JEE Main Mathematics — Algebra previous year questions with solutions.
If the arithmetic mean of two numbers $a$ and $b, a>b>0$ , is five times their geometric mean, then $\frac{a+b}{a-b}$ is equal to:
Let $z\in C,$ the set of complex numbers. Then the equation, $2|z+3i|-|z-i|=0$ represents:
If ${(27)}^{999}$ is divided by $7$, then the remainder is
If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:
A man $X$ has $7$ friends, $4$ of them are ladies and $3$ are men. His wife $Y$ also has $7$ friends, $3$ of them are ladies and $4$ are men. Assume $X$ and $Y$ have no common friends. Then the total number of ways in which $X$ and $Y$ together can throw a party inviting $3$ ladies and $3$ men, so that $3$ friends of each of $X$ and $Y$ are in this party is:
If $A=[\begin{matrix}2 & -3 \\ -4 & 1\end{matrix}]$ , then $\mathrm{Adj}(3{A}^{2}+12A)$ is equal to:
If three positive numbers $a$, $b$ and $c$ are in A.P. such that $abc=8$, then the minimum possible value of $b$ is:
Let $\omega$ be a complex number such that $2\omega +1=z$ where $z=\sqrt{-3}$ . If $|\begin{matrix}1 & 1 & 1 \\ 1 & -{\omega }^{2}-1 & {\omega }^{2} \\ 1 & {\omega }^{2} & {\omega }^{7}\end{matrix}|=3k,$ Then $k$ can be equal to:
The coefficient of ${x}^{-5}$ in the binomial expansion of ${(\frac{x+1}{{x}^{\frac{2}{3}}-{x}^{\frac{1}{3}}+1 }-\frac{x-1}{x-{x}^{\frac{1}{2}}})}^{10}$ where $x\neq 0,1$ is
For any three positive real numbers $a,b$ and $c$. If $9(25{a}^{2}+{b}^{2})+25({c}^{2}-3ac)=15b(3a+c).$ Then
If $S={x\in [0, 2\pi ] :|\begin{matrix}0 & \mathrm{cos}x & -\mathrm{sin}x \\ \mathrm{sin}x & 0 & \mathrm{cos}x \\ \mathrm{cos}x & \mathrm{sin}x & 0\end{matrix}|=0},$ then $\underset{x \in S}{\sum }\mathrm{tan}(\frac{\pi }{3}+x)$ is equal to:
The number of real values of $\lambda$ for which the system of linear equations, $2x+4y-\lambda z=0$, $4x+\lambda y+2z=0$ and $\lambda x+2y+2z=0$, has infinitely many solutions, is:
Let $f(x)={2}^{10}x+1$ and $g(x)={3}^{10}x-1.$ If $(fog)(x)=x,$ then $x$ is equal to:
The function $f :R\rightarrow [-\frac{1}{2},\frac{1}{2}]$ defined as $f(x)=\frac{x}{1+{x}^{2}},$ is:
The function $f :N\rightarrow I$ defined by $f(x)=x-5[\frac{x}{5}]$ , where $N$ is the set of natural numbers and $[x]$ denotes the greatest integer less than or equal to $x$, is:
If the sum of the first $n$ terms of the series $\sqrt{3}+ \sqrt{75}+ \sqrt{243}+ \sqrt{507}+\ldots$ is $435\sqrt{3},$ then $n$ equals:
The number of ways in which$5$ boys and $3$ girls can be seated on a round table if a particular boy ${B}_{1}$ and a particular girl ${G}_{1}$ never sit adjacent to each other, is:
The equation $Im(\frac{iz-2}{z-i})+1=0, z\in C, z\neq i$ represents a part of a circle having radius equal to :
If $S$ is the set of distinct values of $b$ for which the following system of linear equations $x+y+z=1$ $x+ay+z=1$ $ax+by+z=0$ has no solution, then $S$ is:
Let $a, b, c\in R$ . If $f(x)=a{x}^{2}+bx+c$ is such that $a+b+c=3$ and $f(x+y)=f(x)+f(y)+xy, \forall x, y\in R$ , then $\sum _{ n=1 }^{ 10 } f(n)$ is equal to:
Let $p(x)$ be a quadratic polynomial such that $p(0)=1.$ If $p(x)$ leaves remainder $4$ when divided by $x-1$ and it leaves remainder $6$ when divided by $x+1$ then:
The sum of all the real values of $x$ Satisfying the equation ${2}^{(x-1)({x}^{2}+5x-50)}=1$ is:
If, for a positive integer $n$, the quadratic equation, $x(x+1)+(x+1)(x+2)+...+(x+\bar{n-1})(x+n)=10n$ has two consecutive integral solutions, then $n$ is equal to:
Let $A$ be any $3\times 3$ invertible matrix. Then which one of the following is not always true?