The unit's digit of \(2^{2025}\) is

If \(x, y\) and \(z\) are non-zero distinct numbers, then \(\left|\begin{array}{ccc}x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1\end{array}\right|\) is equal to

In context of Alligation and mixture the ratio of quantity of cheaper ingredient to the quantity of dearer ingredient =

Which of the following functions are increasing on \(x \in\left(0, \frac{\pi}{2}\right)\) ?
(A) \(f(x)=\sin x\)
(B) \(f(x)=\cos x\)
(C) \(f(x)=\tan x\)
(D) \(f(x)=\cos 3 x\)
Choose the correct answer from the options given below :

\(\int \frac{e^{2 x}-e^{-2 x}}{e^{2 x}+e^{-2 x}} d x \) is equal to :

A box contains 10 balls, each marked with one of the digits 0 to 9 .
If four balls are drawn successively with replacement from the box,
then the probability that none is marked with the digit \(0\) is :

If \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=0\) then
\(\left|\begin{array}{ccc}1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c\end{array}\right|\) is equal to :

Identify correctly:
A. \(\begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{bmatrix}\) is a symmetric matrix
B. \(\begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\) is a null matrix
C. \(\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}\) is an Identity matrix
D. \(\begin{bmatrix} 0 & 1 & 2 \\ -1 & 0 & 3 \\ -2 & -3 & 0 \end{bmatrix}\) is a skew symmetric matrix
E. \(\begin{bmatrix} \sqrt{3} & 0 & 0 \\ 0 & \sqrt{3} & 0 \\ 0 & 0 & \sqrt{3} \end{bmatrix}\) is a scalar matrix
Choose the correct answer from the options given below:

In the depression of freezing point experiment, it is found that :
(A) The vapour pressure of the solution is less than that of the pure solvent.
(B) The vapour pressure of solution is more than that of the pure solvent.
(C) Only the solute molecules solidify at the freezing point.
(D) Only the solvent molecules solidify at the freezing point.
Choose the correct answer from the options given below :

Read the passage carefully and answer the questions
Nearly all the transition elements display typical metallic properties such as high tensile strength, ductility, malleability, high thermal and electrical conductivity and metallic lustre. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. They have high enthalpies of atomization. lons of the same charge in a given series show progressive decrease in radius with increasing atomic number. However, the variation within a series is quite small. The filling of 4f before 5d orbital results in a regular decrease in atomic radii called Lanthanoid contraction which essentially compensates for the expected increase in atomic size with increasing atomic number. The net result of the lanthanoid contraction is that the second and the third d series exhibit similar radii (e.g., Zr 160 pm, Hf 159 pm) and have very similar physical and chemical properties. There is an increase in ionisation enthalpy along each series of the transition elements from left to right. The first ionisation enthalpy, in general, increases, but the magnitude of the increase in the second and third ionisation enthalpies for the successive elements, is much higher along a series. One of the notable features of a transition elements is the great variety of oxidation states these may show in their compounds.
Among \(\mathrm{Cr}(\mathrm{Z}=24), \mathrm{Co}(\mathrm{Z}=27), \mathrm{Mn}(\mathrm{Z}=25)\) and \(\mathrm{Fe}(\mathrm{Z}=26)\); which will show the maximum variety of oxidation states?

Amniocentesis is used to detect the :

The central dogma was proposed by:

Which one of the given assisted reproductive technologies (ART) involves transfer of fertilized egg into the fallopian tube?