The number of different words that can be formed from the letters of the word "INTERMEDIATE" such that two vowels never come together, is

An ellipse having the coordinate axes as its axes and its major axis along \(Y\)-axis, passes through the point \((-3,1)\) and has eccentricity \(\sqrt{\frac{2}{5}}\). Then its equation is

Which one of the following is false?

If the power of the point $(1,6)$ with respect to the circle $x^2+y^2+4x-6y-a=0$ is $-16$ then ${}^{\text{'}}a^{\text{'}}$ equals

If \(\sin x \cosh y=\cos \theta\) and \(\cos x \sinh y=\sin \theta\), then \(\sin ^2 x+\cosh ^2 y=\)

If \(A=\left[a_{i j}\right], 1 \leq i, j \leq n\) with \(\mathrm{n} \geq 2\) and \(a_{i j}=i+j\) is a matrix, then the rank of \(A\) is

The pair of straight lines represented by the equation \(3 d x^2-5 x y+\left(d^2-2\right) y^2=0\). If the lines are perpendicular to each other, for how many values of \(d\) this condition will be satisfied?

The length of the latus rectum of \(16 x^2+25 y^2=400\) is

The ground and first excited state energies are \(E_1\) and \(E_2\) respectively. Which pair of species has same energy? [Note that energy is indicated in the bracket].

If two angles of \(\triangle A B C\) are \(45^{\circ}\) and \(60^{\circ}\), then the ratio of the smallest and the greatest sides are

The \(\Delta_0\) of a coordination complex of a metal ion \(\left(3 d^1\right)\) is \(1000 \mathrm{~kJ} \mathrm{~mol}^{-1}\). If the energy of \(t_{2 g}\) orbitals is \(-400 \mathrm{~kJ} \mathrm{~mol}^{-1}\), the energy (in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) of \(e_g\) orbitals is

The correct order of increasing bond lengths of \(\mathrm{C}-\mathrm{H}, \mathrm{O}-\mathrm{H}, \mathrm{C}-\mathrm{C}\) and \(\mathrm{H}-\mathrm{H}\) is

When ' \(\mathrm{X}\) ' \(\mathrm{g}\) of graphite is completely burnt in a bomb calorimeter in excess of \(\mathrm{O}_2\) at \(298 \mathrm{~K}\) and \(1 \mathrm{~atm}\) pressure as given in the equation
\(\mathrm{C}\) (graphite) \(+\mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})\)
The temperature of calorimeter raised from \(298 \mathrm{~K}\) to \(302 \mathrm{~K}\). If the heat capacity of the calorimeter and molar enthalpy change for the reaction at \(1 \mathrm{~atm}\) and \(298 \mathrm{~K}\) are \(20.7 \mathrm{~kJ} \mathrm{~K}^{-1}\) and \(-248.4 \mathrm{~kJ} \mathrm{~mol}^{-1}\), ' \(\mathrm{X}^{\prime}\) in \(\mathrm{g}\) is