List of top Questions asked in JEE Main

Identify the incorrect statement from the following

Let the matrix \(A=\begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{bmatrix}\) and the matrix \(B_0=A^{49}+2 A^{98}\) If \(B_n=\text{Adj}\left(B_{n-1}\right)\) for all \(n \geq 1\), then \(\text{det}\left( B _4\right)\) is equal to :

If $a =\displaystyle\lim _{ n \rightarrow \infty} \sum_{ k =1}^{ n } \frac{2 n }{ n ^2+ k ^2}$ and $f(x)=\sqrt{\frac{1-\cos x}{1+\cos x}}, x \in(0,1)$, then :

In young's double slit experiment, the fringe width is $12\, mm$ If the entire arrangement is placed in water of refractive index $\frac{4}{3}$, then the fringe width becomes (in $mm$ )

The remainder when \(7^{2022}+3^{2022}\) is divided by \(5\) is:

A point $P$ moves so that the sum of squares of its distances from the points $(1,2)$ and $(-2,1)$ is $14$. Let $f(x, y)=0$ be the locus of $P$, which intersects the $x$-axis at the points $A , B$ and the $y$-axis at the point $C, D$. Then the area of the quadrilateral $ACBD$ is equal to

Which of the following relation is not correct?

Let the tangent drawn to the parabola $y ^2=24 x$ at the point $(\alpha, \beta)$ is perpendicular to the line $2 x+2 y=5$. Then the normal to the hyperbola $\frac{x^2}{\alpha^2}-\frac{y^2}{\beta^2}=1$ at the point $(\alpha+4, \beta+4)$ does NOT pass through the point :

If the tangents drawn at the points \(P\) and \(Q\) on the parabola \(y^2=2 x-3\) intersect at the point \(R (0,1)\), then the orthocentre of the triangle \(PQR\) is :

The length of the perpendicular from the point $(1,-2,5)$ on the line passing through $(1,2,4)$ and parallel to the line $x+y-z=0=x-2 y+3 z-5$ is :

For kinetic study of the reaction of iodide ion with \(H _2 O _2\) at room temperature : 
(A) Always use freshly prepared starch solution 
(B) Always keep the concentration of sodium thiosulphate solution less than that of \(KI\) solution 
(C) Record the time immediately after the appearance of blue colour 
(D) Record the time immediately before the appearance of blue colour 
(E) Always keep the concentration of sodium thiosulphate solution more than that of \(KI\) solution Choose the correct answer from the options given below :

Statements about Enzyme Inhibitor Drugs are given below:

1. There are Competitive and Noncompetitive inhibitor drugs
2.  These can bind at the active sites and allosteric sites
3.  Competitive Drugs are allosteric site blocking drugs
4.  Non-competitive Drugs are active site blocking drugs 

Choose the correct answer from the options given below :

Terylene polymer is obtained by condensation of :

The magnetic field of a plane electromagnetic wave is given by $\vec{ B }=2 \times 10^{-8} \sin \left(05 \times 10^3 x +15 \times 10^{11} t \right) \hat{ j } T$ The amplitude of the electric field would be

Choose the correct option for the following reactions

In a series LR circuit $X_L=R$ and power factor of the circuit is $P _1$ When capacitor with capacitance $C$ such that $X _{ L }= X _{ C }$ is put in series, the power factor becomes $P _2$ The ratio $\frac{ P _1}{ P _2}$ is

A charge particle is moving in a uniform magnetic field $(2 \hat{ i }+3 \hat{ j }) T$ If it has an acceleration of $(\alpha \hat{i}-4 \hat{j}) m / s ^2$, then the value of $\alpha$ will be

Identify the correct statement for the below given transformation

The total charge on the system of capacitance $C _1=1\, \mu F , C _2=2 \,\mu F , C _3=4 \,\mu F $ and $C _4=3\, \mu F$ connected in parallel is (Assume a battery of $20 \,V$ is connected to the combination)

When a particle executes simple Harmonicmotion, the nature of graph of velocity asfunction of displacement will be :

Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally to \(\frac{1}{8}\) of its original volume while the gas in B is com pressed adiabatically to \(\frac{1}{8}\) of its original volume. The ratio of final pressure of gas in B to that of gas in A is

Match List-I with List-II
 

List-I		List-II
(A)	Cd(s)+2Ni(OH)3(s)→CdO(s)+2Ni(OH)2(s)+H2O(l)	(I)	Primary battery
(B)	Zn(Hg)+HgO(s)→ZnO(s)+Hg(l)	(II)	Discharging of secondary battery
(C)	2PbSO4(s)+2H2O(l)→Pb(s)+PbO2(s)+2H2SO4(aq)	(III)	Fuel cell
(D)	2H2(g)+O2(g)→2H2O(l)	(IV)	Charging of secondary battery

Choose the correct answer from the options given below:

A water drop of radius $1 \,cm$ is broken into $729$ equal droplets If surface tension of water is $75 \,dync / cm$, then the gain in surface energy upto first decimal place will be : [Given $\pi=314]$

The percentage decrease in the weight of a rocket, when taken to a height of $32 \,km$ above the surface of earth will, be : (Radius of earth $=6400 \,km$ )

Considering only the principal values of the inverse trigonometric functions, the domain of the function $f(x)=\cos ^{-1}\left(\frac{x^2-4 x+2}{x^2+3}\right)$ is :