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2021 JEE PYQ

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2021
Let $J_{n, m}=\int_0^{\frac{1}{2}} \frac{x^n}{x^m-1} d x, \forall n>m$ and $m \in N$. Consider a matrix $A=\left[a_{i j}\right]_{3 \times 3}$ where $...
JEE Main Mathematics Hard
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Q JEE MAIN_2021_
The number of neutrons and electrons, respectively, present in the radioactive isotope of hydrogen is :-
JEE Main Chemistry Medium
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Q JEE MAIN 2021
The function $f(\mathrm{x})=\mathrm{x}^3-6 \mathrm{x}^2+\mathrm{ax}+\mathrm{b}$ is such that $f(2)=f(4)=0$. Consider two statements.
(S1) there exists $\mathrm{x}_1, \mathrm{x}_2 \in(2,4), \mathrm{x}_1<\mathrm{x}_2$, such that $f^{\prime}\left(\mathrm{x}_1\right)=-1$ and $f^{\prime}\left(\mathrm{x}_2\right)=0$.
(S2) there...
JEE Main Mathematics Hard
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Q JEE MAIN_2021_
Consider the above reaction, the major product "P" formed is :-
JEE Main Chemistry Medium
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Q JEE-Main_2021_
Which one of the following set of elements can be detected using sodium fusion extract ?
JEE Main Chemistry Easy
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Q JEE MAIN_2021
Let $...
JEE Main Mathematics Medium
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Q JEE MAIN 2021
If $n$ is the number of solutions of the equation $2 \cos x\left(4 \sin \left(\frac{\pi}{4}+x\right) \sin \left(\frac{\pi}{4}-x\right)-1\right)=1, x \in[0, \pi]$ and $S$ is the sum...
JEE Main Mathematics Medium
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Q JEE MAIN_2021
The term independent of ' $x$ ' in the expansion of $\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right)^{10}$, where $x \neq 0,1$ is equal to
JEE Main Mathematics Medium
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Q _JEE MAIN_202
If $\alpha, \beta$ are roots of the equation $x^2+5(\sqrt{2}) x+10=0, \alpha>\beta$ and $P_n=\alpha^n-\beta^n$ for each positive integer $n$, then the value of $...
JEE Main Mathematics Medium
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Q _JEE MAIN_2021_
There are 5 students in class 10, 6 students in class 11 and 8 students in class 12. If the number of ways, in which...
JEE Main Mathematics Medium
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