List of top Mathematics Questions on Algebra asked in TS EAMCET

If the coefficient of \(3^{\text{rd}}\) term from the beginning in the expansion of \( \left(ax^2 - \frac{8}{bx}\right)^9 \) is equal to the coefficient of \(3^{\text{rd}}\) term from the end in the expansion of \( \left(ax - \frac{2}{bx^2}\right)^9 \) then the relation between \( a \) and \( b \) is

If the sum of two roots of the equation \( x^4 - 2x^3 + x^2 + 4x - 6 = 0 \) is zero then the sum of the squares of the other two roots is

If the roots of the equation \( 32x^3 - 48x^2 + 22x - 3 = 0 \) are in arithmetic progression, then the square of the common difference of the roots is

The number of integral values of 'a' for which the quadratic equation \( ax^2 + ax + 5 = 0 \) cannot have real roots is

If \( \omega \) is a complex cube root of unity and \( x = \omega^2 - \omega + 2 \) then

If \( \frac{2+3i}{i-2} - \frac{4i-3}{3+4i} = x+iy \), then \( 3x+y = \)

If \( \Delta_r = \begin{vmatrix} 1 & 2 & r\\ 3r-2 & 3r-5 & 2 \\ 0 & 3 & 3r+1 \end{vmatrix} \) (inferred), then \( \sum_{r=1}^{33} \Delta_r' = \)
(Note: Based on the answer options, the question implies a telescoping sum resulting in 0.99, likely \( \sum \frac{3}{(3r-2)(3r+1)} \).)

1+(1+3)+(1+3+5)+(1+3+5+7)+... to 10 terms =

The range of the real valued function \( f(x)=\sin ^{-1}\left(\sqrt{x^{2}+x+1}\right) \) is

If \( e^{(\sinh^{-1} 2 + \cosh^{-1} \sqrt{6})} = a + (b+\sqrt{c})\sqrt{a} + b\sqrt{c} \), then \( a+b+c = \)

If \( \frac{x^2-3}{(x+2)(x^2+1)} = \frac{A}{x+2} + \frac{Bx+C}{x^2+1} \), then \( 3A+2B-C = \)

The inverse of the function \( y = \frac{10^x - 10^{-x}}{10^x + 10^{-x}} + 1 \) is \( x = \)

The value of the greatest positive integer \( k \), such that \( 49^k + 1 \) is a factor of \( 48(49^{125} + 49^{124} + \dots + 49^2 + 49 + 1) \) is

If \( f: \mathbb{R}-\{0\} \to \mathbb{R} \) is defined by \( 3f(x) + 4f\left(\frac{1}{x}\right) = \frac{2-x}{x} \), then \( f(3) = \)