letters that forms the same words when read both forward and backward. Restriction endonucleases are used in genetic engineering as molecular scissors.
Overhanging stretches on each strand is called:

Choose an incorrect statement from the following about Kirchhoff's rules of electric circuits: