JEE Main Mathematics — Algebra previous year questions with solutions.
The number of five-digit numbers, greater than $40000$ and divisible by $5$, which can be formed using the digits $0,1,3,5,7$ and $9$ without repetition, is equal to
If the ${1011}^{\mathrm{th}}$ term from the end in the binomial expansion of ${(\frac{4x}{5}-\frac{5}{2x})}^{2022}$ is $1024$ times ${1011}^{\mathrm{th}}$ term from the beginning, then $32|x|$ is equal to
Let the complex number $z=x+iy$ be such that $\frac{2z-3i}{2z+i}$ is purely imaginary. If $x+{y}^{2}=0$, then ${y}^{4}+{y}^{2}-y$ is equal to
Let $S={1,2,3,4,5,6}$. Then the number of oneone functions $f:S\rightarrow P(S)$, where $P(S)$ denote the power set of $S$, such that $f(n)\subset f(m)$ where $n<m$ is
Let $A={1,2,3,5,8,9}$. Then the number of possible functions $f:A\rightarrow A$ such that $f(m\cdot n)=f(m)\cdot f(n)$ for every $m,n\in A$ with $m\cdot n\in A$ is equal to
The number of integral solution $x$ of ${\mathrm{log}}_{(x+\frac{7}{2})}{(\frac{x-7}{2x-3})}^{2}\geq 0$ is
Let $C$ be the circle in the complex plane with centre ${z}_{0}=\frac{1}{2}(1+3i)$ and radius $r=1$. Let ${z}_{1}=1+i$ and the complex number ${z}_{2}$ be outside circle $C$ such that $|{z}_{1}-{z}_{0}||{z}_{2}-{z}_{0}|=1$. If ${z}_{0},{z}_{1}$ and ${z}_{2}$ are collinear, then the smaller value of ${|{z}_{2}|}^{2}$ is equal to
The minimum number of elements that must be added to the relation $R=(a,b),(b,c)$ on the set ${a,b,c}$ so that it becomes symmetric and transitive is:
Let the first term a and the common ratio $r$ of a geometric progression be positive integers. If the sum of squares of its first three terms is $33033$, then the sum of these three terms is equal to
If the number of words, with or without meaning. which can be made using all the letters of the word MATHEMATICS in which $C$ and $S$ do not come together, is $(6!)k$ then $k$ is equal to
If all the six digit numbers ${x}_{1}{x}_{2}{x}_{3}{x}_{4}{x}_{5}{x}_{6}$ with $0<{x}_{1}<{x}_{2}<{x}_{3}<{x}_{4}<{x}_{5}<{x}_{6}$ are arranged in the increasing order, then the sum of the digits in the ${72}^{\text{th }}$ number is _______.
Number of $4$-digit numbers that are less than or equal to $2800$ and either divisible by $3$ or by $11$ , is equal to _____ .
If $f(x)=\frac{{2}^{2x}}{{2}^{2x}+2}$, $x\in R$, then $f(\frac{1}{2023})+f(\frac{2}{2023})+f(\frac{3}{2023}).........f(\frac{2022}{2023})$ is equal to
If the coefficient of ${x}^{7}$ in ${(ax-\frac{1}{b{x}^{2}})}^{13}$ and the coefficient of ${x}^{-5}$ in ${(ax+\frac{1}{b{x}^{2}})}^{13}$ are equal, then ${a}^{4}{b}^{4}$ is equal to:
The complex number $z=\frac{i-1}{\mathrm{cos}\frac{\pi }{3}+i\mathrm{sin}\frac{\pi }{3}}$ is equal to:
Let $z=1+i$ and ${z}_{1}=\frac{1+i\bar{z}}{\bar{z}(1-z)+\frac{1}{z}}\cdot$ Then $\frac{12}{\pi }$ $\mathrm{arg}({z}_{1})$ is equal to
The number of integral solution $x$ of ${\mathrm{log}}_{(x+\frac{7}{2})}{(\frac{x-7}{2x-3})}^{2}\geq 0$ is
Let $\alpha ,\beta$ be the roots of the quadratic equation ${x}^{2}+\sqrt{6}x+3=0$. Then $\frac{{\alpha }^{23}+{\beta }^{23}+{\alpha }^{14}+{\beta }^{14}}{{\alpha }^{15}+{\beta }^{15}+{\alpha }^{10}+{\beta }^{10}}$ is equal to
If $a$ and $b$ are the roots of the equation ${x}^{2}-7x-1=0$, then the value of $\frac{{a}^{21}+{b}^{21}+{a}^{17}+{b}^{17}}{{a}^{19}+{b}^{19}}$ is equal to
Let $\alpha ,\beta ,\gamma$ be the three roots of the equation ${x}^{3}+bx+c=0$ if $\beta \gamma =1=-\alpha$ then ${b}^{3}+2{c}^{3}-3{\alpha }^{3}-6{\beta }^{3}-8{\gamma }^{3}$ is equal to
The sum of all the roots of the equation $|{x}^{2}-8x+15|-2x+7=0$ is
The equation ${e}^{4x}+8{e}^{3x}+13{e}^{2x}-8{e}^{x}+1=0,x\in R$ has :
If the value of real number $\alpha >0$ for which ${x}^{2}-5\alpha x+1=0$ and ${x}^{2}-\alpha x-5=0$ have a common real roots is $\frac{3}{\sqrt{2\beta }}$ then $\beta$ is equal to ________
The number of integral values of $k$, for which one root of the equation $2{x}^{2}-8x+k=0$ lies in the interval $(1,2)$ and its other root lies in the interval $(2,3)$, is :