List of top Mathematics Questions asked in AP EAPCET

If the roots of the equation \[ 6x^3 - 11x^2 + 6x - 1 = 0 \] are in harmonic progression, then the roots of \[ x^3 - 6x^2 + 11x - 6 = 0 \] will be in

If \( \alpha \) and \( \beta \) are respectively the order and degree of the differential equation \[ y = e^{\frac{d^2y}{dx^2}}, \] then the value of \( \alpha + \alpha^\beta + \alpha^{2\beta} + \dots + \alpha^{2023\beta} \) is:

The sum of the global minimum and global maximum values of the function \[ f(x) = \frac{4}{3}x^3 - 4x \quad \text{in } [0, 2] \text{ is} \]

In \(\triangle ABC\), if \(a, b, c\) are in arithmetic progression and \(C = 2A\), then \(a : c = \)

Evaluate the integral: \[ \int_0^1 \left( \sqrt{10} \right)^{2x} \, dx \]

\(\displaystyle \int_{0}^{\pi} \frac{\cos x}{\sqrt{1 - \sin^2 x}} \, dx =\)

Let \( S = \{ z \in \mathbb{C} : |z - 1 + i| = 1 \} \) represents:

If \( \alpha \) and \( \beta \) are the roots of the equation \( x^2 + x + 1 = 0 \), then the quadratic equation whose roots are \( \alpha^{2023} \) and \( \beta^{2012} \) is

Evaluate the following integral: \[ \int (x^3 + x^2 m + x^m) (2x^{2m} + 3x^m + 6x^m) \, dx \]

Let \( f(x) = |x| \) and \( g(x) = |x| + a \), \( (a>0) \). For \( 0 \le x \le b \), \( \{(x, y) / g(x) \le y \le f(x)\} \) represents all the points in the interior of

If $ X $ is a random variable with the probability distribution \[ P(X = k) = \frac{(k+1)c}{2^k}, \quad k = 0, 1, 2, ..., \] then $ P(X \geq 3) $ is:

Evaluate: \[ \frac{1}{\cos 290^\circ} + \frac{1}{\sqrt{3} \sin 250^\circ} \]

If \( f(x) = \frac{x^3 + 5}{\sqrt{12 + x}} \) and } \[ \int_{-5}^{5}f(x) \, dx = \int_{0}^{5} \left( f(x) + g(x) \right) \, dx, \text{ then } g(x) = \]

If \[ \int \frac{x^3}{\sqrt{1 + x^2}} \, dx = A(1 + x^2)^{\frac{3}{2}} + B(1 + x^2)^{\frac{1}{2}} + C, \text{ then } A + B = \]

The greatest integer \( r \) such that \( 30^r \) divides \( 30! \) is:

The mean of 5 observations is 4.4 and their variance is 8.24. If three of those observations are 1, 2, and 6, then the other two observations are:

If \( \cos(\theta - \alpha), \cos \theta \) and \( \cos(\theta + \alpha) \) are in harmonic progression, then \( 2 \tan^2 \theta = \)

If two angles \( \alpha, \beta \) are such that \( 0<\alpha, \beta<\frac{\pi}{4} \), \( \sqrt{1 + \cos 2\alpha} = \frac{3}{\sqrt{5}} \) and \( \frac{\sqrt{1 - \cos 2\beta}}{\sqrt{1 + \cos 2\beta}} = \frac{1}{7} \), then \( (2\alpha + \beta) = \)