List of top Questions asked in JEE Main- 2023

If $a_r$ is the coefficient of $x^{10-r}$ in the Binomial expansion of $(1+x)^{10}$, then $\displaystyle\sum_{r=1}^{10} r^3\left(\frac{a_r}{a_{r-1}}\right)^2$ is equal to
The combined equation of the two lines $a x+b y+c=0$ and $a^{\prime} x+b^{\prime} y+c^{\prime}=0$ can be written as $(a x+b y+c)\left(a^{\prime} x+b^{\prime} y+c^{\prime}\right)=0$
The equation of the angle bisectors of the lines represented by the equation $2 x^2+x y-3 y^2=0$ is
The shortest distance between the lines \(\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}\) and \(\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}\) is
Let $\alpha$ be a root of the equation $(a-c) x^2+(b-a) x+(c-b)=0$where $a , b , c$ are distinct real numbers such that the matrix $\begin{bmatrix}\alpha^2 & \alpha & 1 \\ 1 & 1 & 1 \\ a & b & c\end{bmatrix}$is singular Then, the value of $\frac{(a-c)^2}{(b-a)(c-b)}+\frac{(b-a)^2}{(a-c)(c-b)}+\frac{(c-b)^2}{(a-c)(b-a)}$ is

Let the mean and variance of 12 observations be \( \frac{9}{2} \) and 4, respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is \( \frac{m}{n} \), where \( m \) and \( n \) are coprime, then \( m + n \) is equal to:

If four distinct points with position vectors \(\overrightarrow a,\overrightarrow b,\overrightarrow c\)  and \(\overrightarrow d\)  are coplanar, then \([\overrightarrow a \overrightarrow b \overrightarrow c]\) is equal to
The number of common tangents, to the circles \( x^2 + y^2 - 18x - 15y + 131 = 0 \) and \( x^2 + y^2 - 6x - 6y - 7 = 0 \), is 
Match the terms in Column-I with their description in Column-II and choose the correct option:
 Column I Column II
(A).Biodegradable(P).Polyacrylonitrie
(B).Synthetic(Q).PHBV
(C).Natural(R).Dacron
(D).Polyester(S).Rubber
Which of the following statements is correct about freons?
CH3CH2-Br \(\overrightarrow{Acetone}^{NaI}\) CH3-CH2-I+NaBr
Which of the following statement is correct ? 
Statement I : Dipole moment is a vector quantity and by convention it is depicted by a small arrow with tail on the negative centre and head pointing towards the positive centre
Statement II : The crossed arrow of the dipole moment symbolizes the direction of the shift of charges in the molecules.
In the light of the above statements, choose the most appropriate answer from the options given below:
For micelle formation, which of the following statements are correct?
(A) Micelle formation is an exothermic process
(B) Micelle formation is an endothermic process
(C) The entropy change is positive
(D) The entropy change is negative
Group–13 elements react with \( O_2 \) in amorphous form to form oxides of type \( M_2O_3 \) (M = element). Which among the following is the most basic oxide?

Match items of Row I with those of Row II

In the depression of freezing point experiment 

A. Vapour pressure of the solution is less than that of pure solvent 

B. Vapour pressure of the solution is more than that of pure solvent 

C. Only solute molecules solidify at the freezing point 

D. Only solvent molecules solidify at the freezing point 

Choose the most appropriate answer from the options given below:

Inert gases have positive electron gain enthalpy Its correct order is
According to MO theory the bond orders for \(O_2^{2−},CO\,\, \text {and} \,\,NO^+\) respectively, are
The magnetic moment is measured in Bohr Magneton (BM).
Spin only magnetic moment of Fe in [Fe(H2O)6] 3+ and [Fe(CN)6] 3– complexes respectively is:

The major products ' A ' and ' B ', respectively, are

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A): $Cu ^{2+}$ in water is more stable than $Cu ^{+}$
Reason (R): Enthalpy of hydration for $Cu ^{2+}$ is much less than that of $Cu ^{+}$ 
In the light of the above statements, choose the correct answer from the options given below :
Compound A from the following reaction sequence is 
Br2 , C S 2 0 − 5 ° C 0 − 5 ° 𝐶 → 𝐵 𝑟 2 , 𝐶 𝑆 2 B. N a N O 2 / H C l

The kinetic energy of a particle is 10000 joule with the mass 2kg. Find the momentum for the particle?

\([Co(NH_3)_6]^{3+} \text{is} \) ________\(\text{hybridised and}\)________

Separation between earth and sun is given by 1.5 × 106 km. Time period of another planet is 2.83 year. Find distance of another planet from sun?

Ratio of molar heat capacity at constant pressure and at constant volume for monoatomic and diatomic gas is?