Mathematics Algebra questions from JEE Main 2002.
$r$ and $n$ are positive integers $r>1, n>2$ and coefficient of $(r+2)^{\text {th }}$ term and $3 r^{\text {th }}$ term in the expansion of $(1+x)^{2 n}$ are equal, then $n$ equals
$z$ and $w$ are two non zero complex no.s such that $|z|=|w|$ and $\operatorname{Arg} z+\operatorname{Arg} w=\pi$ then $z$ equals
$l, m, n$ are the $p^{\text {th }}, q^{\text {th }}$ and $r^{\text {th }}$ term of a G.P. all positive, then $\left|\begin{array}{ccc}\log l & p & 1 \\ \log m & q & 1 \\ \log n & r & 1\end{array}\right|$ equals
Difference between the corresponding roots of $x^2+a x+b=0$ and $x^2+b x+a=0$ is same and $a \neq b$, then
Fifth term of a GP is 2, then the product of its 9 terms is
Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4, 6 and 7 without repetition. Total number of such numbers are
If $p$ and $q$ are the roots of the equation $x^2+p x+q=0$, then
If $f(x+y)=f(x) \cdot f(y) \forall x \cdot y$ and $f(5)=2, f^{\prime}(0)=3$ then $f^{\prime}(5)$ is
If $a, b, c$ are distinct $+v e$ real numbers and $a^2+b^2+c^2=1$ then $a b+b c+c a$ is
If $1, \log _9\left(3^{1-x}+2\right), \log _3\left(4.3^x-1\right)$ are in A.P. then $x$ equals
If $\alpha \neq \beta$ but $\alpha^2=5 \alpha-3$ and $\beta^2=5 \beta-3$ then the equation having $\alpha / \beta$ and $\beta / \alpha$ as its roots is
If $a>0$ discriminant of $a x^2+2 b x+c$ is -ve, then $\left|\begin{array}{ccc}a & b & a x+b \\ b & c & b x+c \\ a x+b & b x+c & 0\end{array}\right|$ is
If $|z-4| < |z-2|$, its solution is given by
If the sum of the coefficients in the expansion of $(a+b)^n$ is 4096 , then the greatest coefficient in the expansion is
If $2 a+3 b+6 c=0(a, b, c \in R)$ then the quadratic equation $a x^2+b x+c=0$ has
Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed) is
Product of real roots of the equation $t^2 x^2+|x|+9=0$
$1^3-2^3+3^3-4^3+\ldots .+9^3=$
Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is
The coefficients of $x^p$ and $x^q$ in the expansion of $(1+x)^{p+q}$ are
The domain of $\sin ^{-1}\left[\log _3(x / 3)\right]$ is
The locus of the centre of a circle which touches the circle $\left|z-z_1\right|=a$ and $\left|z-z_2\right|=b$ externally ( $z, z_1$ and $z_2$ are complex numbers) will be
The positive integer just greater than $(1+0.0001)^{10000}$ is
The sum of integers from 1 to 100 that are divisible by 2 or 5 is
The value of $2^{1 / 4}, 4^{1 / 8}, 8^{1 / 6}+\ldots \ldots \infty$ is
Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are
Which one is not periodic