List of top Mathematics Questions asked in AP EAMCET

Evaluate the given trigonometric expression: \[ 4 \cos \frac{\pi}{7} \cos \frac{\pi}{5} \cos \frac{2\pi}{7} \cos \frac{2\pi}{5} \cos \frac{4\pi}{7} = \]
If \( M_1 \) and \( M_2 \) are the maximum values of \( \frac{1}{11 \cos 2x + 60 \sin 2x + 69} \) and \( 3 \cos^2 5x + 4\sin^2 5x \) respectively, then \( \frac{M_1}{M_2} = \):
If \( |x| < 1 \), the coefficient of \( x^2 \) in the power series expansion of \( \frac{x^4}{(x+1)(x-2)} \) is:
If \( |x| < 1 \), then the number of terms in the expansion of \( \left[ \frac{1}{2} (1.2 + 2.3x + 3.4x^2 + \dots) \right]^{-25} \) is:
If the \(2^{\text{nd}}\), \(3^{\text{rd}}\), and \(4^{\text{th}}\) terms in the expansion of \( (x + a)^n \) are 96, 216, and 216 respectively, and \( n \) is a positive integer, then \( a + x \) is:
The rank of the word "TABLE" counted from the rank of the word "BLATE" in dictionary order is:
If \( \alpha \) and \( \beta \) are two distinct negative roots of the equation \( x^5 - 5x^3 + 5x^2 - 1 = 0 \), then the equation of least degree with integer coefficients having \( \sqrt{-\alpha} \) and \( \sqrt{-\beta} \) as its roots is:
If both the roots of the equation \( x^2 - 6ax + 2 - 2a + 9a^2 = 0 \) exceed 3, then:
If \( \alpha, \beta \) are the roots of the equation \( x^2 - 6x - 2 = 0 \), \( \alpha > \beta \), and \( a_n = \alpha^n - \beta^n, n \geq 1 \), then the value of \( \frac{a_{10} - 2 a_8}{2 a_9} \) is:
All values of \( (8i)^{\frac{1}{3}} \) are:
The locus of the complex number \( Z \) satisfying \( \arg \left( \frac{Z - 1}{Z + 1} \right) = \frac{\pi}{4} \) is:
If \( A = \begin{bmatrix} a & 1 & 2 \\ 1 & b & 3 \\ c & 1 & 3 \end{bmatrix} \) and \( \text{Adj } A = \begin{bmatrix} 7 & -1 & -5 \\ -3 & 9 & 5 \\ 1 & -3 & 5 \end{bmatrix} \), then \( a^2 + b^2 + c^2 = \) ?
If the system of equations has a unique solution, find the values of \( a \) and \( b \).
The domain of the real-valued function \( f(x) = \sqrt{9 - \sqrt{x^2 - 144}} \) is
The solution of the differential equation \[ (x + 2y^3) \frac{dy}{dx} = y \] is:
If \[ y = a e^{bx} + c e^{dx} + x e^{bx} \] is the general solution of a differential equation, where \( a \) and \( c \) are arbitrary constants and \( b \) is a fixed constant, then the order of the differential equation is:
The differential equation formed by eliminating \( a \) and \( b \) from the equation \[ y = ae^{2x} + bxe^{2x} \] is:
The area of the region under the curve \( y = |\sin x - \cos x| \) in the interval \( 0 \leq x \leq \frac{\pi}{2} \), above the x-axis, is (in square units):
If \[ \int_{1}^{n} f(x) \,dx = 120, \] then \( n \) is:
If \[ f(x) = \begin{cases} \frac{6x^2 + 1}{4x^3 + 2x + 3}, & 0 < x < 1 \\ x^2 + 1, & 1 \leq x < 2 \end{cases} \] then \[ \int_{0}^{2} f(x) \,dx = ? \]
Evaluate the limit: \[ \lim_{n \to \infty} \frac{17^7 + 27^7 + \dots + n^{77}}{n^{78}}. \]
If \( n \geq 2 \) is a natural number and \( 0<\theta<\frac{\pi}{2} \), then \[ \int \frac{(\cos^n \theta - \cos \theta)^{1/n}}{\cos^{n+1} \theta} \sin \theta \, d\theta = \]
If \[ 729 \int_1^3 \frac{1}{x^3 (x^2 + 9)^2} \, dx = a + \log b, \] then \( a - b = \) ?
If \[ \int \frac{1}{1 - \cos x} \, dx = \tan \left( \frac{x}{4} + \beta \right) + c, \] then one of the values of \( \frac{\pi}{4} - \beta \) is:
Evaluate the integral: \[ \int e^x \left( \frac{x + 2}{(x+4)} \right)^2 dx. \]