The reaction \(2N_2O_5\,(g) \to  4NO_2\,(g) + O_2\,(g)\) follows first order kinetics. The pressure of a vessel containing only \(N_2O_5\) was found to increase from \(50\,mmHg\) to \(87 .5\,mmHg\) in \(30\,min.\) The pressure exerted by the gases after \(60\,min.\) will be .......... \(mmHg\) (assume temperature remains constant)

On complete reaction of \(FeCl _{3}\) with oxalic acid in aqueous solution containing \(KOH\), resulted in the formation of product \(A\). The secondary valency of \(Fe\) in the product \(A\) is ...... .
(Round off to the Nearest Integer).

Transition metal complex with highest value of crystal field splitting \(\left(\Delta_{0}\right)\) will be ........ .

From the compounds given below, number of compounds which give positive Fehling's test is _______. [Benzaldehyde, Acetaldehyde, Acetone,  Acetophenone,Methanal, \(4-\)nitrobenzaldehyde, cyclohexane carbaldehyde].

The number of given orbitals which have electron density along the axis is \(..........\). \(p _{ x }, p _{ y }, p _{ z }, d _{ xy }, d _{ yz }, d _{ xz }, d _z ^2, d _{ x ^2- y ^2}\)

Elevation in boiling point for \(1.5\) molal solution of glucose in water is \(4 \,K\). The depression in freezing point for \(4.5\) molal solution of glucose in water is \(4\, K\) The ratio of molal elevation constant to molal depression constant \(\left( K _{ b } / K _{ f }\right)\) is \(....\)

Given below are two statements Statement \(I :\) The \(E ^{\circ}\) value of \(Ce ^{4+} / Ce ^{3+}\) is \(+1.74 \,V\) Statement \(II :\) \(Ce\) is more stable in \(Ce ^{4+}\) state than \(Ce ^{3+}\) state. In the light of the above statements, choose the most appropriate answer from the options given below

For \(m, n > 0\), let \(\alpha(m, n)=\int_0^2 t^m(1+3 t)^n d t\). If \(11 \alpha(10,6)+18 \alpha(11,5)= p (14)^6\), then \(p\) is equal to \(......\).

If the variance of the first \(n\) natural numbers is \(10\) and the variance of the first m even natural numbers is \(16\), then \(m + n\) is equal to

Let \(y=y(t)\) be a solution of the differential equation \(\frac{d y}{d t}+\alpha y=\gamma e^{-\beta t}\) Where, \(\alpha > 0, \beta > 0\) and \(\gamma > 0\). Then \(\operatorname{Lim}_{t \rightarrow \infty} y(t)\)

If \(a\) and \(b\) are real numbers such that \((2+\alpha)^{4}=a+b \alpha,\) where \(\alpha=\frac{-1+i \sqrt{3}}{2},\) then \(a+b\) is equal to

Let M denote the set of all real matrices of order \(3 \times 3\) and let \(\mathrm{S}=\{-3,-2,-1,1,2\}\). Let
\(\mathrm{S}_1=\left\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: \mathrm{A}=\mathrm{A}^{\mathrm{T}} \text { and } a_{\mathrm{ij}} \in \mathrm{~S}, \forall \mathrm{i}, \mathrm{j}\right\}, \)
\( \mathrm{S}_2=\left\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: \mathrm{A}=-\mathrm{A}^{\mathrm{T}} \text { and } a_{\mathrm{ij}} \in \mathrm{~S}, \forall \mathrm{i}, \mathrm{j}\right\}, \)
\( \mathrm{S}_3=\{\mathrm{A}=\left[a_{\mathrm{ij}}\right] \in \mathrm{M}: a_{11}+a_{22}+a_{33}=0\) and \(a_{\mathrm{ij}} \in \mathrm{~S}, \forall \mathrm{i}, \mathrm{j}\}\)
If \(n\left(\mathrm{~S}_1 \cup_2 \mathrm{US}_3\right)=125 \alpha\), then \(\alpha\) equals _______

Two long current carrying conductors are placed parallel to each other at a distance of \(8 \,cm\) between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is \(300 \,\mu T\). The equal current flowing in the two conductors is ...............