List of top Questions asked in AP EAMCET- 2024

If $ y = f(x) $ is a thrice differentiable function and a bijection, then \[ \frac{d^2x}{dy^2} \left(\frac{dy}{dx}\right)^3 + \frac{d^2y}{dx^2} = ? \]

$\int\left(\frac{x}{x\cos x - \sin x}\right)^2 dx = $

If a tangent of slope 2 to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ touches the circle $x^2 + y^2 = 4$, then the maximum value of ab is:

The normal drawn at a point $ (2, -4) $ on the parabola $ y^2 = 8x $ cuts again the same parabola at $ (\alpha, \beta) $. Then $ \alpha + \beta $ is:

The locus of the midpoints of the chords of the hyperbola $ x^2 - y^2 = a^2 $ which touch the parabola $ y^2 = 4ax $ is:

If the product of the eccentricities of the ellipse $ \frac{x^2}{16} + \frac{y^2}{b^2} = 1 $ and the hyperbola $ \frac{x^2}{9} - \frac{y^2}{16} = 1 $ is 1, then the value of $ b^2 $ is:

If $$ y = (1 + a + a^2 + \dots)e^{nx} $$ then the relative error in $y$ is:

If the equation of the tangent at (2, 3) on y² = ax³ + b is y = 4x - 5, then the value of a² + b² is:

Given the function:

\[ f(x) = \begin{cases} \frac{2x e^{1/2x} - 3x e^{-1/2x}}{e^{1/2x} + 4e^{-1/2x}}, & \text{if } x \neq 0 \\ 0, & \text{if } x = 0 \end{cases} \]

Determine the differentiability of $ f(x) $ at $ x = 0 $.

If $ (\alpha, \beta, \gamma) $ are the direction cosines of an angular bisector of two lines whose direction ratios are (2,2,1) and (2,-1,-2), then $ (\alpha + \beta + \gamma)^2 $ is:

While solving a system of linear equations $ AX = B $ using Cramer’s rule, if \includegraphics[]{6.png}

The set of all real values of $ a $ such that the function $ f(x) = x^3 + 2ax^2 + 3(a+1)x + 5 $ is strictly increasing in its entire domain is:

If $ 4x - 3y - 5 = 0 $ is a normal to the ellipse $ 3x^2 + 8y^2 = k $, then the equation of the tangent at point (-2,m) is:

The line $ x - 2y - 3 = 0 $ cuts the parabola $ y^2 = 4ax $ at points P and Q. If the focus of this parabola is $ \left(\frac{1}{4}, k\right) $, then PQ is:

If the line $ 5x - 2y - 6 = 0 $ is a tangent to the hyperbola $ 5x^2 - ky^2 = 12 $, then the equation of the normal to this hyperbola at $ (\sqrt{6}, p) $ is:

If the angle between the asymptotes of the hyperbola $ x^2 - ky^2 = 3 $ is $ \frac{\pi}{3} $ and e is its eccentricity, then the pole of the line $ x + y - 1 = 0 $ w.r.t. this hyperbola is:

A point moves on the curve $ y = x^3 - 3x^2 + 2x - 1 $ and its y-coordinate increases at a rate of 6 units per second. When the point is at (2,-1), the rate of change of its x-coordinate is:

The length of the tangent drawn at the point $ P \left( \frac{\pi}{4} \right) $ on the curve $ x^{2/3} + y^{2/3} = 2^{2/3} $ is:

Assertion (A): Thymosin plays a major role in cell-mediated immunity
Reason (R): Thymosin promotes the production of antibodies

In some non chordates, during embryonic development, mesoderm occupies only a part of blastocoel adjoining ectoderm. The unoccupied portion of blastocoel persists as.

Identify the correct statements:
I. Veins are bright red in colour and provided with wide lumen
II. Veins are non-valvular and blood flows in veins by jerks.
III. Arteries are provided with thick tunica media.
IV. Veins end in capillaries and arteries start with capillaries.

Comparatively these are less harmful to the organisms

Book published by John Ray.

Match the following

Identify different types of intra uterine devices among the following