List of top Mathematics Questions asked in TS EAMCET

If \( (2,3) \) is the focus and \( x - y + 3 = 0 \) is the directrix of a parabola, then the equation of the tangent drawn at the vertex of the parabola is:
The equation of the common tangent to the parabola \(y^2 = 8x\) and the circle \(x^2 + y^2 = 2\) is \(ax + by + 2 = 0\). If \(-\frac{a}{b}>0\), then \(3a^2 + 2b + 1 =\)
If \(6x-5y-20=0\) is a normal to the ellipse \(x^2 + 3y^2 = k\), then \(k =\)
If \( a, b, c \) are the intercepts made on X, Y, Z-axes respectively by the plane passing through the points \( (1, 0, -2) \), \( (3, -1, 2) \), and \( (0, -3, 4) \), then \( 3a + 4b + 7c = \)?
The system of equations \( x + 3y + 7 = 0 \), \( 3x + 10y - 3z + 18 = 0 \), and \( 3y - 9z + 2 = 0 \) has:
The domain of the real valued function: \[ f(x) \;=\; \sqrt[3]{\frac{x \,-\, 2}{2x^2 \,-\, 7x \,+\,5}} \;+\; \log\bigl(x^2 \,-\, x \,-\, 2\bigr). \]

Solving the System of Linear Equations

If (x,y,z) = (α,β,γ) is the unique solution of the system of simultaneous linear equations:

    3x - 4y + 2z + 7 = 0,    2x + 3y - z = 10,    x - 2y - 3z = 3,    

then α = ?

The product of all the values of \(\bigl(\sqrt{3} - i\bigr)^{25}\) is ?

The number of common roots among the 12th and 30th roots of unity is ?

\(\frac{1}{3.6} + \frac{1}{6.9} + \frac{1}{9.12} + \dots\) up to 9 terms \(=\)

Matrix Inverse Sum Calculation

Given the matrix:

    A =    | 1  2  2 |    | 3  2  3 |    | 1  1  2 |    

The inverse matrix is represented as:

    A-1 =    | a11  a12  a13 |    | a21  a22  a23 |    | a31  a32  a33 |    

The sum of all elements in A-1 is:

∑ aij = 3

If \(AX = D\) represents the system of linear equations \[ 3x - 4y + 7z + 6=0,\quad 5x + 2y - 4z + 9=0,\quad 8x - 6y - z + 5=0, \] then AX = D ?
If \[ \frac{3x^4 - 2x^2 +1}{(x-2)^4} = A + \frac{B}{x-2} + \frac{C}{(x-2)^2} + \frac{D}{(x-2)^3} + \frac{E}{(x-2)^4}, \] then \(2A + 3B - C - D + E =\;?\)
The solution set of the equation \(\cos^2(2x) + \sin^2(3x) = 1\) is \;?

If the function \( f(x) = x^3 + ax^2 + bx + 40 \) satisfies the conditions of Rolle's theorem on the interval \( [-5, 4] \) and \( -5, 4 \) are two roots of the equation \( f(x) = 0 \), then one of the values of \( c \) as stated in that theorem is:

If are the roots of the equation \[ 2x^3 \;-\; 5x^2 \;+\; 4x \;-\; 3 \;=\; 0, \] then \[ \sum \alpha\beta(\alpha+\beta) \;=\;? \]
\[ x^5 + 4x^4 - 13x^3 - 52x^2 + 36x + 144 = 0, \]
If \( x \) and \( y \) are two positive integers such that \( x + y = 24 \) and \( x^3 y^5 \) is maximum, then \( x^2 + y^2 \) is:
If \(2\,\tan^{-1}x = 3\,\sin^{-1}x\) and \(x \neq 0\), then \(8x^2 +1 =\;?\)
Among the 4-digit numbers that can be formed using the digits \(\{1,2,3,4,5,6\}\) without repeating any digit, the number of such numbers which are divisible by 6 is \;?
If the number of circular permutations of 9 distinct things taken 5 at a time is \(n_1\), and the number of linear permutations of 8 distinct things taken 4 at a time is \(n_2\), then what is \(\frac{n_1}{n_2}\)?
The number of ways in which 4 different things can be distributed to 6 persons so that no person gets all the things is \;?
If \( y = \log \left[ \tan \left( \sqrt\frac{2x - 1}{2x + 1} \right) \right] \) for \( x>0 \), then find \[ \left( \frac{dy}{dx} \right)_{x = 1}. \]
If the coefficients of three consecutive terms in the expansion of (1 + x)23 are in arithmetic progression, then those terms are ?
If \( y = \cos^{-1}\left( \frac{6x^2 - 2x^2 - 4}{2x^2 - 6x + 5} \right) \), then find \( \frac{dy}{dx} \).