If the present value for a sequence of payments made at the end of each 6 months and continuing forever is ₹6000. If the money is worth 4% compounded semi-annually, then, the value of sequence of payment made is:

The value of \(\lim _{x \rightarrow 0} \frac{1-\cos x}{2 x^2}\) is:

If order of matrix \(A\) is \(m \times p\) and order of matrix \(B\) is \(p \times n\), then what is the order of matrix \(A B\) ?

Two parallel plate capacitors of capacitances \(2 \mu F\) and \(3 \mu F\) are joined in series and connected to a battery of \(V\) volts. The values of potential across the two capacitors V1 and V2 and energy stored in them U1 and U2 are related as :

The area bounded by \(y=3 x+1, x=0, y=0\) and \(x=a\) is 8 Sq.units. Then value of \(a\) (where \(a>0\) ) is

The area (in sq. units) of the region bounded by the line \(2 y+x=8\), the \(x\)-axis and the lines \(x=2\) and \(x=4\) is

A spherical balloon has a variable radius. The rate at which its volume is increasing with respect to its radius when the radius is 5 cm is:

Identify the hormone releasing IUDs -

Which of the following methyl halide will have the highest value of dipole moment?

When the electronic configuration of a transition metal element \(X\) in +3 oxidation state is \([ Ar ] 3 d^5\), what is its atomic number?

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?

If \(\left|\begin{array}{ccc}-a^2 & a b & a c \\ b a & -b^2 & b c \\ a c & b c & -c^2\end{array}\right|=4 x\), then \(x=\)

The kinetic energy of an electron in a given orbit in a hydrogen atom is : (symbols have their usual meaning)