List of top Mathematics Questions asked in AP EAPCET

If $$ \sin x \sqrt{\cos y} - \cos y \sqrt{\sin x} = 0, $$ then find $$ \frac{dy}{dx}. $$

If the tangent of the curve $$ 4y^3 = 3ax^2 + x^3 $$ drawn at the point $ (a, a) $ forms a triangle of area $\frac{25}{24}$ sq. units with the coordinate axes, then find $ a $.

If $$ f(x) = 2 + |\sin^{-1} x|, $$ and $$ A = \{ x \in \mathbb{R} \mid f'(x) \text{ exists} \}, $$ then find $ A $.

The points $ A(-1, 2, 3), B(2, -3, 1), C(3, 1, -2) $ are:

If $ \theta $ is the angle subtended by a latus rectum at the center of the hyperbola having eccentricity $$ \frac{2}{\sqrt{7} - \sqrt{3}}, $$ then find $ \sin \theta $.

The tangent drawn at an extremity (in the first quadrant) of latus rectum of the hyperbola $$ \frac{x^2}{4} - \frac{y^2}{5} = 1 $$ meets the x-axis and y-axis at $ A $ and $ B $ respectively. If $ O $ is the origin, find $$ (OA)^2 - (OB)^2. $$

If the equation of the plane passing through point $ (3, 2, 5) $ and perpendicular to the planes $$ 2x - 3y + 5z = 7, \quad 5x + 2y - 3z = 11 $$ is $$ x + by + cz + d = 0, $$ then find $ 2b + 3c + d $.

Evaluate: $$ \lim_{x \to \infty} \left[ x - \log(\cosh x) \right] $$

Evaluate: $$ \lim_{x \to \infty} \left( \sqrt[3]{x^3 + 4x^2} - \sqrt{x^2 - 3x} \right) $$

The direction cosines of the line making angles $$ \frac{\pi}{4}, \frac{\pi}{3} $$ and $ \theta $ (where $ 0<\theta<\frac{\pi}{2} $) with X, Y, and Z axes respectively are:

The circles $$ x^2 + y^2 - 2x - 4y - 4 = 0 $$ and $$ x^2 + y^2 + 2x + 4y - 11 = 0 $$ ...

If the line $$ 4x - 3y + 7 = 0 $$ touches the circle $$ x^2 + y^2 - 6x + 4y - 12 = 0 $$ at $ (\alpha, \beta) $, then find $ \alpha + 2\beta $.

The slope of the common tangent drawn to the circles $$ x^2 + y^2 - 4x + 12y - 216 = 0 $$ and $$ x^2 + y^2 + 6x - 12y + 36 = 0 $$ is:

If $ r_1 $ and $ r_2 $ are radii of two circles touching all the four circles $$ (x \pm r)^2 + (y \pm r)^2 = r^2, $$ then find the value of $$ \frac{r_1 + r_2}{r}. $$

If the equation of the circle having the common chord to the circles $$ x^2 + y^2 + x - 3y - 10 = 0 $$ and $$ x^2 + y^2 + 2x - y - 20 = 0 $$ as its diameter is $$ x^2 + y^2 + \alpha x + \beta y + \gamma = 0, $$ then find $ \alpha + 2\beta + \gamma $.

If $ x - y - 3 = 0 $ is a normal drawn through the point $ (5, 2) $ to the parabola $ y^2 = 4x $, then the slope of the other normal that can be drawn through the same point to the parabola is?

If the normal drawn at the point $$ P \left(\frac{\pi}{4}\right) $$ on the ellipse $$ x^2 + 4y^2 - 4 = 0 $$ meets the ellipse again at $ Q(\alpha, \beta) $, then find $ \alpha $.

If the incentre of the triangle formed by lines $$ x - 2 = 0, \quad x + y - 1 = 0, \quad x - y + 3 = 0 $$ is $ (\alpha, \beta) $, then find $ \beta $.

The points $ (2,3) $ and $ \left(-4, \frac{4}{3}\right) $ lie on opposite sides of the line $$ L = 5x - 6y + k = 0, $$ and $ k $ is an integer. If the points $ (1, 2) $ and $ (4, 5) $ lie on the same side of the line, then the perpendicular distance from the origin to the line $ L = 0 $ is?

If the equation of the pair of straight lines intersecting at $ (a, b) $ and perpendicular to the pair $$ 3x^2 - 4xy + 5y^2 = 0 $$ is $$ lx^2 + 2hxy + my^2 = 0, $$ then find $$ \frac{a + b + c}{l + h + m}. $$

Let $ A(4, 3), B(2, 5) $ be two points. If $ P $ is a variable point on the same side of the origin as that of line $ AB $ and at most 5 units from the midpoint of $ AB $, then the locus of $ P $ is:

PQR is a right angled isosceles triangle with right angle at $ P(2, 1) $. If the equation of the line $ QR $ is $$ 2x + y = 3, $$ then the equation representing the pair of lines $ PQ $ and $ PR $ is:

By shifting the origin to the point (2, 3) through translation of axes, if the equation of the curve $$ x^2 + 3xy - 2y^2 + 4x - y - 20 = 0 $$ is transformed to the form $$ Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0, $$ then find $ D + E + F $.

From the word "CURVE", how many 3-letter words can be formed out of all 2-letter or more combinations (with all distinct letters)? Find probability of getting a 3-letter word.