List of top Questions asked in AP EAPCET- 2025

Evaluate the limit: \[ \lim_{x \to 0} \frac{x^2 \sin^2(3x) + \sin^4(6x)}{(1 - \cos(3x))^2} \]
Let \([x]\) represent the greatest integer function. If \(\lim_{x \to 0^+} \frac{\cos[x] - \cos(kx - [x])}{x^2} = 5\), then \(k =\)
Evaluate $ \lim_{x \to 3} \frac{x^2 - x - 6}{x - 3} $.
Evaluate: $$ \lim_{x \to \infty} \left[ x - \log(\cosh x) \right] $$
If \( \alpha, \beta \) are the roots of \( x^2 - 5x - 68 = 0 \) and \( \gamma, \delta \) are the roots of \( x^2 - 5\alpha x - 6\beta = 0 \), then \( \alpha + \beta + \gamma + \delta = \) ?
When the roots of \( x^3 + \alpha x^2 + \beta x + 6 = 0 \) are increased by 1, if one of the resultant values is the least root of \( x^4 - 6x^3 + 11x^2 - 6x = 0 \), then
If \( \frac{1}{2} \leq \frac{x^2+x+a}{x^2-x+a} \leq 2 \ \forall x \in \mathbb{R} \), then \( a = \)
If \( \alpha, \beta, \gamma \) are the roots of the equation \[ x^3 + px^2 + qx + r = 0, \] then \[ (\alpha + \beta)(\beta + \gamma)(\gamma + \alpha) =\ ? \]

If $x^2 + y^2 = 25$ and $xy = 12$, then what is the value of $x^4 + y^4$? 

If \(\alpha\) and \(\beta\) (\(\alpha>\beta\)) are the multiple roots of the equation \[ 4x^4 + 4x^3 - 23x^2 - 12x + 36 = 0, \] then find \(2\alpha - \beta\).
When the roots of \( x^3 + \alpha x^2 + \beta x + 6 = 0 \) are increased by 1, if one of the resultant values is the least root of \( x^4 - 6x^3 + 11x^2 - 6x = 0 \), then
An aeroplane is flying at a constant speed, parallel to the horizontal ground at a height of 5 kms. A person on the ground observed that the angle of elevation of the plane is changed from \(15^\circ\) to \(30^\circ\) in the duration of 50 seconds, then the speed of the plane (in kmph) is
If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 + ax^2 + bx + c = 0 \), then \( (\alpha + \beta - 2\gamma)(\beta + \gamma - 2\alpha)(\gamma + \alpha - 2\beta) = \)
In \( \triangle ABC \), if \( \sin^2 B = \sin A \) and \( 2\cos^2 A = 3\cos^2 B \), then the triangle is:
If \( x^2 - 5x + 6 \) is a factor of \( f(x) = x^4 - 17x^3 + kx^2 - 247x + 210 \), find the other quadratic factor of \( f(x) \).
The set of all real values of x satisfying the inequation \( \frac{8x^2-14x-9}{3x^2-7x-6}>2 \) is
If \(\alpha, \beta, \gamma\) are the roots of the equation \[ x^3 - 13x^2 + kx + 189 = 0 \] such that \(\beta - \gamma = 2\), then find the ratio \(\beta + \gamma : k + \alpha\).
After the roots of the equation $6x^3 + 7x^2 - 4x - 2 = 0$ are diminished by $h$, if the transformed equation does not contain $x$ term, then the product of all possible values of $h$ is
If \(x^2 + y^2 = 25\) and \(xy = 12\), then what is the value of \(x^4 + y^4\)?
If \( a \pm bi \) and \( b \pm ai \) are roots of \( x^4 - 10x^3 + 50x^2 - 130x + 169 = 0 \), then find the value of \( \frac{a}{b} + \frac{b}{a} \).
Let 'a' be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation \( x^3 - ax^2 + ax - 1 = 0 \) is identical with this cubic equation, then 'a' =
If \( \frac{1}{2} \leq \frac{x^2+x+a}{x^2-x+a} \leq 2 \ \forall x \in \mathbb{R} \), then \( a = \)
The equation \[ x^{\frac{3}{4}(\log_{x} x)^2 + \log_{x} x^{-\frac{5}{4}}} = \sqrt{2} \] has
An aeroplane is flying at a constant speed, parallel to the horizontal ground at a height of 5 kms. A person on the ground observed that the angle of elevation of the plane is changed from \(15^\circ\) to \(30^\circ\) in the duration of 50 seconds, then the speed of the plane (in kmph) is
All the values of \(k\) such that the quadratic expression \(2kx^2 - (4k+1)x + 2\) is negative for exactly three integral values of \(x\), lie in the interval: