List of top Mathematics Questions asked in AP EAPCET

From a collection of eight cards numbered 1 to 8, if two cards are drawn at random, one after the other with replacement, then the probability that the product of numbers that appear on the cards is a perfect square is:
In $ \triangle ABC $, if $ r $ is the inradius and $ r_1, r_2, r_3 $ are the ex-radii, then \[ \frac{1}{4} \left[ b^2 \sin 2C + c^2 \sin 2B \right] = \]

If $f(x) = \frac{1 - x + \sqrt{9x^2 + 10x + 1}}{2x}$, then $\lim_{x \to -1^-} f(x) =$

If \( -1 \) is a twice repeated root of the equation \( a(x^3 + x^2) + bx + c = 0 \), then the ratio \( a : b : c \) is:
If \( \lim_{x \to \infty} y(x) = \frac{\pi}{2} \), then the solution of \( x^3 \sin y \frac{dy}{dx} = 2 \) is \( \cos y = \)
In \( \triangle ABC \), \( (\cot A + \cot B)(\cot B + \cot C)(\cot C + \cot A) = \)
The ordinates of the points on the curve \( y = \tan^{-1}(\sin(\sqrt{x})) \), \( 0 \leq x \leq 8\pi^2 \), at which the tangent is parallel to the X-axis are:
For a positive real number \( \lambda \), if the vector \( \vec{a} = \lambda \vec{i} - 5\vec{j} + 6\vec{k} \) satisfies the equation \[ \left[ \vec{i} \times (\vec{a} \times \vec{i}) + \vec{j} \times (\vec{a} \times \vec{j}) + \vec{k} \times (\vec{a} \times \vec{k}) \right]^2 = 440, \] then \( \lambda = \)
One out of 9 ships is likely to sink when they are set on sail. When 6 ships are set on sail, the probability that exactly 3 of them will not arrive safely is:
The coefficient of \( x^3 \) in the expansion of \( (1 - x)^{\frac{3}{2}} \), where \( |x|<1 \), is:
If the extremities of a diagonal of a square are \( (1, -2, 3) \) and \( (2, -3, 5) \), then the length of its side is:
The set \( \{ x \in \mathbb{R} : 4 + 11x - 3x^2>0 \} \) is the interval:
The equation of a tangent to the circle \(x^2 + y^2 + 2x - 12y - 132 = 0\) which is perpendicular to the line \(12x + 5y + k = 0\) is:
If \( \int_0^{2024\pi} \frac{2023^{\sin^2 x}}{2023^{\sin^2 x} + 2023^{\cos^2 x}} dx = k \), then \( \left( \frac{2k}{\pi} + 1 \right) = \)
If \[ \frac{x + 2}{x^2 - 3} \text{ is one of the partial fractions of } \frac{3x^3 - x^2 - 2x + 17}{x^4 + x^2 - 12}, \text{ then the other partial fraction of it is:} \]
If \( 1, \omega, \omega^2 \) are the cube roots of unity and \( f(x, y) = (x + y)(x\omega + y\omega^2)(x\omega^2 + y\omega) \), then \( f(2, 3) \) is:
Assertion (A): \(\displaystyle \int_0^{\frac{\pi}{2}} (\sin^6 x + \cos^6 x)\, dx\) lies in the interval \(\left(\frac{\pi}{8}, \frac{\pi}{2}\right)\) Reason (R): \(\sin^6 x + \cos^6 x\) is a periodic function with period \(\dfrac{\pi}{2}\)
If \( \sqrt{-3 - 4i} = re^{i\theta} \), then \( r^2 \tan \theta = \)
In $ \triangle ABC $, if $ r = 1 $, $ R = 4 $, and $ \Delta = 8 $, then \[ \frac{1}{ab} + \frac{1}{bc} + \frac{1}{ca} = \]
If \( P, Q \) and \( R \) are \( 3 \times 3 \) matrices such that} \[ P = \begin{bmatrix} 3x^2 + x + 3 & 2x^2 - x + 4 & 7x^2 + 8x + 5 \\ 5x^2 + 3x + 2 & 4x^2 - 2x - 1 & 7x^2 + 5x + 8 \\ 3x^2 + 2x + 5 & 4x^2 - x - 2 & 3x^2 + 8x + 7 \end{bmatrix} = Px^2 + Qx + R \] then det \( R = \) ?
Let \( (1, 2) \) be the focus and \( x + y + 1 = 0 \) be the directrix of a hyperbola. If \( \sqrt{3} \) is the eccentricity of the hyperbola, then its equation is:
Assertion (A): The difference of the slopes of the lines represented by \( y^2 - 2xy \sec^2 \alpha + (3 + \tan^2 \alpha) \left( 1 + \tan^2 \alpha \right) \cos^2 \theta = 0 \) is 4. Reason (R): The difference of the slopes represented by \( ax^2 + 2hxy + by^2 = 0 \) is \( \frac{2\sqrt{h^2 - ab}}{|b|} \).
The number of natural numbers less than 10000 which are divisible by 5 and that no digit is repeated in the same number, is
\( \lim_{x \to -9} \frac{(2.5)^{81 - x^2} - (0.4)^{x + 9}}{x + 9} = \)
Planes $\pi_1$ and $\pi_2$ are defined by vectors. If $|\vec{a}| = \sqrt{14}$ and $\vec{a}$ is parallel to their intersection, then $|\vec{a} \cdot (\hat{i} + \hat{j} + \hat{k})| = $