List of top Questions asked in VITEEE

The roots of
\[ (x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0 \] where \(a\in \mathbb{R}\) are always

Let \(f(x)=x^2+ax+b\), where \(a,b\in \mathbb{R}\). If \(f(x)=0\) has all its roots imaginary, then the roots of \(f(x)+f'(x)+f''(x)=0\) are

If \(f(x)=2x^4-13x^2+ax+b\) is divisible by \(x^2-3x+2\), then \((a,b)\) is equal to

If \(p,q,r\) are all positive and are the \(p^{th}\), \(q^{th}\) and \(r^{th}\) terms of a geometric progression respectively, then the value of the determinant
\[ \left|\begin{matrix} \log x & p & 1 \\ \log y & q & 1 \\ \log z & r & 1 \end{matrix}\right| \] equals

If \(n\) is an integer which leaves remainder one when divided by three, then
\[ (1+\sqrt{3}i)^{n}+(1-\sqrt{3}i)^{n} \] equals

Calculate \(\Delta H_f^\circ\) for the reaction:
\[ Na_2O(s) + SO_3(g) \rightarrow Na_2SO_4(g) \]
given the following:
(A) \(Na(s)+H_2O(l)\rightarrow NaOH(s)+\frac{1}{2}H_2(g)\), \(\Delta H^\circ=-146\,kJ\)
(B) \(Na_2SO_4(s)+H_2O(l)\rightarrow 2NaOH(s)+SO_3(g)\), \(\Delta H^\circ=+418\,kJ\)
(C) \(2Na_2O(s)+2H_2(g)\rightarrow 4Na(s)+2H_2O(l)\), \(\Delta H^\circ=+259\,kJ\)

If \(f:[2,3]\rightarrow \mathbb{R}\) is defined by \(f(x)=x^3+3x-2\), then the range \(f(x)\) is contained in the interval

The number of subsets of \(\{1,2,3,\ldots,9\}\) containing at least one odd number is

A binary sequence is an array of 0's and 1's. The number of \(n\)-digit binary sequences which contain even number of 0's is

Consider the following reaction:
\[ C_2H_5Cl + AgCN \xrightarrow[\text{EtOH/H}_2O]{} X \;(\text{major}) \]
Which one of the following statements is true for \(X\)?
(I) It gives propionic acid on hydrolysis
(II) It has an ester functional group
(III) It has nitrogen linked to ethyl carbon
(IV) It has a cyanide group

What are \(X\) and \(Y\) in the following reaction sequence?
\[ C_2H_5OH \xrightarrow{Cl_2} X \xrightarrow{Cl_2} Y \]

What are \(A\), \(B\), \(C\) in the following reactions?
\[ (i)\; (CH_3CO)_2Ca \xrightarrow{\Delta} A \]
\[ (ii)\; CH_3CO_2H \xrightarrow{HI,\;Red\,P} B \]
\[ (iii)\; 2CH_3CO_2H \xrightarrow{P_4O_{10}} C \]

One percent composition of an organic compound \(A\) is carbon: \(85.71%\) and hydrogen \(14.29%\). Its vapour density is \(14\). Consider the following reaction sequence:
\[ A \xrightarrow{Cl_2/H_2O} B \xrightarrow{(i)KCN/EtOH\;(ii)H_3O^+} C \]
Identify \(C\).

The average kinetic energy of one molecule of an ideal gas at \(27^\circ C\) and \(1\,atm\) pressure is

Assertion (A): \(K\), \(Rb\) and \(Cs\) form superoxides. Reason (R): The stability of superoxides increases from \(K\) to \(Cs\) due to decrease in lattice energy.

pH of a buffer solution decreases by \(0.02\) units when \(0.12\,g\) of acetic acid is added to \(250\,mL\) of a buffer solution of acetic acid and potassium acetate at \(27^\circ C\). The buffer capacity of the solution is

Match the following:
List I List II
(A) Felspar (I) \([Ag_3Sb_3]\)
(B) Asbestos (II) \(Al_2O_3\cdot H_2O\)
(C) Pyrargyrite (III) \(MgSO_4\cdot H_2O\)
(D) Diaspore (IV) \(KAlSi_3O_8\)
(V) \(CaMg_3(SiO_3)_4\)

Which one of the following order is correct for the first ionisation energies of the elements?

The chemical entities present in thermosphere of the atmosphere are

In Gattermann reaction, a diazonium group is replaced by \(X\) using \(Y\). \(X\) and \(Y\) are

One mole of alkene on ozonolysis gave one mole of acetate aldehyde and one mole of acetone. IUPAC name of \(X\) is

Which one of the following sets correctly represents the increase in the paramagnetic property of the ions?

Current flow in each of the following circuit A and B respectively are

A bullet of mass \(0.02\,kg\) travelling horizontally with velocity \(250\,m\,s^{-1}\) strikes a block of wood of mass \(0.23\,kg\) which rests on a rough horizontal surface. After the impact, the block and bullet move together and come to rest after travelling a distance of \(40\,m\). The coefficient of kinetic friction on the rough surface is \((g = 9.8\,m\,s^{-2})\)