List of top Questions asked in JEE Main

The set of all values of \(λ\) for which the equation \(cos^2⁡2x−2sin^4⁡x−2cos^2⁡x=λ\) has a real solution x, is 
The area of the region A = \({(x,y):|cos⁡x−sin⁡x|≤y≤sin⁡x,0≤x≤\frac{π}{ 2} }\) is
The set of all values of \(t∈R\), for which the matrix \(\begin{bmatrix} e^t & e^{−t}(sin⁡\ t−2cos\ ⁡t) & e^{−t}(−2sin⁡\ t−cos\ ⁡t) \\[0.3em] e^t & e^{−t}(2sin\ ⁡t+cos\ ⁡t) & e^{−t}(sin\ ⁡t−2cos\ ⁡t) \\[0.3em] e^t & e^{−tcos\ ⁡t}& e^{−tsin\ ⁡t} \end{bmatrix}\) is invertible, is
Let f and g be twice differentiable functions on R such that
f''(x)=g''(x)+6x
f''(1)=4g'(1)-3=9
f(2)=3g(2)=12.
Then which of the following is NOT true?
Let 𝐾 be the sum of the coefficients of the odd powers of 𝑥 in the expansion of $(1+𝑥)^{99}$. Let 𝑎 be the middle term in the expansion of \((2+\frac{1}{\sqrt 2} )^{200}\). If $\frac{⁡^{200}𝐶_{99} 𝐾}{𝑎} =\frac{2^𝑙 𝑚}{𝑛} $, where 𝑚 and 𝑛 are odd numbers, then the ordered pair (𝑙, 𝑛) is equal to
The value of the integral \(\int^2_1\bigg(\frac{t^4+1}{t^6+1}\bigg)\)dt is 
Let $𝑆={𝑤_1,𝑤_2,…….}$ be the sample space associated to a random experiment. Let $𝑃(𝑤_𝑛)= \frac{𝑃(𝑤_{𝑛−1})}{2} ,𝑛≥2.$ Let 𝐴=${(2𝑘+3𝑙:k,𝑙∈ℕ)}$ and $𝐵={𝑤_𝑛:𝑛∈𝐴}$. Then 𝑃( 𝐵) is equal to
If \(\overrightarrow a =\hat i+2\hat k,\overrightarrow b =\hat i+\hat j+\hat k,\overrightarrow c =7\hat i−3\hat j+4\hat k,r ×\hat b +\hat b ×\overrightarrow c =\overrightarrow0\) and \(\overrightarrow r .\overrightarrow a =0\). Then \(\overrightarrow r. \overrightarrow c\)  is equal to 

In the circuit shown, the energy stored in the capacitor is \( n \, \mu \text{J} \). The value of \( n \) is: 

 

The shortest distance between the lines $\frac{x−1}2 =\frac{y−2}1 =\frac{z−6}{-3} $ and $\frac{x−1}2 =\frac{y+8}{-7} =\frac{z−4}{5} $ is
Left hand side and right hand side rings are named as 'A' and 'B'
In the above reaction. Left hand side and right hand side rings are named as 'A' and 'B' respectively. They undergo ring expansion. The correct statement for this process is:
2-Methyl propyl bromide reacts with C2H5O- and gives 'A' whereas on reaction with C2H5OH it gives 'B'. The mechanism followed in these reactions and the products 'A' and 'B' respectively are
The equations of the sides $AB , BC$ and $CA$ of a triangle $ABC$ are : $2 x+y=0, x+p y=21 a,(a \neq 0)$ and $x-y=3$ respectively Let $P (2, a )$ be the centroid of $\triangle ABC$ Then $( BC )^2$ is equal to
In the following reaction 'X' is
CH3 (CH2)4 CH3 \(\frac{A n h y . A l C l _3 }{HCL\triangle}X\) major product
If the shortest between the lines $\frac{x+\sqrt{6}}{2}=\frac{y-\sqrt{6}}{3}=\frac{z-\sqrt{6}}{4}$ and $\frac{x-\lambda}{3}=\frac{y-2 \sqrt{6}}{4}=\frac{z+2 \sqrt{6}}{5}$ is $6$ , then the square of sum of all possible values of $\lambda$ is
Which of the following complex is octahedral, diamagnetic and the most stable?

Arrange the following orbitals in decreasing order of energy 
A. $n=3, l =0, m =0$ 
B. $n =4, l =0, m =0$ 
C. $n =3, l =1, m =0$ 
D. $n =3, l =2, m =1$ 
The correct option for the order is :

Let the sum of the coefficients of the first three terms in the expansion of $\left(x-\frac{3}{x^2}\right)^n, x \neq 0 n \in N$, be $376$. Then the coefficient of $x^4$ is ______

The mismatched combinations are
A. Chlorophyll - Co 
B. Water hardness - EDTA 
C. Photography - [Ag(CN)2]- 
D. Wilkinson catalyst - [(Ph3P)3 RhCl]  
E. Chelating ligand-D- Penicillamine
The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c),(b, d)\}$ on the set $\{a, b, c, d\}$ so that it is an equivalence relation, is _______

Evaluate the following statements for their correctness 
A. The elevation in boiling point temperature of water will be same for $01 \,M \,NaCl$ and $01\, M$ urea 
B. Azeotropic mixtures boil without change in their composition
C. Osmosis always takes place from hypertonic to hypotonic solution 
D. The density of $32 \% H _2 SO _4$ solution having molarity $409\, M$ is approximately $126\, g mL ^{-1}$ 
E. A negatively charged sol is obtained when KI solution is added to silver nitrate solution
Choose the correct answer from the options given below :

Let $f$ be $a$ differentiable function defined on $\left[0, \frac{\pi}{2}\right]$ such that $f(x)>0;$ and $f(x)+\int\limits_0^x f(t) \sqrt{1-\left(\log _e f(t)\right)^2} d t=e, \forall x \in\left[0, \frac{\pi}{2}\right]$ Then $\left(6 \log _e f\left(\frac{\pi}{6}\right)\right)^2$ is equal to _______

When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of water. What is the molecular formula of $A$?

If $\frac{1^3+2^3+3^3+\ldots \text { up to } n \text { terms }}{1 \cdot 3+2 \cdot 5+3 \cdot 7+\ldots \text { up to } n \text { terms }}=\frac{9}{5}$, then the value of $n$ is
ClF5 at room temperature is: