List of top Mathematics Questions asked in AP EAPCET

The equation of a circle which touches the straight lines $x + y = 2$, $x - y = 2$ and also touches the circle $x^2 + y^2 = 1$ is:

If the ordinates of points $ P $ and $ Q $ on the parabola \[ y^2 = 12x \] are in the ratio 1:2, then the locus of the point of intersection of the normals to the parabola at $ P $ and $ Q $ is:

The product of perpendiculars from the two foci of the ellipse $$ \frac{x^2}{9} + \frac{y^2}{25} = 1 $$ on the tangent at any point on the ellipse is:

The value of $ c $ such that the straight line joining the points \[ (0,3) \quad \text{and} \quad (5,-2) \] is tangent to the curve \[ y = \frac{c}{x+1} \] is:

If the plane \[ x - y + z + 4 = 0 \] divides the line joining the points \[ P(2,3,-1) \quad \text{and} \quad Q(1,4,-2) \] in the ratio $ l:m $, then $ l + m $ is:

If the line with direction ratios \[ (1, a, \beta) \] is perpendicular to the line with direction ratios \[ (-1,2,1) \] and parallel to the line with direction ratios \[ (\alpha,1,\beta), \] then $ (\alpha, \beta) $ is:

The equation of the plane which bisects the angle between the planes $$ 3x - 6y + 2z + 5 = 0 \quad \text{and} \quad 4x - 12y + 3z - 3 = 0 \quad \text{which contains the origin is:} $$

Evaluate the limit: \[ \lim_{x \to 0} \frac{\sin(\pi \cos^2 x)}{x^2}. \]

If the function \[ f(x) = \frac{\sqrt{1+x} - 1}{x} \] is continuous at $ x = 0 $, then $ f(0) $ is:

If \[ \frac{d}{dx} \left(\frac{1 + x^2 + x^4}{1 + x + x^2}\right) = ax + b, \] then $ (a,b) $ is:

If the percentage error in the radius of a circle is 3, then the percentage error in its area is:

The distance $ s $ traveled by a particle in time $ t $ is given by: $$ s = 4t^2 + 2t + 3. $$ The velocity of the particle when $ t = 3 $ seconds is:

Evaluate the integral \[ \int \frac{\sin^6 x}{\cos^8 x} \, dx. \]

Evaluate the integral \[ \int \frac{x^5}{x^2 + 1} dx. \]

Evaluate the integral \[ \int \sum_{r=0}^{\infty} \frac{x^r 3^r}{2r} dx. \]

Evaluate the integral \[ \int e^x (x+1)^2 dx. \]

Evaluate the integral \[ I = \int_1^5 \left( |x - 3| + |1 - x| \right) \, dx \]

The solution of the differential equation \[ \frac{dy}{dx} = \frac{y + x \tan \left( \frac{y}{x} \right)}{x}. \] \[ \sin\frac{y}{x} = \]

Sum of the positive roots of the equation: \[ \begin{vmatrix} x^2 + 2x + 2 & x + 2 & 1 \\ 2x + 1 & x - 1 & 1 \\ x + 2 & -1 & 1 \end{vmatrix} = is \; 0. \]

If the point $ P $ represents the complex number $ z = x + iy $ in the Argand plane and if \[ \frac{z\bar{z} + 1}{z - 1} \] is a purely imaginary number, then the locus of $ P $ is:

The set $ S = \{ z \in \mathbb{C} : |z + 1 - i| = 1 \} $ represents:

If $ 2x^2 + 3x - 2 = 0 $ and $ 3x^2 + \alpha x - 2 = 0 $ have one common root, then the sum of all possible values of $ \alpha $ is:

If a polygon of $ n $ sides has 275 diagonals, then $ n $ is:

If $ a_n = \sum_{r=0}^{n} \frac{1}{\binom{n}{r}} $, then $ \sum_{r=0}^{n} r \binom{n}{r} = $:

Given the equation: $$ \frac{A}{x-a} + \frac{Bx + C}{x^2 + b^2} = \frac{1}{(x-a)(x^2 + b^2)} $$ then $ C $=