For an ideal solution of two components \(A\) and \(B\), which of the following is true?

Metals generally melt at very high temperature. Amongst the following, the metal with the highest melting point will be \(......\)

When \(400\, \mathrm{~mL}\) of \(0.2\, \mathrm{M} \,\mathrm{H}_{2} \mathrm{SO}_{4}\) solution is mixed with \(600\, \mathrm{~mL}\) of \(0.1\, \mathrm{M} \,\mathrm{NaOH}\) solution, the increase in temperature of the final solution is \(....\,\times 10^{-2} \,\mathrm{~K}\). (Round off to the Nearest Integer). \(\left[\right.\) Use \(: \mathrm{H}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}) \rightarrow \mathrm{H}_{2} \mathrm{O}: \Delta_{\mathrm{\gamma}} \mathrm{H}=-57.1\, \mathrm{k} \mathrm{J} \,\mathrm{mol}^{-1}\) Specific heat of \(\mathrm{H}_{2} \mathrm{O}=4.18 \mathrm{Jk}^{-} \mathrm{g}^{-}\) density of \(\mathrm{H}_{2} \mathrm{O}=1.0\, \mathrm{~g} \mathrm{~cm}^{-3}\) Assume no change in volume of solution on mixing.]

Given below are two statements:

Statement I: \(3\)-phenylpropene reacts with HBr and gives secondary alkyl bromide having a chiral carbon atom as the major product.

Statement II: Aryl chlorides and aryl cyanides can be prepared by Sandmeyer reaction as well as Gattermann reaction.

In the light of the above statements, choose the correct answer from the options given below

In the presence of a small amount of phosphorous, aliphatic carboxylic acids react with chlorine or bromine to yield a compound in which \(\alpha -\) hydrogen has been replaced by halogen. This reaction is known as

A solution of copper sulphate \((CuSO_4)\) is electrolysed for \(10\, minutes\) with a current of \(1.5\, amperes\). The mass of copper deposited at the cathode (at . mass of \(Cu = 63\,u\)) is ............ \(\mathrm{g}\)

\(1.80\,g\) of solute \(A\) was dissolved in \(62.5\,cm ^{3}\) of ethanol and freezing point of the solution was found to be \(155.1\,K\). The molar mass of solute \(A\) is \(..........g\,\,mol ^{-1}\). [Given: Freezing point of ethanol is \(156.0 K\) Density of ethanol is \(0.80\,g\,cm ^{-3}\). Freezing point depression constant of ethanol is \(\left.2.00\,K\,kg\,mol\,m ^{-1}\right]\)

The compounds which give positive Fehling's test are :
(A)

(B)

(C) \(\mathrm{HOCH}_2-\mathrm{CO}-(\mathrm{CHOH})_3-\mathrm{CH}_2-\mathrm{OH}\)
(D)

(E)

Choose the correct answer from the options given below :

The value of numerical aperature of the objective lens of a microscope is \(1.25\). If light of wavelength \(5000\,\mathop A\limits^o \) is used, the minimum separation between two points, to be seen as distinct, will be....\(\mu m\)

A body of mass \(m_1\) moving with an unknown velocity of \(v_1 \hat i\) undergoes a collinear collision with a body of mass \(m_2\) moving with a velocity \(v_2 \hat i\) . After collision \(m_1\) and \(m_2\) move with velocities of \(v_3 \hat i\) and \(v_4 \hat i\) respectively. If \(m_2 = 0.5\, m_1\) and \(v_3 = 0.5\, v_1\) then \(v_1\) is:

Match the LIST-I with LIST-II

List-I (Compound)	List-II (Test)
A. Cyclohexanol	I. Hinsberg's reagent test
B. Cyclohexylamine	II. Phthalein dye test
C. Cyclohexanecarbaldehyde	III. Lucas test
D. Phenol	IV. Tollen's test

Choose the correct answer from the options given below:

Suppose a differentiable function \(f ( x )\) satisfies the identity \(f(x+y)=f(x)+f(y)+x y^{2}+x^{2} y\) for all real \(x\) and \(y .\) If \(\lim \limits_{x \rightarrow 0} \frac{f(x)}{x}=1,\) then \(f^{\prime}(3)\) is equal to 

Let \(f: R \rightarrow R\) be a function defined as \(f(x)=a \sin \left(\frac{\pi[x]}{2}\right)+[2-x], a \in R\), where [t] is the greatest integer less than or equal to \(t\). If \(\lim _{x \rightarrow-1} f(x)\) exists, then the value of \(\int_{0}^{4} f(x) d x\) is equal to.