List of top Questions asked in JEE Main- 2022

Suppose \( \mathop {\lim }\limits_{x \to 0} {{F(x)} \over {{x^3}}} \) exists and is equal to L, where

\( F(x) = \left| {\matrix{ {a + \sin {x \over 2}} & { - b\cos x} & 0 \cr { - b\cos x} & 0 & {a + \sin {x \over 2}} \cr 0 & {a + \sin {x \over 2}} & { - b\cos x} \cr } } \right| \).

Then, \( - \)112 L is equal to ___________.

Let \( \alpha = \tan \left( {{{5\pi } \over {16}}\sin \left( {2{{\cos }^{ - 1}}\left( {{1 \over {\sqrt 5 }}} \right)} \right)} \right) \) and \( \beta = \cos \left( {{{\sin }^{ - 1}}\left( {{4 \over 5}} \right) + {{\sec }^{ - 1}}\left( {{5 \over 3}} \right)} \right) \) where the inverse trigonometric functions take principal values. Then, the equation whose roots are \( \alpha \) and \( \beta \) is :

Let the eccentricity of the ellipse \( {x^2} + {a^2}{y^2} = 25{a^2} \) be b times the eccentricity of the hyperbola \( {x^2} - {a^2}{y^2} = 5 \), where a is the minimum distance between the curves y = e^x and y = log_ex. Then \( {a^2} + {1 \over {{b^2}}} \) is equal to :

If xy⁴ attains maximum value at the point (x, y) on the line passing through the points (50 + \( \alpha \), 0) and (0, 50 + \( \alpha \)), \( \alpha \) > 0, then (x, y) also lies on the line :

Let \( \alpha \)₁, \( \alpha \)₂ (\( \alpha \)₁ < \( \alpha \)₂) be the values of \( \alpha \) fo the points (\( \alpha \), \( - \)3), (2, 0) and (1, \( \alpha \)) to be collinear. Then the equation of the line, passing through (\( \alpha \)₁, \( \alpha \)₂) and making an angle of \( {\pi \over 3} \) with the positive direction of the x-axis, is :

Let m and M respectively be the minimum and the maximum values of \( f(x) = {\sin ^{ - 1}}2x + \sin 2x + {\cos ^{ - 1}}2x + \cos 2x,\,x \in \left[ {0,{\pi \over 8}} \right] \). Then m + M is equal to :

For two positive real numbers a and b such that \( {1 \over {{a^2}}} + {1 \over {{b^3}}} = 4 \), then minimum value of the constant term in the expansion of \( {\left( {a{x^{{1 \over 8}}} + b{x^{ - {1 \over {12}}}}} \right)^{10}} \) is :

Let \( f(x) = 4{x^3} - 11{x^2} + 8x - 5,\,x \in R \). Then f :

Let S be the set of all integral values of \( \alpha \) for which the sum of squares of two real roots of the quadratic equation \( 3{x^2} + (\alpha - 6)x + (\alpha + 3) = 0 \) is minimum. Then S :

How many of the following drugs belong to the tranquilizer class _____________ ?

Veronal, Luminal, Propanal, Seconal

Let \( {S_1} = \left\{ {x \in R - \{ 1,2\} :{{(x + 2)({x^2} + 3x + 5)} \over { - 2 + 3x - {x^2}}} \ge 0} \right\} \) and \( {S_2} = \left\{ {x \in R:{3^{2x}} - {3^{x + 1}} - {3^{x + 2}} + 27 \le 0} \right\} \). Then, \( {S_1} \cup {S_2} \) is equal to :

100 mL of 0.3 M acetic acid is shaken with 0.8 g of wood charcoal. The final concentration of acetic acid in the solution after adsorption is 0.125 M. The mass of acetic acid adsorbed per gram of carbon is _____________ \( \times \) 10^{\( - \)4} g.

(Given : Molar mass of acetic acid = 60 g mol^{\( - \)1})

The real part of the complex number \( {{{{(1 + 2i)}^8}\,.\,{{(1 - 2i)}^2}} \over {(3 + 2i)\,.\,\overline {(4 - 6i)} }} \) is equal to :

Let \( A = \left[ {\matrix{ 1 & { - 2} & \alpha \cr \alpha & 2 & { - 1} \cr } } \right] \) and \( B = \left[ {\matrix{ 2 & \alpha \cr { - 1} & 2 \cr 4 & { - 5} \cr } } \right],\,\alpha \in C \). Then the absolute value of the sum of all values of \( \alpha \) for which det(AB) = 0 is :

Correct statement about alkali metal oxides is :

Match List - I with List - II :

Correct answer is :

Which one of the following chemicals has not been used for the dry cleaning of clothes?

Match List - I with List - II.

Choose the correct match from the options given below :

An element X has a body centred cubic (bcc) structure with a cell edge of 200 pm. The density of the element is 5 g cm^{\( - \)3}. The number of atoms present in 300 g of the element X is _______________.

Given : Avogadro constant, N_A = 6.0 \( \times \) 10²³ mol^{\( - \)1}.

TLC analysis of a mixture having 3 components (A, B, C) using silica gel as the stationary phase gave following R_f values; for A = 0.72, B = 0.48, C = 0.20.

Regarding the above observations, which one of the following statements is not correct for column chromatography of the mixture?

1.0 mol of monoatomic ideal gas is expanded from state 1 to state 2 as shown in the figure. The magnitude of the work done for the expansion of gas from state 1 to state 2 at 300 K is ____________ J. (Nearest integer)

(Given : R = 8.3 J K^{\( - \)1} mol^{\( - \)1}, ln10 = 2.3, log2 = 0.30)

In the following brown complex, the oxidation state of iron is +_____________.

\( {[Fe{({H_2}O)_6}]^{2 + }} + NO \to \mathop {{{[Fe{{({H_2}O)}_5}(NO)]}^{2 + }}}\limits_{\text{Brown complex}} + {H_2}O \)

Spin only magnetic moment (\( \mu \)_s) of \( {K_3}[Fe{(CN)_6}] \) is ____________ B.M.

(Nearest integer)

A hydrocarbon 'X' is found to have molar mass of 80. A 10.0 mg of compound 'X' on hydrogenation consumed 8.40 mL of H₂ gas (measured at STP). Ozonolysis of compound 'X' yields only formaldehyde and dialdehyde. The total number of fragments/molecules produced from the ozonolysis of compound 'X' is _____________.

For the reaction P \( \to \) B, the values of frequency factor A and activation energy E_A are 4 \( \times \) 10¹³ s^{\( - \)1} and 8.3 kJ mol^{\( - \)1} respectively. If the reaction is of first order, the temperature at which the rate constant is 2 \( \times \) 10^{\( - \)6} s^{\( - \)1} is _____________ \( \times \) 10^{\( - \)1} K.

(Given : ln 10 = 2.3, R = 8.3 J K^{\( - \)1} mol^{\( - \)1}, log2 = 0.30)