The molar solubility of \(\mathrm{Zn}(\mathrm{OH})_{2}\) in \(0.1 \,\mathrm{M} \,\mathrm{NaOH}\) solution is \(\mathrm{x} \times 10^{-18} \,\mathrm{M}\). The value of \(\mathrm{x}\) is ...... . (Nearest integer) (Given : The solubility product of \(\mathrm{Zn}(\mathrm{OH})_{2}\) is \(\left.2 \times 10^{-20}\right)\)

Below are two statements, one labeled as Assertion \((A)\) and the other as Reason \((R):\) Assertion \((A)\): Among group \(13\) elements, boron's melting point is unusually high \((2453 \mathrm{~K})\). Reason \((R):\) Solid boron has a strong crystalline lattice. In the context of the above statements, choose the correct answer from the following options:

\(2.5 \mathrm{~g}\) of a non-volatile, non-electrolyte is dissolved in \(100 \mathrm{~g}\) of water at \(25^{\circ} \mathrm{C}\). The solution showed a boiling point elevation by \(2^{\circ} \mathrm{C}\). Assuming the solute concentration in negligible with respect to the solvent concentration, the vapour pressure of the resulting aqueous solution is _______ \(\mathrm{mm}\) of \(\mathrm{Hg}\) (nearest integer) [Given : Molal boiling point elevation constant of water \(\left(\mathrm{K}_{\mathrm{b}}\right)=0.52 \mathrm{K.} \mathrm{kg} \mathrm{mol}^{-1}\), \(1 \mathrm{~atm}\) pressure \(=760 \mathrm{~mm}\) of \(\mathrm{Hg}\), molar mass of water \(=18 \mathrm{~g} \mathrm{~mol}^{-1}\)

Consider three metal chlorides x, y and z, where x is water soluble at room temperature, y is sparingly soluble in water at room temperature and z is soluble in hot water. x, y and z are respectively:

Given below are two statements :
Statement (I) : On nitration of m-xylene with \(\mathrm{HNO}_3, \mathrm{H}_2 \mathrm{SO}_4\) followed by oxidation, 4-nitrobenzene-1,3-dicarboxylic acid is obtained as the major product.
Statement (II) : \(-\mathrm{CH}_3\) group is o/p-directing while \(-\mathrm{NO}_2\) group is m-directing group.
In the light of the above statements, choose the correct answer from the options given below :

The difference between spin only magnetic moment values of \(\left[ Co \left( H _{2} O \right)_{6}\right] Cl _{2}\) and \(\left[ Cr \left( H _{2} O \right)_{6}\right] Cl _{3}\) is \(....\)

\(2-\) chloro \(-2-\) methylpentane on reaction with sodium methoxide in methanol yields : \((1)\,\,\begin{array}{*{20}{c}}
  {\,\,\,\,\,\,C{H_3}} \\ 
  | \\ 
  {{C_2}{H_5}C{H_2}C - OC{H_3}} \\ 
  | \\ 
  {\,\,\,\,\,\,\,\,C{H_3}} 
\end{array}\) \((2)\,\,\begin{array}{*{20}{c}}
  {{C_2}{H_5}C{H_2}C = C{H_2}} \\ 
  {\,\,\,\,|} \\ 
  {\,\,\,\,\,\,\,\,\,\,C{H_3}} 
\end{array}\) \((3)\,\,\begin{array}{*{20}{c}}
  {{C_2}{H_5}CH = C - C{H_3}} \\ 
  {\,\,\,\,\,\,\,\,\,\,\,|} \\ 
  {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,C{H_3}} 
\end{array}\)

The metallic bob of simple pendulum has the relative density \(5\). The time period of this pendulum is \(10\,s\). If the metallic bob is immersed in water, then the new time period becomes \(5 \sqrt{ x } s\). The value of \(x\) will be.

An electron is moving along \(+x\) direction with a velocity of \(6 \times 10^{6}\, ms ^{-1}\). It enters a region of uniform electric field of \(300 \,V / cm\) pointing along \(+ y\) direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the \(x\) direction will be

Which of the following statements are NOT true about the periodic table?
A. The properties of elements are function of atomic weights.
B. The properties of elements are function of atomic numbers.
C. Elements having similar outer electronic configurations are arranged in same period.
D. An element's location reflects the quantum numbers of the last filled orbital.
E. The number of elements in a period is same as the number of atomic orbitals available in energy level that is being filled.
Choose the correct answer from the options given below:

A straight the through a fixed point \((2, 3)\) intersects the coordinate axes at distinct points \(P\) and \(Q.\) If \(O\) is the origin and the rectangle \(OPRQ\) is completed, then the locus of \(R\) is:

A \(dc\) source of \(emf \,E_1 = 100\,V\) and internal resistance \(r = 0.5\,\Omega ,\) a storage battery of emf \(E_2 = 90\,V\) and an external resistance \(R\) are connected as shown in figure. For what value of \(R\) no current will pass through the battery ? ................ \(\Omega\)

Which one of the following reactions will not yield propionic acid?