List of top Questions asked in JEE Main

Let awards in event A is 48 and awards in event B is 25 and awards in event C is 18 and also n(A ∪ B ∪ C) = 60, n(A ⋂ B ⋂ C) = 5, then how many got exactly two awards is?

The domain of the function f(x) = $\frac{1}{\sqrt{[x]^2-3[x]-10}}$ is (where [x] denotes the greatest integer less than or equal to x)

Let $f^1(x)=\frac{3 x+2}{2 x+3}, x \in R -\left\{\frac{-3}{2}\right\}$ For $n \geq 2$, define $f^{ n }(x)=f^1 o f^{ n -1}(x)$ if $f^5(x)=\frac{ a x+ b }{ b x+ a }, \operatorname{gcd}( a , b )=1$, then $a + b$ is equal to ______ .

The absolute minimum value, of the function $f(x)=\left|x^2-x+1\right|+\left[x^2-x+1\right]$, where $[t]$ denotes the greatest integer function, in the interval $[-1,2]$, is:

Let a and b are roots of $x^2 – 7x – 1 = 0$. The value of $\frac{(a_{21} + b_{21} + a_{17} + b_{17})}{(a_{19} + b_{19})}$ is?

Let A = {1, 2, 3, 4} and R be a relation on the set AxA defined by R = {((a, b), (c, d)): 2a+3b = 4c +5d}. Then the number of elements in R is

An object moves with speed $v_1, v_2$ and $v_3$ along a line segment $AB , BC$ and $C D$ respectively as shown in figure Where $AB = BC$ and $AD =3 AB$, then average speed of the object will be:

When vector $\overrightarrow A = 2\hat i+3\hat J+2\hat k$ is subtracted from vector $\overrightarrow B$ , it gives a vector equal to $2\hat j$ . Then the magnitude of vector $\overrightarrow B$ will be :

$\displaystyle\lim _{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3$

Two resistances are given as $R_1=(10 ±0.5) Ω$ and $R_2= (15±0.5) Ω$. The percentage error in the measurement of equivalent resistance when they are connected in parallel is -

The sum of roots of |x² - 8x + 15| - 2x + 7 = 0 is:

If the position of a particle is changing with time as r=t²-2t (m). Find the velocity at t=2s.

The one giving maximum number of isomeric alkenes on dehydrohalogenation reaction is
(excluding rearrangement)

Let $A=\begin{pmatrix}1 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & 12 & -3\end{pmatrix}$ Then the sum of the diagonal elements of the matrix $(A+I)^{11}$ is equal to :

Let $M$ be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $S =\left\{x \in Z : x(66-x) \geq \frac{5}{9} M\right\}$ and the event $A =\{x \in S : x$ is a multiple of 3$\}$. Then $P ( A )$ is equal to

Isomeric amines with molecular formula C₈ H₁₁N give the following tests
Isomer (P) ⇒ Can be prepared by Gabriel phthalimide synthesis
Isomer (Q) ⇒ Reacts with Hinsberg’s reagent to give solid insoluble in NaOH
Isomer (R) ⇒ Reacts with HONO followed by β-naphthol in NaOH to give red dye.
Isomers (P), (Q) and (R) respectively are

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R:
S-1 $\rightarrow$ Steel is used in construction of a bridge and house.
S–2 $\rightarrow$ Modulus of elasticity of steel is high.
In the light of the above statements, choose the correct answer from the options given below

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height Choose the correct statement out of the following (Assume negligible air friction)

A parallel plate capacitor of capacitance 2 F is charged to a potential V. The energy stored in the capacitor is E. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is E₅. The ratio $ E_5 / E_1 $ is:

If $f(x)=x^3-x^2 f^{\prime}(1)+x f^{\prime \prime}(2)-f^{\prime \prime \prime}(3), x \in R$, then

For three low density gases $A , B , C$ pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point ' $K$ ' is :

Let A = {2, 3, 4} and B = {8, 9, 12}. Then the number of elements in the relation R = {((a₁, b₁), (a₂, b₂)) ∈ (A × B, A × B) : a₁ divides b₂ and a₂ divides b₁} is

Find out the major products from the following reaction sequence.

If 1000 droplets of water of surface tension 0.07 N/m, having same radius 1 mm each, combine to from a single drop In the process the released surface energy is - (Take π=$\frac {22}{7}$)

If $a_1,a_2,.......a_n$ are in arithmetic progression with common difference $d>n$, then find limit $\lim_{n \to \infty}\sqrt{\frac{d}{n}}(\frac{1}{\sqrt{a_1}+\sqrt{a_2}})+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+.......+\frac{1}{\sqrt{a_n}+\sqrt{a_{n-1}}})$ is____.