List of top Mathematics Questions on Algebra asked in JEE Main

If the constant term in the expansion of \((1 + 2x - 3x^3) \left(\frac{3}{2}x^2 - \frac{1}{3x}\right)^9\) is \( p \), then \( 108p \) is equal to _________.

The number of real solutions of the equation x |x + 5| + 2|x + 7| – 2 = 0 is _____.

The number of distinct real roots of the equation \[ |x + 1| |x + 3| - 4|x + 2| + 5 = 0, \] is _______.

The number of distinct real roots of the equation \[ |x| \, |x + 2| - 5|x + 1| - 1 = 0 \] is _________.

The number of real solutions of the equation\[x \left( x^2 + 3|x| + 5|x - 1| + 6|x - 2| \right) = 0\]is ______.

If $0<x<1$, then $\frac{3}{2}x^2 + \frac{5}{3}x^3 + \frac{7}{4}x^4 + \dots$, is equal to :

$\sum_{k=0}^{20} (^{20}C_k)^2$ is equal to :