In an atom, total number of electrons having quantum numbers \(\mathrm{n}=4,\left|\mathrm{~m}_{\mathrm{l}}\right|=1\) and \(\mathrm{m}_{\mathrm{s}}=-\frac{1}{2}\) is _______.

The correct order of the atomic radii of \(C, Cs, Al\) and \(S\) is

Given below are two statements : Statement \(I:\) Upon heating a borax bead dipped in cupric sulphate in a luminous flame, the colour of the bead becomes green. Statement \(II:\) The green colour observed is due to the formation of copper(I) metaborate. In the light of the above statements, choose the most appropriate answer from the options given below :

The amount of oxygen in \(3.6\, moles\) of water is ............ \(\mathrm{g}\)

The spin only magnetic moment of \(\left[ Mn \left( H _2 O \right)_6\right]^{2+}\) complexes is \(........B.M.\) (Nearest integer)(Given : Atomic no. of \(Mn\) is \(25\) )

The decreasing order of reactivity towards dehydrohalogenation \((E_1)\) reaction of the following compounds is

\(\mathrm{AB}_{3}\) is an interhalogen \(T-\)shaped molecule. The number of lone pairs of electrons on \(\mathrm{A}\) is ...... .

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R .
Assertion A : If oxygen ion \(\left(\mathrm{O}^{-2}\right)\) and Hydrogen ion \(\left(\mathrm{H}^{+}\right)\)enter normal to the magnetic field with equal momentum, then the path of \(\mathrm{O}^{-2}\) ion has a smaller curvature than that of \(\mathrm{H}^{+}\).
Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.
In the light of the above statements, choose the correct answer from the options given below :

Correct Bernoulli's equation is _______. (symbols have their usual meaning)

The equations of the sides \(A B, B C \& C A\) of a triangle \(A B C\) are \(2 x+y=0, x+p y=21 a(a \neq 0)\) and \(x-y=3\) respectively. Let \(P(2, a)\) be the centroid of the triangle \(A B C\), then \((B C)^2\) is equal to

Two masses \(m\) and \(\frac{m}{2}\) are connected at the two ends of a massless rigid rod of length \(l\). The rod is suspended by a thin wire of torsional constant \(k\) at the centre of mass of the rodmass system (see figure). Because of torsional constant \(k\), the restoring torque is \(\tau  = k\,\theta \) for angular displacement \(\theta \). If the rod is rotated by \(\theta _0\) and released, the tension in it when it passes through its mean position will be

If \(m\) is a non-zero number and \(\int \frac{x^{5 m-1}+2 x^{4 m-1}}{\left(x^{2 m}+x^{m}+1\right)^{3}} d x=f(x)+c\) , then \(f(x)\) is

The amplitude of magnetic field in an electromagnetic wave propagating along \(y\)-axis is \(6.0 \times 10^{-7}\,T\). The maximum value of electric field in the electromagnetic wave is: