Mathematics Algebra questions from JEE Main 2006.
All the values of $m$ for which both roots of the equations $x^2-2 m x+m^2-1=0$ are greater than $-2$ but less than 4 , lie in the interval
At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is
For natural numbers $m, n$ if $(1-y)^m(1+y)^n=1+a_1 y+a_2 y^2+\ldots$, and $a_1=a_2=10$ then $(\mathrm{m}, \mathrm{n})$ is
If $A$ and $B$ are square matrices of size $n \times n$ such that $A^2-B^2=(A-B)(A+B)$, then which of the following will be always true?
If $a_1, a_2, \ldots, a_n$ are in H.P., then the expression $a_1 a_2+a_2 a_3+\ldots+a_{n-1} a_n$ is equal to
If the expansion in powers of $x$ of the function $\frac{1}{(1-a x)(1-b x)}$ is $a_0+a_1 x+a_2 x^2+a_3 x^3+\ldots$, then $a_n$ is
If the roots of the quadratic equation $x^2+p x+q=0$ are $\tan 30^{\circ}$ and $\tan 15^{\circ}$, respectively then the value of $2+q-p$ is
If $z^2+z+1=0$, where $z$ is a complex number, then the value of $$ \left(z+\frac{1}{z}\right)^2+\left(z^2+\frac{1}{z^2}\right)^2+\left(z^3+\frac{1}{z^3}\right)^2+\cdots+\left(z^6+\frac{1}{z^6}\right)^2 $$
Let $A=\left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right)$ and $B=\left(\begin{array}{ll}a & 0 \\ 0 & b\end{array}\right), a, b \in N$. Then
Let $a_1, a_2, a_3, \ldots$ be terms of an A.P. If $\frac{a_1+a_2+\cdots a_p}{a_1+a_2+\cdots+a_q}=\frac{p^2}{q^2}, p \neq q$, then $\frac{a_6}{a_{21}}$ equals
Let W denote the words in the English dictionary. Define the relation R by : $R=\{(x, y) \in W \times W \mid$ the words $x$ and $y$ have at least one letter in common $\}$. Then $R$ is