List of top Questions asked in JEE Main

The number of integers, greater than $7000$ that can be formed, using the digits $3,5,6,7,8$ without repetition, is

For the system of linear equations
$x+y+z=6$
$\alpha x+\beta y+7 z=3$
$x+2 y+3 z=14$.
which of the following is NOT true ?

For the system of linear equations$\alpha x+y+z=1, x+\alpha y+z=1, x+y+\alpha z=\beta$ which one of the following statements is NOT correct ?

Among the relations
$S=\left\{(a, b): a, b \in R -\{0\}, 2+\frac{a}{b}>\right\}$
and $T=\left\{(a, b): a, b \in R , a^2-b^2 \in Z\right\}$,

Let $ (\alpha, \beta) $ be the centroid of the triangle formed by the lines $ 15x - y = 82 $, $ 6x - 5y = -4 $, and $ 9x + 4y = 17 $. Then $ \alpha + 2\beta $ and $ 2\alpha - \beta $ are the roots of the equation:

If the set $\left( Re \left( \frac{z-\bar{z}+z\bar{z}}{2-3z+5\bar{z}}\right) : z ∈ C, Re(z)=3 \right)$ is equal to the interval (α,β), then 24(β-α) is equal to

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

Let the solution curve y = y(x) of the differential equation$\frac{dy}{dx} - \frac{3x^5 \tan^{-1}(x^3)}{(1 + x^6)^{3/2}} y = 2x \exp\left(x^3 - \frac{\tan^{-1}(x^3)}{1 + x}\right)^6$pass through the origin. Then y(1) is equal to:

Let $S=\left\{z∈C : \bar{z}=i(z^2+Re(\bar{z}))\right\}$. Then $\sum\limits_{z∈S}|z|^2$ is equal to

The statement ~[p v (~(p ∧ q))] is equivalent to

For all $z \in C$ on the curve $C_1:|z|=4$, let the locus of the point $z+\frac{1}{z}$ be the curve $C_2$ Then:

The number of values of $r \in\{p, q, \sim p, \sim q\}$ for which $((p \wedge q) \Rightarrow(r \vee q)) \wedge((p \wedge r) \Rightarrow q)$ is a tautology, is :

Let
$A=\{(x,y) ∈R^2:y≥0,2x≤y≤\sqrt{4-(x-1)^2} \}$
and
$B=\{(x,y) ∈R\times R:0≤y≤min \{2x,\sqrt{4-(x-1)^2}\}\}$
Then the ratio of the area of A to the area of B is

If for z=α+iβ, |z+2|=z+4(1+i), then α +β and αβ are the roots of the equation

Let the shortest distance between the lines $L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0$ and $L_1: x+1=y-1=4-z$ be $2 \sqrt{6}$ If $(\alpha, \beta, \gamma)$ lies on $L$, then which of the following is NOT possible?

The minimum value of the function $f(x)=\int\limits_0^2 e^{|x-t|} d t$ is :

Let α and β be real numbers. Consider a $3 \times 3$ matrix A such that $A^2 = 3A + \alpha I$. If $A^4 = 21A + \beta I$, then

Let the image of the point P(1, 2, 6) in the plane passing through the points A(1, 2, 0), B(1, 4, 1) and C(0, 5, 1) be Q (α, β, γ). Then (α² + β² + γ²) is equal to

If the coefficients of $ x $ and $ x^2 $ in $ (1 + x)^p(1 - x)^q $ are 4 and -5 respectively, then $ 2p + 3q $ is equal to:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason $R$
Assertion A :

can be easily reduced using $Zn - Hg / HCl$ to

Reason R : $ Zn \cdot Hg / HCl$ is used to reduce carbonyl group to $- CH _2-$ group.

In the light of the above statements, choose the correct answer from the options given below:

The major product formed in the following reaction is

Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from $n =4$ to $n =2$ of $He ^{+}$spectrum

Given below are two statements, one is labelled as Assertion $A$ and the other is labeled as Reason $R$
Assertion A : The alkali metals and their salts impart characteristic colour to reducing flame
Reason R : Alkali metals can be detected using flame tests
In the light of the above statements, choose the most appropriate answer from the options given below

The correct representation in six-membered pyranose form for the following sugar $ [X]$ is

In which of the following pairs of elements electron gain enthalpy difference is highest?