List of top Mathematics Questions asked in AP EAPCET

Equation of tangent to the curve \( y = x + \frac{4}{x^2} \) which is parallel to x-axis is

The normal to the curve y = f(x) at the points (3, 4) makes an angle \( \frac{3\pi}{4} \) with positive x-axis then \(f'(3) = \)

The minimum distance of a point on the curve \( y = x^2 - 4 \) from the origin is

If the centroid of a triangle with vertices \((4, p, -3), (-1, -1, 2)\) and \((3, 5, -8)\) is given by mid point of \((1, 4, -2)\) and \((q, 2, -4)\), then \(p^2+q^2 = \)

\( \lim_{x \to 0} x^3 (\sqrt{x^2+\sqrt{x^4+1}} - \sqrt{2}x) = \)

\( \lim_{x \to a} \frac{x^3+a^3}{x+a} = 7 \implies a = \)

\( \lim_{x \to \frac{\pi}{2}} \frac{1-\tan\frac{x}{2}}{1+\tan\frac{x}{2}} \cdot \frac{1-\sin x}{(\pi-2x)^3 = \)}

A ray makes angles \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) with Y and Z-axes respectively. Then the value of the sine of the angle made by the ray with X-axis is

A plane meets the X, Y, Z -- axes in A, B, C respectively. If the centroid of the triangle ABC is \((2, -3, 5)\) then the perpendicular distance from origin to the given plane is

In a square ABCD of side length a, suppose AB and AD are along the coordinate axes. Then the circle that circumscribes the square is

The length of the latus rectum of the parabola \( y^2-4x-4y+8=0 \) is

The eccentricity of the ellipse \( 9x^2+16y^2=144 \) is

If the equation of the tangent to the circle \(x^2+y^2=a^2\) at \(P(x_1, y_1)\) is \(x x_1 + y y_1 = K\), then K =

The locus of the point of intersection on the line \( \sqrt{3}x - y - 4\sqrt{3}k = 0 \) and \( \sqrt{3}kx + ky - 4\sqrt{3} = 0 \) for different real values of k is a hyperbola H. If e is the eccentricity of H then \(4e^2 = \)

The equation of the line which is a normal to the curve \(3x^2-xy+y^2=3\) at \((1,1)\) is

Suppose ABOC is a rhombus in the first quadrant with O being the origin. If the vertices B and C of \(\triangle ABC\) lie respectively on \(y=\frac{x}{\sqrt{3}}\) and \(y=0\), and the side BC passes through \((\frac{2}{3}, \frac{2}{3})\), then the midpoint of BC is

If \( ax^2 - 34xy - 5y^2 + 2x + 26y - 5 = 0 \) represents a pair of straight lines, then the value of a is

The equations of the lines perpendicular to \(x^2 - 5xy + 4y^2 = 0\) and passing through (2, 1) is

The straight line touching the circle \(x^2+y^2-2x-3=0\) and remaining normal to the circle \(x^2+y^2-4y-6=0\) is

The ratio of the areas of the greatest and the smallest circles touching \((x \pm 1)^2 + (y \pm 1)^2 = 1\) is (The equation \((x \pm 1)^2 + (y \pm 1)^2 = 1\) represents four circles with radius 1, centered at (1,1), (1,-1), (-1,1), (-1,-1).)

The equation of circle with centre (2, -3) and touching x-axis is

Suppose the hypotenuse and its opposite vertex of an isosceles right angled triangle are \(3x+4y-4=0\) and \((2,2)\) respectively. Then, which of the following is another side of the triangle?

A point P on a line is at a distance of 4 units from the origin (0, 0). If the line makes 60\(^\circ\) with the negative direction of the x-axis, then P is

A point P(x, y) is such that the sum of squares of its distances from (a, 0) and (--a, 0) is \(2b^2\). The equation representing the locus of P is

From a well shuffled pack of 52 cards, two cards are drawn at random. Then, the probability of both the cards being kings is