JEE Main Mathematics — Algebra previous year questions with solutions.
If the number of five digit numbers with distinct digits and $2$ at the ${10}^{th}$ place is $336k$ , then $k$ is equal to:
The number of real roots of the equation, ${e}^{4x}+{e}^{3x}-4{e}^{2x}+{e}^{x}+1=0$ is:
If for some $\alpha$ and $\beta$ in $R$ , the intersection of the following three planes $x+4y-2z=1$ $x+7y-5z=\beta$ $x+5y+\alpha z=5$ is a line in ${R}^{3}$ , then $\alpha +\beta$ is equal to:
If $a$ and $b$ are real numbers such that ${(2+\alpha )}^{4}=a+b\alpha$, where $\alpha =\frac{-1+i\sqrt{3}}{2}$, then $a+b$ is equal to:
The number of distinct solutions of the equation, ${\mathrm{log}}_{\frac{1}{2}}|\mathrm{sin}x|=2-{\mathrm{log}}_{\frac{1}{2}}|\mathrm{cos}x|$ in the interval $[0,2\pi ],$ is ________
If the system of linear equations, $x+y+z=6$ $x+2y+3z=10$ $3x+2y+\lambda z=\mu$ has more than two solutions, then $\mu -{\lambda }^{2}$, is equal to.
The following system of linear equations $7x+6y-2z=0$ $3x+4y+2z=0$ $x-2y-6z=0,$ has
Let $\cup _{i=1}^{50}{X}_{i}=\cup _{i=1}^{n}{Y}_{i}=T$, where each ${X}_{i}$ contains $10$ elements and each ${Y}_{i}$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of sets ${X}_{i}$'s and exactly $6$ of sets ${Y}_{i}$'s then $n$ is equal to :
The greatest positive integer $k,$ for which ${49}^{k}+1$ is a factor of the sum ${49}^{125}+{49}^{124}+\ldots +{49}^{2}+49+1,$ is
If $A={x\in R:|x|<2}$ and $B={x\in R:|x-2|\geq 3};$ then
If $\alpha$ and $\beta$ are the roots of the equation $2x(2x+1)=1$, then $\beta$ is equal to :
Let $\lambda \neq 0$ be in $R$. If $\alpha$ and $\beta$ are the roots of the equation, ${x}^{2}-x+2\lambda =0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3{x}^{2}-10x+27\lambda =0,$ then $\frac{\beta \gamma }{\lambda }$ is equal to:
If $\alpha$ and $\beta$ be two roots of the equation ${x}^{2}-64x+256=0.$ Then the value of ${(\frac{{\alpha }^{3}}{{\beta }^{5}})}^{\frac{1}{8}}+{(\frac{{\beta }^{3}}{{\alpha }^{5}})}^{\frac{1}{8}}$ is :
The set of all real values of $\lambda$ for which the quadratic equation $({\lambda }^{2}+1){x}^{2}-4\lambda x+2=0$ always have exactly one root in the interval $(0,1)$ is :
If $\alpha$ and $\beta$ are the roots of the equation ${x}^{2}+px+2=0$ and $\frac{1}{\alpha }$ and $\frac{1}{\beta }$ are the roots of the equation $2{x}^{2}+2qx+1=0,$ then $(\alpha -\frac{1}{\alpha })(\beta -\frac{1}{\beta })(\alpha +\frac{1}{\beta })(\beta +\frac{1}{\alpha })$ is equal to :
Let $\alpha$ and $\beta$ be the roots of the equation, $5{x}^{2}+6x-2=0$. If ${S}_{n}={\alpha }^{n}+{\beta }^{n},n=1,2,3,....,$ then
The least positive value of ‘ $a$ ’ for which the equation, $2{x}^{2}+(a-10)x+\frac{33}{2}=2a$ has real roots is ___________.
If the four complex numbers $z,\bar{z},\bar{z}-2Re(\bar{z})$ and $z-2Re(z)$ represent the vertices of a square of side $4$ units in the Argand plane, then $|z|$ is equal to :
If ${(\frac{1+i}{1-i})}^{\frac{m}{2}}={(\frac{1+i}{i-1})}^{\frac{n}{3}}=1,(m,n\in N)$ then the greatest common divisor of the least values of $m$ and $n$ is
If $Re(\frac{z-1}{2z+i})=1,$ where $z=x+iy,$ then the point $(x,y)$ lies on a
If $\frac{3+isin\theta }{4-icos\theta },\theta \in [0,2\pi ],$ is a real number, then an argument of $sin\theta +icos\theta$ is
A test consists of $6$ multiple choice questions, each having $4$ alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is ___________
Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated ?
The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $\mathrm{EXAMINATION}$ is