List of top Mathematics Questions asked in AP EAMCET

cos 6° sin 24° cos 72° =
The values of \( x \) in \( (-\pi, \pi) \) which satisfy the equation \( \cos x + \cos 2x + \cos 3x + \cdots = 4^3 \) are:
tan 9$^\circ$ - tan 27$^\circ$ - tan 63$^\circ$ + tan 81$^\circ$ =
Evaluate \[ \cot \left( \sum_{n=1}^{50} \tan^{-1} \left( \frac{1}{1 + n + n^2} \right) \right).= \]
If the coefficients of the \( r^{th} \), \( (r+1)^{th \), and \( (r+2)^{th} \) terms in the expansion of \( (1 + x)^n \) are in the ratio \( 4:15:42 \), then \( n - r \) is:}
If the coefficients of the \( (2r + 6)^{th \) and \( (r - 1)^{th} \) terms in the expansion of \( (1 + x)^{21} \) are equal, then the value of \( r \) is:}
If \[ \frac{13x+43}{2x^2 + 17x + 30} = \frac{A}{2x+5} + \frac{B}{x+6} \text{ then } A + B = \]
The number of ways of arranging 9 men and 5 women around a circular table so that no two women come together are:
There were two women participating with some men in a chess tournament. Each participant played two games with the other. The number of games that the men played among themselves is 66 more than the number of games the men played with the women. Then the total number of participants in the tournament is:
If there are 6 alike fruits, 7 alike vegetables, and 8 alike biscuits, then the number of ways of selecting any number of things out of them such that at least one from each category is selected, is:
If \( \alpha_1, \alpha_2, \alpha_3, \alpha_4, \alpha_5 \) are the roots of the equation \[ x^5 - 5x^4 + 9x^3 - 9x^2 + 5x - 1 = 0, \] then find the value of \[ \frac{1}{\alpha_1^2} + \frac{1}{\alpha_2^2} + \frac{1}{\alpha_3^2} + \frac{1}{\alpha_4^2} + \frac{1}{\alpha_5^2}. \]
If \( a \) is a rational number, then the roots of the equation \( x^2 - 3ax + a^2 - 2a - 4 = 0 \) are:
The quotient when \[ 3x^5 - 4x^4 + 5x^3 - 3x^2 + 6x - 8 \] is divided by \( x^2 + x - 3 \) is:
Given \[ A = \begin{bmatrix} 0 & 1 & 2 \\ 4 & 0 & 3 \\ 2 & 4 & 0 \end{bmatrix} \] \(\quad B \text{ is a matrix such that }\) \(AB = BA. \text{ If } AB \text{ is not an identity matrix, then the matrix that can be taken as } B \text{ is:} \)
Consider the system of linear equations: \[ x + 2y + z = -3, \] \[ 3x + 3y - 2z = -1, \] \[ 2x + 7y + 7z = -4. \] Determine the nature of its solutions.
Find the argument of the given complex expression: \[ \text{Arg} \left[ \frac{(1 + i \sqrt{3}) \cdot (\sqrt{3} - i)}{(1 - i) \cdot ( -i)} \right] = \]
If \( \alpha, \beta \) (\(\alpha<\beta\)) are the values of \( x \) such that the determinant of the matrix \[ \begin{bmatrix} x - 2 & 0 & 1 \\ 1 & x + 3 & 2 \\ 2 & 0 & 2x - 1 \end{bmatrix} \] is zero (i.e., the matrix is singular), then the value of \( 2\alpha + 3\beta + 4\gamma \) is:
The range of the real valued function \( f(x) = \frac{15}{3 \sin x + 4 \cos x + 10} \) is:
Evaluate the limit: \[ \lim_{x \to 1} \frac{x + x^2 + x^3 + \dots + x^n - n}{x - 1}. \]
Let \( P(x_1, y_1, z_1) \) be the foot of the perpendicular drawn from the point \[ Q(2, -2, 1) \] to the plane \[ x - 2y + z = 1. \] If \( d \) is the perpendicular distance from the point \( Q \) to the plane and \[ I = x_1 + y_1 + z_1, \] then \( I + 3d^2 \) is:
If the line with direction ratios \[ (1, a, \beta) \] is perpendicular to the line with direction ratios \[ (-1,2,1) \] and parallel to the line with direction ratios \[ (\alpha,1,\beta), \] then \( (\alpha, \beta) \) is:
If the plane \[ x - y + z + 4 = 0 \] divides the line joining the points \[ P(2,3,-1) \quad {and} \quad Q(1,4,-2) \] in the ratio \( l:m \), then \( l + m \) is:

The descending order of magnitude of the eccentricities of the following hyperbolas is: 
A. A hyperbola whose distance between foci is three times the distance between its directrices. 
B. Hyperbola in which the transverse axis is twice the conjugate axis. 
C. Hyperbola with asymptotes \( x + y + 1 = 0, x - y + 3 = 0 \).

The value of \( c \) such that the straight line joining the points \[ (0,3) \quad {and} \quad (5,-2) \] is tangent to the curve \[ y = \frac{c}{x+1} \] is:
The product of perpendiculars from the two foci of the ellipse \[ \frac{x^2}{9} + \frac{y^2}{25} = 1 \] on the tangent at any point on the ellipse is: