JEE Main 2023 Question Paper with Solutions

If the points $\mathrm{P}$ and $\mathrm{Q}$ are respectively the circumcenter and the orthocentre of a $\triangle \mathrm{ABC}$ , then $\overrightarrow{\mathrm{PA}}+\overrightarrow{\mathrm{PB}}+\overrightarrow{\mathrm{PC}}$ is equal to :

Two projectiles are projected at 30 ∘ and 60 ∘ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

A person travels $x$ distance with velocity $v_{1}$ and then $x$ distance with velocity $v_{2}$ in the same direction. The average velocity of the person is $\mathrm{v}$ , then the relation between $v, v_{1}$ and $v_{2}$ will be.

For a periodic motion represented by the equation y = sin ⁡ ω t + cos ⁡ ω t the amplitude of the motion is

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : An electric fan continues to rotate for some time after the current is switched off. Reason R : Fan continues to rotate due to inertia of motion. In the light of above statements, choose the most appropriate answer from the options given below.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Physical properties of isotopes of hydrogen are different. Reason R : Mass difference between isotopes of hydrogen is very large. In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : $3.1500 \mathrm{~g}$ of hydrated oxalic acid dissolved in water to make $250.0 \mathrm{~mL}$ solution will result in $0.1 \mathrm{~M}$ oxalic acid solution. Reason $\mathbf{R}$ : Molar mass of hydrated oxalic acid is $126 \mathrm{~g} \mathrm{~mol}^{-1}$ In the light of the above statements, choose the correct answer from the options given below.

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : The energy required to form $\mathrm{Mg}^{2+}$ from $\mathrm{Mg}$ is much higher than that required to produce $\mathrm{Mg}^+$ Reason $\mathbf{R}: \mathrm{Mg}^{2+}$ is small ion and carry more charge than $\mathrm{Mg}^{+}$ In the light of the above statements, choose the correct answer from the options given below.

The decreasing order of hydride affinity for following carbocations is: Choose the correct answer from the options given below:

In Carius tube, an organic compound ' $\mathrm{X}$ ' is treated with sodium peroxide to form a mineral acid 'Y'. The solution of $\mathrm{BaCl}_{2}$ is added to ' $\mathrm{Y}$ ' to form a precipitate 'Z'. 'Z' is used for the quantitative estimation of an extra element. ' $\mathrm{X}$ ' could be

Let the number ( 22 ) 2022 + ( 2022 ) 22 leave the remainder α when divided by 3 and β when divided by 7. Then ( α 2 + β 2 ) is equal to :

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-baqh{text-align:center;vertical-align:top} ${x_i}$ 0 1 2 3 4 5 ${f_i}$ $k + 2$ $2k$ ${k^2} - 1$ ${k^2} - 1$ ${k^2} + 1$ $k - 3$ where $\sum f_{i}=62$ . If $[x]$ denotes the greatest integer $\leq x$ , then $\left[\mu^{2}+\sigma^{2}\right]$ is equal to :

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is :

Let $\mathrm{A}=\{2,3,4\}$ and $\mathrm{B}=\{8,9,12\}$ . Then the number of elements in the relation $\mathrm{R}=\left\{\left(\left(a_{1}, \mathrm{~b}_{1}\right),\left(a_{2}, \mathrm{~b}_{2}\right)\right) \in(A \times B, A \times B): a_{1}\right.$ divides $\mathrm{b}_{2}$ and $\mathrm{a}_{2}$ divides $\left.\mathrm{b}_{1}\right\}$ is :

The statement $\sim[p \vee(\sim(p \wedge q))]$ is equivalent to :

If each diode has a forward bias resistance of 25   Ω in the below circuit, Which of the following options is correct :

The distance between two plates of a capacitor is $\mathrm{d}$ and its capacitance is $\mathrm{C}_{1}$ , when air is the medium between the plates. If a metal sheet of thickness $\frac{2 d}{3}$ and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes $\mathrm{C}_{2}$ . The ratio $\frac{\mathrm{C}_{2}}{\mathrm{C}_{1}}$ is

The variation of stopping potential $\left(\mathrm{V}_{0}\right)$ as a function of the frequency $(v)$ of the incident light for a metal is shown in figure. The work function of the surface is

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

Let $\mathrm{g}(x)=f(x)+f(1-x)$ and $f^{\prime \prime}(x) > 0, x \in(0,1)$ . If $\mathrm{g}$ is decreasing in the interval $(0, a)$ and increasing in the interval $(\alpha, 1)$ , then $\tan ^{-1}(2 \alpha)+\tan ^{-1}\left(\frac{1}{\alpha}\right)+\tan ^{-1}\left(\frac{\alpha+1}{\alpha}\right)$ is equal to :

For $\alpha, \beta, \gamma, \delta \in \mathbb{N}$ , if $\int\left(\left(\frac{x}{e}\right)^{2 x}+\left(\frac{e}{x}\right)^{2 x}\right) \log _{e} x d x=\frac{1}{\alpha}\left(\frac{x}{e}\right)^{\beta x}-\frac{1}{\gamma}\left(\frac{e}{x}\right)^{\delta x}+C$ , where e = ∑ n = 0 ∞ 1 n ! and $\mathrm{C}$ is constant of integration, then $\alpha+2 \beta+3 \gamma-4 \delta$ is equal to :

Let f be a continuous function satisfying ∫ 0 t 2 ( f ( x ) + x 2 ) d x = 4 3 t 3 , ∀ t > 0 . Then f ( π 2 4 ) is equal to :

For the system of linear equations $2x - y + 3z = 5$ $3x + 2y - z = 7$ $4x + 5y + \alpha z = \beta$ , which of the following is NOT correct?

The shortest distance between the lines ${{x + 2} \over 1} = {y \over { - 2}} = {{z - 5} \over 2}$ and ${{x - 4} \over 1} = {{y - 1} \over 2} = {{z + 3} \over 0}$ is :

Buna-S can be represented as:

The reaction used for preparation of soap from fat is :

The major product 'P' formed in the given reaction is:

In the reaction given below: The product 'X' is:

The correct order of the number of unpaired electrons in the given complexes is A. $\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}$ B. $\left[\mathrm{Fe} \mathrm{F}_{6}\right]^{3-}$ C. $\left[\mathrm{CoF}_{6}\right]^{3-}$ D. $\left.[\mathrm{Cr} \text { (oxalate})_{3}\right]^{3-}$ E. $\left[\mathrm{Ni}(\mathrm{CO})_{4}\right]$ Choose the correct answer from the options given below: