The solubility of \(Ca ( OH )_{2}\) in water is ....... . [Given : The solubility product of \(Ca ( OH )_{2}\) in water \(\left.=5.5 \times 10^{-6}\right]\)

Which oxoacid of phosphorous has the highest number of oxygen atoms present in its chemical formula?

Total number of possible stereoisomers of dimethyl cyclopentane is ....

Match List - I with List - II.

List - I (Transition metal ion)		List - II (Spin only magnetic moment (B.M.))
(A)	Ti3+	(I)	3.87
(B)	V2+	(II)	0.00
(C)	Ni2+	(III)	1.73
(D)	Sc3+	(IV)	2.84

Choose the correct answer from the options given below :

Vanillin compound obtained from vanilla beans, has total sum of oxygen atoms and \(\pi\) electrons is _______.

For a first order reaction \(A \rightarrow B\), the rate constant, \(k =5.5 \times 10^{-14} \,s ^{-1}\). The time required for \(67\, \%\) completion of reaction is \(x \,\times 10^{-1}\) times the half life of reaction. The value of \(x\) is \(....\) (Nearest integer)

\(\mathrm{CrCl}_3 \cdot \mathrm{xNH}_3\) can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of \(0.558^{\circ} \mathrm{C}\). Assuming \(100 \%\) ionisation of this complex and coordination number of Cr is 6 , the complex will be _______.
(Given \(\mathrm{K}_{\mathrm{f}}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\) )

In a meter bridge experiment the balance point in obtained if the gaps are closed by \(2\,\Omega\) and \(3\,\Omega\). A shunt of \(x\,\Omega\) is added to \(3\,\Omega\) resistor to shift the balancing point by \(22.5\,cm\). The value of \(X\) is \(................\)

In the circuit shown here, the voltage across \(L\) and \(C\) are respectively \(300\, V\) and \(400\, V\). The voltage \(E\) of the ac source is......\(Volt\)

The number of molecules which gives haloform test among the following molecules is \(.......\).

For the reaction, \( N_{2}O_{4}\rightleftharpoons 2NO_{2}, \) graph is plotted as shown below. Identify correct statements.
A. Standard free energy change for the reaction is -5.40 kJ mol⁻¹.
B. As \( \Delta G^{\ominus} \) in graph is positive, \( N_{2}O_{4} \) will not dissociate into \( NO_{2} \) at all.
C. Reverse reaction will go to completion.
D. When 1 mole of \( N_{2}O_{4} \) changes into equilibrium mixture, value of \( \Delta G^{\ominus}=-0.84 \, kJ \, mol^{-1} \).
E. When 2 mole of \( NO_{2} \) changes into equilibrium mixture, \( \Delta G^{\ominus} \) for equilibrium mixture is -6.24 kJ mol⁻¹.

Choose the correct answer from the options given below:

Let \(\left(5, \frac{a}{4}\right)\), be the circumcenter of a triangle with vertices \(A(a,-2), B(a, 6)\) and \(C\left(\frac{a}{4},-2\right)\). Let \(\alpha\) denote the circumradius, \(\beta\) denote the area and \(\gamma\) denote the perimeter of the triangle. Then \(\alpha+\beta+\gamma\) is ...........

A body weights \(49\,N\) on a spring balance at the north pole. ..... \(N\) will be its weight recorded on the same weighing machine, if it is shifted to the equator? (Use \(g=\frac{G M}{R^{2}}=9.8 \,ms ^{-2}\) and radius of earth, \(R =6400\, km .]\)