List of top Questions asked in JEE Main, KCET

Let \( S = \{z \in \mathbb{C} : z^2 + \sqrt{6}\,iz - 3 = 0 \}. \) Then \( \displaystyle \sum_{z \in S} z^8 \) is equal to:

Consider the quadratic equation \( (n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0, \; n \in \mathbb{R}. \) Let \( \alpha \) be the minimum value of the product of its roots and \( \beta \) be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is \( \alpha \) and the common ratio is \( \dfrac{\alpha}{\beta} \), is:

Let \( f : \mathbb{R} \to \mathbb{R} \) be defined as \( f(x) = \dfrac{2x^2 - 3x + 2}{3x^2 + x + 3} \). Then \( f \) is:

Decomposition of a hydrocarbon follows the equation} \[ k = (5.5 \times 10^{11}\, s^{-1})\, e^{\frac{-28000}{T}} \] The activation energy of reaction is _____ kJ mol\(^{-1}\). (Nearest Integer)} Given: \(R = 8.3\, J\,K^{-1}\,mol^{-1}\)}

In a closed flask at 600 K, one mole of \(X_2Y_4(g)\) attains equilibrium as given below :} \[ X_2Y_4(g) \rightleftharpoons 2XY_2(g) \] At equilibrium, 75% \(X_2Y_4(g)\) was dissociated and the total pressure is 1 atm. The magnitude of \(\Delta G^\circ\) (in kJ mol\(^{-1}\)) at this temperature is _____. (Nearest Integer)}

500 mL of 0.2 M \(MnO_4^-\) solution in basic medium when mixed with 500 mL of 1.5 M KI solution, oxidises iodide ions to liberate molecular iodine. This liberated iodine is then titrated with a standard \(M\) thiosulphate solution in presence of starch till the end point. If 300 mL of thiosulphate was consumed, the value of \(x\) is _____.

An alkane (Y) requires 8 moles of oxygen for complete combustion and on chlorination with \(Cl_2/h\nu\), (Y) gives only one monochlorinated product (Z). The total number of primary carbon atoms in (Y) is _____.

An excess of \(AgNO_3\) is added to \(100\) mL of a \(0.05\) M solution of tetraaquodichloridochromium (III) chloride. The number of moles of \(AgCl\) precipitated will be ______\(\times 10^{-3}\). (Nearest integer)}

Treatment of a gas \(X\) with a freshly prepared ferrous sulphate solution gives a compound \(Y\) as a brown ring. The compounds \(X\) and \(Y\) are :

Consider the following reactions. Total number of electrons in the \(\pi\)-bonds and lone pair of electrons in the product (X) is :}

The number of compounds from the following which can undergo reaction with \(Br_2/KOH\) (alcoholic) to give respective products and these products can also be obtained separately by Gabriel phthalimide reaction is :}

Consider the following organic reaction sequence. Choose the final product (X) from the following (consider the major product in all intermediate reactions).

Consider the following reaction}

Statement I:} In the above reaction, product formed will be a mixture of benzyl alcohol and iodobenzene.
Statement II:} In the above reaction, the \(-O-CH_2-\) bond is cleaved to give the product. Choose the correct answer.

An optically active alkyl bromide \(C_4H_9Br\) reacts with ethanolic KOH to form major compound [A] which reacts with bromine to give compound [B]. Compound [B] reacts with ethanolic KOH and sodamide to give compound [C]. One molecule of water adds to compound [C] on warming with mercuric sulphate and dilute sulphuric acid at \(333\,K\) to form compound [D]. The functional group in compound D is confirmed by :

\(X\) is the product obtained by hydrolysis of prop-1-yne in the presence of mercuric sulphate under dilute acidic medium. \(Y\) is obtained by the reaction of ethanenitrile with methyl magnesium bromide in dry ether followed by hydrolysis. IUPAC name of product obtained from \(X\) and \(Y\) in presence of barium hydroxide followed by heating is :

Shown below is the structure of methyl acetate with three different \(\alpha\), \(\beta\) and \(\gamma\) carbon–oxygen bonds. The correct order of bond lengths of these bonds is :}

Given below are two statements:} Statement I:} A mixture of \(C_{12}H_{22}O_{11}\) (sugar) and \(NaCl\) can be separated by dissolving sugar in alcohol, due to differential solubility. Statement II:} Rose essence from rose petals is separated by steam distillation due to its high volatility and insolubility in \(H_2O\). Choose the correct answer.

Which of the following sequences of hybridisation, geometry and magnetic nature are correct for the given coordination compounds?}

• [A.] \([NiCl_4]^{2-}\) -- \(sp^3\), tetrahedral, paramagnetic
• [B.] \([Ni(NH_3)_6]^{2+}\) -- \(sp^3d^2\), octahedral, paramagnetic
• [C.] \([Ni(CO)_4]\) -- \(sp^3\), tetrahedral, paramagnetic
• [D.] \([Ni(CN)_4]^{2-}\) -- \(dsp^2\), square planar, diamagnetic

Choose the correct answer.

The correct order of first \((\Delta_iH_1)\) and second \((\Delta_iH_2)\) ionisation enthalpy values of Cr and Mn are:}

• [A.] \( \Delta_iH_1: Cr>Mn \)
• [B.] \( \Delta_iH_2: Cr>Mn \)
• [C.] \( \Delta_iH_1: Mn>Cr \)
• [D.] \( \Delta_iH_2: Mn>Cr \)

Choose the correct answer.

In a period, the first ionisation enthalpy of the element at extreme left and the negative electron gain enthalpy of the extreme right element, except noble gases, are respectively.

For a general redox reaction} \[ \text{Anode: } \text{Red}_1 \rightarrow \text{Ox}_1^{n_1+} + n_1e^- \] \[ \text{Cathode: } \text{Ox}_2 + n_2e^- \rightarrow \text{Red}_2^{n_2-} \] Which of the following statement is incorrect?

Given is a concentrated solution of a weak electrolyte \(A_xB_y\) of concentration \(c\) and dissociation constant \(K\). The degree of dissociation is given by:

Given below are two statements:} A semipermeable membrane separates two chambers:

Statement I:} \(H_2O\) molecules move from chamber 1 to chamber 2. Statement II:} The osmotic pressure of a solution prepared by dissolving \(50\,\text{mg}\) of potassium sulphate \((\text{molar mass}=174\,\text{g mol}^{-1})\) in \(2\,\text{L}\) of water (at \(27^\circ\text{C}\)) is \(0.0107\,\text{bar}\). \((R=0.083\,\text{dm}^3\text{bar K}^{-1}\text{mol}^{-1})\) Choose the correct answer.

Match List-I with List-II.

Choose the correct answer.