JEE Main Mathematics — Algebra previous year questions with solutions.
Let $A=\{1,2,3,4\}$ and $R: A \rightarrow A$ be the relation defined by $R=\{(1,1),(2,3),(3,4),(4,2)\}$. The correct statement is :
If the system of linear equations : $$ \begin{aligned} & x_1+2 x_2+3 x_3=6 \\ & x_1+3 x_2+5 x_3=9 \\ & 2 x_1+5 x_2+a x_3=b \end{aligned} $$ is consistent and has infinite number of solutions, then :
If the equations ${x}^{2} + 2 x + 3 = 0$ and $a{x}^{2} +bx+c=0,$ $a,b,c\in R,$ have a common root, then $a:b:c$ is:
If the 7th term in the binomial expansion of $\left(\frac{3}{\sqrt[3]{84}}+\sqrt{3} \ln x\right)^9, x>0$, is equal to 729 , then $x$ can be:
If $P=[\begin{matrix}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{matrix}]$ is the adjoint of a $3\times 3$ matrix $A$ and $|A|=4$, then $\alpha$ is equal to
If $z$ is a complex number of unit modulus and argument $\theta$, then arg $(\frac{1+z}{1+\overset{-}{z}})$ can be equal to $(\mathrm{given} z\neq -1)$
If for positive integers $r>1, n>2$, the coefficients of the $(3 r)^{\text {th }}$ and $(r+2)^{\text {th }}$ powers of $x$ in the expansion of $(1+x)^{2 n}$ are equal, then $n$ is equal to:
If $a, b, c$ are sides of a scalene triangle, then the value of $\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|$ is :
If $x,y,z$ are positive numbers in $A.P.$ and ${\mathrm{tan}}^{-1}x$, ${\mathrm{tan}}^{-1}y$ and ${\mathrm{tan}}^{-1}z$ are also in $A.P.$, then which of the following is correct.
If $a_1, a_2, a_3, \ldots, a_n, \ldots$. are in A.P. such that $a_4-a_7$ $+a_{10}=m$, then the sum of first 13 terms of this A.P., is :
If $p, q, r$ are 3 real numbers satisfying the matrix equation, $[p q r]\left[\begin{array}{lll}3 & 4 & 1 \\ 3 & 2 & 3 \\ 2 & 0 & 2\end{array}\right]=\left[\begin{array}{lll}3 & 0 & 1\end{array}\right]$ then $2 p+q-r$ equals :
If $Z_1 \neq 0$ and $Z_2$ be two complex numbers such that $\frac{Z_2}{Z_1}$ is a purely imaginary number, then $\left|\frac{2 Z_1+3 Z_2}{2 Z_1-3 Z_2}\right|$ is equal to:
If $\alpha$ and $\beta$ are roots of the equation $x^2+p x+\frac{3 p}{4}=0$, such that $|\alpha-\beta|=\sqrt{10}$, then $p$ belongs to the set :
If $p$ and $q$ are non-zero real numbers and $\alpha^3+\beta^3=-p, \alpha \beta=q$, then a quadratic equation whose roots are $\frac{\alpha^2}{\beta}, \frac{\beta^2}{\alpha}$ is :
If a complex number $z$ statisfies the equation $x+\sqrt{2}|z+1|+i=0$, then $|z|$ is equal to :
Given sum of the first $n$ terms of an A.P. is $2 n+$ $3 n^2$. Another A.P. is formed with the same first term and double of the common difference, the sum of $n$ terms of the new A.P. is :
Given a sequence of 4 numbers, first three of which are in G.P. and the last three are in A.P. with common difference six. If first and last terms of this sequence are equal, then the last term is :
A common tangent to the conics $x^2=6 y$ and $2 x^2-4 y^2=9$ is:
A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is :
5 - digit numbers are to be formed using $2,3,5,7$, 9 without repeating the digits. If $p$ be the number of such numbers that exceed 20000 and $q$ be the number of those that lie between 30000 and 90000 , then $p: q$ is:
The value of $\mathrm{k}$ for which the equation $(K-2) x^2+8 x+K+4=0$ has both roots real, distinct and negative is
The sum of the series $1+\frac{4}{3}+\frac{10}{9}+\frac{28}{27}+\ldots$ upto $n$ terms is
The sum of the series $$ \frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\ldots $$ upto 15 terms is