List of top Questions asked in JEE Main

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation $\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)$ is equal to:

The mean and variance of a binomial distribution are $\alpha$ and $\frac{\alpha}{3}$ respectively If $P(X=1)=\frac{4}{243}$, then $P(X=4$ or 5$)$ is equal to :

Which reactant will give the following alcohol on reaction with one mole of phenyl magnesium bromide \(( PhMgBr )\) followed by acidic hydrolysis?

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 :

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:

Identify the correct statement for the below given transformation

Choose the correct option for the following reactions

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 :

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 :

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

Let $f(x)= \begin{cases} x^3-x^2+10 x-7, & x \leq 1 \\ -2 x+\log _2\left(b^2-4\right), & x>1\end{cases}$ Then the set of all values of $b$, for which $f(x)$ has maximum value at $x=1$, is :

The foot of the perpendicular from a point on the circle \(x ^2+ y ^2=1, z =0\) to the plane \(2 x+3 y+z=6\) lies on which one of the following curves ?

If the function $f(x)= \begin{cases} \frac{\log _e\left(1-x+x^2\right)+\log_e\left(1+x+x^2\right)}{\sec x-\cos x}, x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)-\{0\} \\k, \,\,\,\,\, x=0\end{cases}$ is continuous at $x=0$, then $k$ is equal to :

Consider two GPs $2,2^2, 2^3, \ldots$ and $4,4^2$, $4^3, \ldots$ of 60 and $n$ terms respectively. If the geometric mean of all the $60+ n$ terms is $(2)^{\frac{225}{8}}$, then $\displaystyle\sum_{ k =1}^{ n } k ( n - k )$ is equal to :

Match List-I with List-II

The metal salts formed during softening of hardwater using Clark's method are :

Stearic acid and polyethylene glycol react to form which one of the following soaps/detergents ?

The correct stability order of the following diazonium salt is

Drugs used to bind to receptors, inhibiting its natural function and blocking a message are called :

Given below are two statements : Statement I : On heating with \(KHSO _4\), glycerol is dehydrated and acrolein is formed 
Statement II : Acrolein has fruity odour and can be used to test glycerol's presence Choose the correct option

Two capacitors, each having capacitance $40 \mu F$ are connected in series The space between one of the capacitors is filled with dielectric material of dielectric constant $K$ such that the equivalence capacitance of the system became $24 \mu F$ The value of $K$ will be :

Two projectile thrown at $30^{\circ}$ and $45^{\circ}$ with the horizontal respectively, reach the maximum height in same time The ratio of their initial velocities is

A screw gauge of pitch $05 \,mm$ is used to measure the diameter of uniform wire of length $68 \,cm$, the main scale reading is $15\, mm$ and circular scale reading is $7$. The calculated curved surface area of wire to appropriate significant figures is :[Screw gauge has $50$ divisions on the circular scale]

Refining using liquation method is the most suitable for metals with :