JEE Main Mathematics — Algebra previous year questions with solutions.
If $a, b, c, d$ and $p$ are distinct real numbers such that $\left(a^2+b^2+c^2\right) p^2-2 p(a b+b c+c d)+\left(b^2+\right.$ $\left.c^2+d^2\right) \leq 0$, then
Statement 1: If $A$ and $B$ be two sets having $p$ and $q$ elements respectively, where $q>p$. Then the total number of functions from set $A$ to set $B$ is $q^p$ Statement 2: The total number of selections of $p$ different objects out of $q$ objects is ${ }^q \mathrm{C}_p$.
Let $Z$ and $W$ be complex numbers such that $|Z|=|W|$, and $\arg Z$ denotes the principal argument of $Z$. Statement 1:If $\arg Z+\arg W=\pi$, then $Z=-\bar{W}$. Statement 2: $|Z|=|W|$, implies arg $Z-\arg \bar{W}=\pi$.
If the A.M. between $p^{\text {th }}$ and $q^{\text {th }}$ terms of an A.P. is equal to the A.M. between $r^{\text {th }}$ and $s^{\text {th }}$ terms of the same A.P., then $p+q$ is equal to
If $100$ times the $100^{\text {th }}$ term of an $AP$ with non zero common difference equals the $50$ times its $50^{\text {th }}$ term, then the $150^{\text {th }}$ term of this $A P$ is
If $P(S)$ denotes the set of all subsets of a given set $S$, then the number of one-to-one functions from the set $S=\{1,2,3\}$ to the $\operatorname{set} P(S)$ 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
The sum of the series $1^2+2.2^2+3^2+2.4^2+5^2+2.6^2+\ldots . .+2(2 m)^2$ is
If $n={ }^m C_2$, then the value of ${ }^n C_2$ is given by
Consider a quadratic equation $a x^2+b x+c=0$, where $2 a+3 b+6 c=0$ and let $g(x)=a \frac{x^3}{3}+b \frac{x^2}{2}+c x$. Statement 1: The quadratic equation has at least one root in the interval $(0,1)$. Statement 2: The Rolle's theorem is applicable to function $g(x)$ on the interval $[0,1]$.
If $z \neq 1$ and $\frac{z^2}{z-1}$ is real, then the point represented by the complex number $z$ lies
The area of the triangle whose vertices are complex numbers $z, i z, z+i z$ in the Argand diagram 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
Let $X=\{1,2,3,4,5\}$. The number of different ordered pairs $(Y, Z)$ that can be formed such that $Y \subseteq X, Z$ $\subseteq \mathrm{X}$ and $\mathrm{Y} \cap \mathrm{Z}$ is empty, is
If $a, b, c \in \mathrm{R}$ and 1 is a root of equation $a x^2+b x$ $+c=0$, then the curve $y=4 a x^2+3 b x+2 c, a \neq 0$ intersect $x$-axis at
If the sum of the square of the roots of the equation $x^2-(\sin \alpha-2) x-(1+\sin \alpha)=0$ is least, then $\alpha$ is equal to
If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is
Let $Z_1$ and $Z_2$ be any two complex number. Statement 1: $\left|Z_1-Z_2\right| \geq\left|Z_1\right|-\left|Z_2\right|$ Statement 2: $\left|Z_1+Z_2\right| \leq\left|Z_1\right|+\left|Z_2\right|$
If $A=\left\{x \in z^{+}: x < 10\right.$ and $x$ is a multiple of 3 or $4\}$, where $z^{+}$is the set of positive integers, then the total number of symmetric relations on $A$ is
Let $R$ be the set of real numbers This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $R$. Statement-2 : $B=\{(x, y) \in R \times R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on $\mathrm{R}$.
A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after
The number of values of $\mathrm{k}$ for which the linear equations $4 x+k y+2 z=0 ; k x+4 y+z=0 ; 2 x+2 y+z=0$ possess a non-zero solution is
Let $A$ and $B$ be two symmetric matrices of order 3 . This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements. Statement $-1$ : $\mathrm{A}(\mathrm{BA})$ and $(\mathrm{AB}) \mathrm{A}$ are symmetric matrices. Statement - 2 : $\quad A B$ is symmetric matrix if matrix multiplication of $A$ and $B$ is commutative.
The domain of the function $f(x)=\frac{1}{\sqrt{|x|-x}}$ is