List of top Questions asked in JEE Main- 2019

The value of \(\int_0^{\pi/2}\frac{\sin^3x}{\sin x+\cos x}\,dx\) is
Let the sum of the first \(n\) terms of a non-constant A.P., \(a_1,a_2,a_3,\dots\) be \(50n+\frac{n(n-7)}{2}A\), where \(A\) is a constant. If \(d\) is the common difference of this A.P., then the ordered pair \((d,a_{50})\) is equal to
If the function \(f:R-\{1,-1\}\to A\) defined by \(f(x)=\frac{x^2}{1-x^2}\), is surjective, then \(A\) is equal to
Let \(\sum_{k=1}^{10}f(a+k)=16\left(2^{10}-1\right)\) where the function \(f\) satisfies \(f(x+y)=f(x)f(y)\) for all natural numbers \(x,y\) and \(f(1)=2\). then the natural number '\(a\)' is
Let \(\alpha\) and \(\beta\) be the roots of the equation \(x^2+x+1=0\). Then for \(y\ne0\) in \(R\), \(\begin{vmatrix}y+1&\alpha&\beta\\ \alpha&y+\beta&1\\ \beta&1&y+\alpha\end{vmatrix}\) is equal to
If \(f(x)\) is a non-zero polynomial of degree four, having local extreme points at \(x=-1,0,1\); then the set \(S=\{x\in R:f(x)=f(0)\}\) Contains exactly :
The area (in sq. units) of the region \(A=\{(x,y):x^2\le y\le x+2\}\) is
If the standard deviation of the numbers \(-1,0,1,k\) is \(\sqrt5\) where \(k\gt0\), then \(k\) is equal to
All the points in the set \(S=\left\{\frac{\alpha+i}{\alpha-i}:\alpha\in R\right\}\) (\(i=\sqrt{-1}\)) lie on a :
If the fourth term in the binomial expansion of \(\left(\frac{2}{x}+x^{\log_8 x}\right)^6\) (\(x\gt0\)) is \(20\times8^7\), then a value of \(x\) is :
Let \(\vec{\alpha}=3\hat{i}+\hat{j}\) and \(\vec{\beta}=2\hat{i}-\hat{j}+3\hat{k}\). If \(\vec{\beta}=\vec{\beta}_1-\vec{\beta}_2\), where \(\vec{\beta}_1\) is parallel to \(\vec{\alpha}\) and \(\vec{\beta}_2\) is perpendicular to \(\vec{\alpha}\), then \(\vec{\beta}_1\times\vec{\beta}_2\) is equal to
The solution of the differential equation \(x\frac{dy}{dx}+2y=x^2\) (\(x\ne0\)) with \(y(1)=1\), is :
Let \(f(x)=15-|x-10|\); \(x\in R\). Then the set of all values of \(x\), at which the function, \(g(x)=f(f(x))\) is not differentiable, is :
0.27 g of a long chain fatty acid was dissolved in 100 cm3 of hexane. 10 mL of this solution was added dropwise to the surface of water in a round watch glass. Hexane evaporates and a monolayer is formed. The distance from edge to centre of the watch glass is 10 cm. What is the height of the monolayer?
[Density of fatty acid = 0.9 g cm–3, \(\pi\) = 3]
Polysubstitution is a major drawback in:
The major product in the following reaction is :
The major product of the following reaction is:
Which one of the following alkenes when treated with HCl yields majorly an anti Markovnikov product?
The major product obtained in the following reaction is
The ion that has \(sp^3d^2\) hybridization for the central atom, is :
The electric field in a region is given by \(\vec{E} = (Ax + B)\hat{i}\), where \(E\) is in \(\mathrm{NC^{-1}}\) and \(x\) is in metres. The values of constants are \(A = 20\) SI unit and \(B = 10\) SI unit. If the potential at \(x = 1\) is \(V_1\) and that at \(x = -5\) is \(V_2\), then \(V_1 - V_2\) is :-
The calculated spin-only magnetic moments (BM) of the anionic and cationic species of \(\mathrm{[Fe(H_2O)_6]^{2+}}\) and \(\mathrm{[Fe(CN)_6]^{4-}}\), respectively, are :
A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to \(1/1000\) of the original amplitude is close to :-
The major product of the following reaction is:
The correct statement about \(\mathrm{ICl_5}\) and \(\mathrm{ICl_4^-}\) is