List of top Questions asked in JEE Main

Let y = y(x) be the solution curve of the differential equation 

passing through the point (2, √(1/3)). Then √7 y(8) is

The sum of diameters of the circles that touch (i) the parabola \(75x^2 \)= \(64(5y – 3)\) at the point (\(\frac{8}{5}\), \(\frac{6}{5}\)) and (ii) the y-axis is equal to _______.
 

On reaction with stronger oxidizing agent like KIO₄, hydrogen peroxide oxidizes with the evolution of O₂. The oxidation number of I in KIO₄ changes to____.

In an experiment with a convex lens, the plot of the image distance (ν′) against the object distance (μ′) measured from the focus gives a curve ν′μ′ = 225. If all the distances are measured in cm. The magnitude of the focal length of the lens is _______ cm.

The potential energy of a particle of mass \(4 kg\) in motion along the x-axis is given by \(U = 4(1- cos 4x) J\). The time period of the particle for small oscillation \((sin θ ≃ θ)\) is \((\frac{π}{K})\) s. The value of \(K\) is ..........

The distance of centre of mass from end \(A\) of a one dimensional rod (\(AB\)) having mass density \(ρ=ρ_0(1-\frac{x^2}{L^2})kg/m\) and length L. (in meter) is \(\frac{3L}{α} m\). The value of \(α\) is......... (where \(x\) is the distance form end \(A\))

Some drugs bind to a site other than the active site of an enzyme. This site is known as

Let the equation of two diameters of a circle x² + y² – 2x + 2fy + 1 = 0 be 2px – y = 1 and 2x + py = 4p. Then the slope m ∈ (0, ∞) of the tangent to the hyperbola 3x² – y² = 3 passing through the center of the circle is equal to _______.

The compound(s) that is(are) removed as slag during the extraction of copper is 
(A) CaO 
(B) FeO 
(C) Al₂O₃ 
(D) ZnO 
(E) NiO 
Choose the correct answer from the options given below :

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 :

Match List - I with List - II 
                                   List I                                                                                  List II
A \(N _2( g )+3 H _2( g ) \rightarrow 2 NH _3( g )\)                                                                   I \(Cu\)  
B \(CO ( g )+3 H _2( g ) \rightarrow CH _4( g )+ H _2 O ( g )\)                                      II \(Cu / ZnO - Cr _2 O _3\) 
C \(CO ( g )+ H _2( g ) \rightarrow HCHO ( g )\)                                               III \(Fe _x O _y+ K _2 O + Al _2 O _3\) 
D \(CO ( g )+2 H _2\) (g) \(\rightarrow CH _3 OH ( g )\)                                                             IV \(Ni\) 
Choose the correct answer from the optionsgiven below :

Match List - I with List - II 
List-I (Compound)                                              List-II (Shape)
A \(BrF _5\)                                                                    I bent 
B \(\left[ CrF _6\right]^{3-}\)                                                             II square pyramidal
C \(O _3\)                                                                     III trigonal bipyramidal 
D \(PCl _5\)                                                                    IV octahedral 
Choose the correct answer from the optionsgiven below :

Match List - I with List - II 
 

List-I (Processes/Reactions)		List-II (Catalyst)
A	$2 SO _2( g )+ O _2( g ) \rightarrow 2 SO _3( g )$	I	$Fe ( s )$
B	$4 NH _3( g )+5 O _2( g ) \rightarrow$$4 NO ( g )+6 H _2 O ( g )$	II	$Pt ( s )- Rh ( s )$
C	$N _2( g )+3 H _2( g ) \rightarrow 2 NH _3( g )$	III	$V _2 O _5$
D	Vegetable oil $(l)+ H _2 \rightarrow$Vegetable ghee(s	IV	$Ni ( s )$

Choose the correct answer from the options given below:

Let \(ABC\) be a triangle such that \(\overrightarrow{ BC }=\vec{ a }\), \(\overrightarrow{ CA }=\vec{ b }, \overrightarrow{ AB }=\vec{ c },|\vec{ a }|=6 \sqrt{2},|\vec{ b }|=2 \sqrt{3}\) and \(\vec{ b } \cdot \vec{ c }=12\) Consider the statements :\((S1): |(\vec{ a } \times \vec{ b })+(\vec{ c } \times \vec{ b })|-|\vec{ c }|=6(2 \sqrt{2}-1)\)\((S2): \angle ABC =\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\) Then

Let $E_1, E_2, E_3$ be three mutually exclusive events such that $P \left( E _1\right)=\frac{2+3 p }{6}$, $P \left( E _2\right)=\frac{2- p }{8}$ and $P \left( E _3\right)=\frac{1- p }{2}$ If the maximum and minimum values of $p$ are $p _1$ and $p _2$, then $\left( p _1+ p _2\right)$ is equal to :

Given two statements below: 
Statement I: In $Cl _2$ molecule the covalent radius is double of the atomic radius of chlorine. 
Statement II: Radius of anionic species is always greater than their parent atomic radius Choose the most appropriate answer from options given below:

The curve y(x) = ax³ + bx² + cx + 5 touches the x-axis at the point P (–2, 0) and cuts the y-axis at the point Q, where y is equal to 3. Then the local maximum value of y(x) is :

Match List-I with List-II, match the gas evolved during each reaction:
 

List-I		List-II
(A)	$\left( NH _4\right)_2 Cr _2 O _7 \xrightarrow{\Delta}$	(I)	$H _2$
(B)	$KMnO _4+ HCl \rightarrow$	(II)	$N _2$
(C)	$Al + NaOH + H _2 O \rightarrow$	(III)	$O _2$
(D)	$NaNO _3 \xrightarrow{\Delta}$	(IV)	$Cl _2$

Choose the correct answer from the options given below:

Let the solution curve of the differential equation $x d y=\left(\sqrt{x^2+y^2}+y\right) d x, x>0$, intersect the line $x =1$ at $y =0$ and the line $x=2$ at $y=\alpha$. Then the value of $\alpha$ is :

The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$ is equal to:

Let the operations $*, \odot \in\{\wedge, \vee\}$. If $(p * q) \odot(p \odot \sim q)$ is a tautology, then the ordered pair $(*, \odot)$ is :