JEE Main Mathematics — Algebra previous year questions with solutions.
The product ${2}^{\frac{1}{4}}\cdot {4}^{\frac{1}{16}}\cdot {8}^{\frac{1}{48}}\cdot {16}^{\frac{1}{128}}\cdot ....$ to $\infty$ is equal to:
The sum $\sum _{k=1}^{20}(1+2+3+\ldots +k)$ is ___________.
Let ${a}_{1},{a}_{2},{a}_{3},\ldots$, be a $G.P.$ such that ${a}_{1}<0,{a}_{1}+{a}_{2}=4$ and ${a}_{3}+{a}_{4}=16$. If $\sum _{i=1}^{9}{a}_{i}=4\lambda$, then $\lambda$, is equal to.
If $m$ arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between $3$ and $243$ such that ${4}^{th}$ A.M. is equal to ${2}^{nd}$ G.M., then $m$ is equal to:
If the first term of an $A.P.$ is $3$ and the sum of its first $25$ terms is equal to the sum of its next $15$ terms, then the common difference of this $A.P.$is
The number of terms common to the two A.P.’s $3,7,11,\ldots ,407$ and $2,9,16,\ldots ,709$ is ____________.
Let $z=x+\mathrm{iy}$ be a non-zero complex number such that ${z}^{2}=i{|z|}^{2}$, where $i=\sqrt{-1}$, then $z$ lies on the :
The number of words (with or without meaning) that can be formed from all the letters of the word$"LETTER"$ in which vowels never come together is.....
If ${2}^{10}+{2}^{9}\cdot {3}^{1}+{2}^{8}\cdot {3}^{2}+\ldots \ldots +2\cdot {3}^{9}+{3}^{10}=S-{2}^{11}$, then $S$ is equal to
If the determinant |1 2 3; 4 5 6; 7 8 k| = 0, then k equals:
If the ${10}^{th}$, term of an A.P. is $\frac{1}{20}$, and its ${20}^{th}$, term is $\frac{1}{10}$, then the sum of its first $200$, terms is.
Let $S$, be the set of all real roots of the equation, ${3}^{x}({3}^{x}-1)+2=|{3}^{x}-1|+|{3}^{x}-2|$, then
Let $u=\frac{2z+i}{z-ki},z=x+iy$ and $k>0$. If the curve represented by$Re(u)+Im(u)=1$ intersects the $y$-axis at points $P$ and $Q$ where $\mathrm{PQ}=5$ then the value of $k$ is
If $f(x+y)=f(x)f(y)$ and $\Sigma _{x=1}^{\infty }f(x)=2,x,y\in N$, where $N$ is the set of all natural numbers, then the value of $\frac{f(4)}{f(2)}$ is
Let $S$ be the sum of the first $9$ term of the series : ${x+ka}+{{x}^{2}+(k+2)a}+{{x}^{3}+(k+4)a}+{{x}^{4}+(k+6)a}+\ldots$ where $a\neq 0$ and $x\neq 1$. If $S=\frac{{x}^{10}-x+45a(x-1)}{x-1}$ , then $k$ is equal to
The product of the roots of the equation $9{x}^{2}-18|x|+5=0$ is :
Let $a,1{a}_{2},\ldots ,{a}_{n}$ be a given A.P. whose common difference is an integer and ${S}_{n}={a}_{1}+{a}_{2}+\ldots +{a}_{n}$. If ${a}_{1}=1,{a}_{n}=300$ and $15\leq n\leq 50,$ then the ordered pair $({S}_{n-4},{a}_{n-4})$ is equal to:
If $a+x=b+y=c+z+1,$ where $a,b,c,x,y,z$ are non-zero distinct real numbers, then$|\begin{matrix}x & a+y & x+a \\ y & b+y & y+b \\ z & c+y & z+c\end{matrix}|$ is equal to :
If the system of equations $x-2y+3z=9$ $2x+y+z=b$ $x-7y+az=24,$ has infinitely many solutions, then $a-b$ is equal to ______
Let $A=[{a}_{ij}]$ and $B=[{b}_{ij}]$ be two $3\times 3$ real matrices such that ${b}_{ij}={(3)}^{(i+j-2)}{a}_{ij}$ , where $i,j=1,2,3$ . If the determinant of $B$ is $81$ , then determinant of $A$ i s
Let ${(2{x}^{2}+3x+4)}^{10}=\sum _{r=0}^{20}{a}_{r}{x}^{r}.$ Then $\frac{{a}_{7}}{{a}_{13}}$ is equal to ______
The values of $\lambda$ and $\mu$ for which the system of linear equations $x+y+z=2$, $x+2y+3z=5$, $x+3y+\lambda z=\mu$ has infinitely many solutions, are respectively
Let $X={n\in N:1\leq n\leq 50}$. If $A={n\in X:n is a multiple of2}$ and $B={n\in X:n is a multiple of 7}$, then the number of elements in the smallest subset of $X$, containing both $A$ and $B$, is.
The value of $0.{16}^{{\mathrm{log}}_{2.5}(\frac{1}{3}+\frac{1}{{3}^{2}}+\frac{1}{{3}^{3}}+\ldots .\infty )}$ is __________