List of top Questions asked in JEE Main- 2023

To inhibit the growth of tumours, identify the compounds used from the following : A EDTA B Coordination Compounds of Pt C D-Penicillamine D Cis - Platin Choose the correct answer from the option given below:

Match List -I with List-II

LIST-I (Atomic number)LIST-II (Block of periodic table)
(A) 37 (K)I. p-block
(B) 78 (Pt)II. d-block
(C) 52 (Te)III. f-block
(D) 65 (Tb)IV. s-block

Choose the correct answer from the options given below:

If the coefficient of $x^{15}$ in the expansion of $\left(a x^3+\frac{1}{b x^{1 / 3}}\right)^{15}$ is equal to the coefficient of $x^{-15}$ in the expansion of $\left(a x^{1 / 3}-\frac{1}{b x^3}\right)^{15}$, where a and $b$ are positive real numbers, then for each such ordered pair $(a, b)$ :

The number of points on the curve \(y=54 x^5-135 x^4-70 x^3+180 x^2+210 x\) at which the normal lines are parallel \(to x+90 y+2=0\) is 

If $\tan 15^{\circ}+\frac{1}{\tan 75^{\circ}}+\frac{1}{\tan 105^{\circ}}+\tan 195^{\circ}=2 a$, then the value of $\left(a+\frac{1}{a}\right)$ is :
If $[ t ]$ denotes the greatest integer $\leq t$, then the value of $\frac{3( e -1)}{ e } \int\limits_1^2 x^2 e^{[x]+\left[x^3\right]} dx$ is :
Let $y=x+2,4 y=3 x+6$ and $3 y=4 x+1$ be three tangent lines to the circle $(x-h)^2+(y- k )^2= r ^2$ Then $h + k$ is equal to :
If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is:
The coefficient of $x^{301}$ in $(1+x)^{500}+x(1+x)^{499}+x^2(1+x)^{498}+\ldots \ldots +x^{500}$ is :
If $a_n=\frac{-2}{4 n^2-16 n+15}$, then $a_1+a_2+\ldots \ldots+a_{25}$ is equal to:
The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c)\}$ on the set $\{ a , b , c \}$ so that it becomes symmetric and transitive is :
If $P ( h , k )$ be a point on the parabola $x=4 y^2$, which is nearest to the point $Q (0,33)$, then the distance of $P$ from the directrix of the parabola $y^2=4(x+y)$ is equal to :
Let the system of linear equations $ x+y+ kz =2$ $ 2 x+3 y-z=1 $ $ 3 x+4 y +2 z= k$ have infinitely many solutions Then the system $ ( k +1) x+(2 k -1) y=7$ $ (2 k +1) x+( k +5) y=10$ has:

Among the statements : 
\((S1)\) \((( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )\)
\((S2)\)\((( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))\)

Let $A= \begin{pmatrix} m & n \\ p & q\end{pmatrix}, d=|A| \neq 0$ and $|A-d(\operatorname{Adj} A)|=0$ Then
Match List I with List II: 
List - IList - II
A.TorqueI.kg m-1 s-2
B.Energy DensityII.kg ms-1
C.Pressure gradientIII.kg m-2 s-2
D.ImpulseIV.kg m2 s-2
Choose the correct answer from the options given below : 
As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $Q$ in three different regions I, II and III is given by: (I: r $<$ a, II: $a $<$ r $<$ b$, III: $r$>$b)$
Electric Field
An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth Its velocity when it strikes the earth's surface, ignoring air resistance, will be

For a simple harmonic motion in a mass spring system shown, the surface is frictionless When the mass of the block is $1\, kg$, the angular frequency is $\omega_1$ When the mass block is $2 \,kg$ the angular frequency is $\omega_2$ The ratio $\omega_2 / \omega_1$ is
simple harmonic motion in a mass

A force is applied to a steel wire ' $A$ ', rigidly clamped at one end As a result elongation in the wire is $02\, mm$ If same force is applied to another steel wire ' $B$ ' of double the length and a diameter $24$ times that of the wire ' $A$ ', the elongation in the wire ' $B$ ' will be (wires having uniform circular cross sections)
A machine gun of mass $10\, kg$ fires $20 \,g$ bullets at the rate of $180$ bullets per minute with a speed of $100 \,m s ^{-1}$ each The recoil velocity of the gun is
A current carrying rectangular loop $P Q R S$ is made of uniform wire The length $P R=Q S=5 \,cm$ and $P Q=R S=100\, cm$ If ammeter current reading changes from $I$ to $2 I$, the ratio of magnetic forces per unit length on the wire $P Q$ due to wire $R S$ in the two cases respectively $\left(f_{P Q}^I: f_{P Q}^{2 I}\right)$ is:
A current carrying rectangular loop PQRS is made of uniform wire. The length PR=QS=5 cm and PQ=RS=100cm
As shown in the figure, a current of $2 A$ flowing in an equilateral triangle of side $4 \sqrt{3} cm$ The magnetic field at the centroid $O$ of the triangle is
Magnetic field
 (Neglect the effect of earth's magnetic field)
A block of $\sqrt{3} kg$ is attached to a string whose other end is attached to the wall An unknown force $F$ is applied so that the string makes an angle of $30^{\circ}$ with the wall The tension $T$ is:(Given $g =10 \,ms ^{-2}$ )
A block of 3kg is attached
The equivalent resistance between A and B is _________.
equivalent resistance between A and B