The heat of solution of anhydrous \(\mathrm{CuSO}_4\) and \(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\) are \(-70 \mathrm{~kJ} \mathrm{~mol}^{-1}\) and \(+12 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. The heat of hydration of \(\mathrm{CuSO}_4\) to \(\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}\) is \(-\mathrm{xkJ}\). The value of \(\mathrm{x}\) is _______.

Which of the following statements is correct

 Given below are two statements : one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\) : Assertion \((A) :\) A simple distillation can be used to separate a mixture of propanol and propanone. Reason \((R) :\) Two liquids with a difference of more than \(20^{\circ} \mathrm{C}\) in their boiling points can be separated by simple distillations. In the light of the above statements, choose the most appropriate answer from the options given below:

Match List - I with List - II.

List - I (Reaction)	List - II (Type of redox reaction)
(A) \(TiCl _4\)	(I) \(e ^2, t _2^0\)
(B) \(\left[ FeO _4\right]^{2-}\)	(II) \(e^4, t_2^3\)
(C) \(\left[ FeCl _4\right]^{-}\)	(III) \(e^0, t_2^0\)
(D) \(\left[ CoCl _4\right]^{2-}\)	(IV) \(e ^2, t _2^3\)

Choose the correct answer from the options given below :

The IUPAC name of the following compound is _______.-

\(\mathrm{CaCO}_3(\mathrm{~s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{CaCl}_2(\mathrm{aq})+\mathrm{CO}_2(\mathrm{~g}) \mathrm{H}_2 \mathrm{O}(\mathrm{l})\)
Consider the above reaction, what mass of \(\mathrm{CaCl}_2\) will be formed if 250 mL of 0.76 M HCl reacts with 1000 g of \(\mathrm{CaCO}_3\) ?
(Given : Molar mass of \(\mathrm{Ca}, \mathrm{C}, \mathrm{O}, \mathrm{H}\) and Cl are 40, \(12,16,1\) and \(35.5 \mathrm{~g} \mathrm{~mol}^{-1}\), respectively)

Choose the correct statements about the hydrides of group \(15\) elements. \(A\). The stability of the hydrides decreases in the order \(\mathrm{NH}_3>\mathrm{PH}_3>\mathrm{AsH}_3>\mathrm{SbH}_3>\mathrm{BiH}_3\) \(B\). The reducing ability of the hydrides increases in the order \(\mathrm{NH}_3<\mathrm{PH}_3<\mathrm{AsH}_3<\mathrm{SbH}_3<\mathrm{BiH}_3\) \(C\). Among the hydrides, \(\mathrm{NH}_3\) is strong reducing agent while \(\mathrm{BiH}_3\) is mild reducing agent. \(D\). The basicity of the hydrides increases in the order \(\mathrm{NH}_3<\mathrm{PH}_3<\mathrm{AsH}_3<\mathrm{SbH}_3<\mathrm{BiH}_3\)
Choose the most appropriate from the option given below.

The differential equation representing the family of ellipse having foci either on the \(x-\) axis or on the \(y-\) axis centre at the origin and passing through the point  \((0,3)\) is

Four particles \(A, B, C, D\) of mass \(\frac{\mathrm{m}}{2}, \mathrm{~m}, 2 \mathrm{~m}, 4 \mathrm{~m}\), have same momentum, respectively. The particle with maximum kinetic energy is _______.

A hydrogen atom in is ground state absorbs \(10.2\;eV\) of energy. The angular momentum of electron of the hydrogen atom will increase by the value of ............... \(\times 10^{-34} \; J {s}\) (Given, Plank's constant \(\left.=6.6 \times 10^{-34} Js \right)\)

\(\lim \limits_{x \rightarrow 0}\left(\tan \left(\frac{\pi}{4}+x\right)\right)^{\frac{1}{x}}\) is equal to 

The number of points, where the curve \(f(x)=e^{8 x}-e^{6 x}-3 e^{4 x}-e^{2 x}+1, x \in R\) cuts \(x\)-axis, is equal to

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A :\) An electron microscope can achieve better resolving power than an optical microscope. Reason \(R\) : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light. In the light of the above statements, choose the correct answer from the options given below