JEE Main Mathematics — Algebra previous year questions with solutions.
The number of natural numbers less than $7000$ which can be formed by using the digits $0, 1, 3, 7, 9$ (repetition of digits allowed) is equal to:
Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class, if there are two specific boys $A$ and $B,$ who refuse to be the members of the same team, is:
If the sum and product of the first three terms in an $A.P.$ are $33$ and $1155$, respectively, then a value of its ${11}^{th}$ term is:
Let ${S}_{k}=\frac{1 + 2 + 3+\ldots +k}{k}$. If ${S}_{1}^{2}+{S}_{2}^{2}+\ldots +{S}_{10}^{2}=\frac{5}{12}A$, then $A$ is equal to :
If $si{n}^{4}\alpha +4co{s}^{4}\beta +2=4\sqrt{2}sin\alpha cos\beta$, $\alpha ,\beta \in [0,\pi ]$, then $cos(\alpha +\beta )-cos(\alpha -\beta )$ is equal to
Let $a, b$ and $c$ be the ${7}^{th}, {11}^{th}$ and ${13}^{th}$ terms respectively of a non-constant A.P. . If these are also the three consecutive terms of a G.P. , then $\frac{a}{c}$ is equal to:
The sum of the following series $1+6+\frac{9({1}^{2}+{2}^{2}+{3}^{2})}{7}+\frac{12({1}^{2}+{2}^{2}+{3}^{2}+{4}^{2})}{9}+\frac{15({1}^{2}+{2}^{2}+\ldots +{5}^{2})}{11}+....$ up to $15$ terms, is:
For $x \epsilon (0,\frac{3}{2}),$ let $f(x)=\sqrt{x},g(x)=tanx$ and $h(x)=\frac{1-{x}^{2}}{1+{x}^{2}}$ . If $\phi (x)=(hof)og)(x),$ then $\phi (\frac{\pi }{3})$ is equal to:
The total number of irrational terms in the binomial expansion of ${({7}^{\frac{1}{5}}-{3}^{\frac{1}{10}})}^{60}$ is
The sum of the series $1+2\times 3+3\times 5+4\times 7+\ldots$ upto ${11}^{th}$ term is:
If the system of linear equations $x-4y+7z=g$; $3y-5z=h$; $-2x+5y-9z=k$ is consistent, then:
Let $\lambda$ be a real number for which the system of linear equations $x+y+z=6,$ $4x+\lambda y-\lambda z=\lambda -2$ and $3x+2y-4z=-5$ has infinitely many solutions. Then $\lambda$ is a root of the quadratic equation:
Let $\alpha$ and $\beta$ be the roots of the quadratic equation $x^{2} \sin \theta-x(\sin \theta \cos \theta+1)+\cos \theta=0\left(0 < \theta < 45^{\circ}\right),$ and $\alpha < \beta .$ Then $\sum_{n=0}^{\infty}\left(\alpha^{n}+\frac{(-1)^{n}}{\beta^{n}}\right)$ is equal to :
If $a>0$ and $z=\frac{{(1+i)}^{2}}{a-i}$ , has magnitude $\sqrt{\frac{2}{5}}$ , then $\overset{-}{z}$ is equal to:
If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is:
The equation $|z-i|=|z-1|,i=\sqrt{-1},$ represents:
Let $f(x)={x}^{2}, x\in R$ . For any $A\subseteq R,$ define $g(A)={x\in R :f(x)\in A}$ . If $S=[0, 4]$ , then which one of the following statements is not true?
If $\alpha$and $\beta$ are the roots of the equation $375 {x}^{2}-25x-2=0,$ then $\underset{n\rightarrow \infty }{lim}\sum _{r=1}^{n}{\alpha }^{r}+\underset{n\rightarrow \infty }{lim}\sum _{r=1}^{n}{\beta }^{r}$ is equal to:
The sum of all two digit positive numbers which when divided by $7$ yield $2$ or $5$ as remainder is
Let ${z}_{0}$ be a root of quadratic equation, ${x}^{2}+x+1=0.$ If $z=3+6i{z}_{0}^{81}-3i{z}_{0}^{93}$ , then $arg$ $(z)$ is equal to:
The set of all values of $\lambda$ for which the system of linear equations $x-2y-2z=\lambda x$ $x+2y+z=\lambda y$ $-x-y=\lambda z$ has a non-trivial solution :
There are $m$ men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by $84$, then the value of $m$ is :
Let $f: R \rightarrow R$ be defined by $f(x)=\frac{x}{1+x^{2}}, x \in R .$ Then the range of $f$ is
Let $z\in C$ be such that $|z|<1.$ If $\omega =\frac{5+3z}{5(1-z)},$ then: