List of top Mathematics Questions asked in AP EAPCET

The integral $\int \frac{e^x (1 + x)}{\cos^2(x e^x)} \, dx =$

If $y = e^{a \sin^{-1} x}$, then $(1 - x^2) y_2 - x y_1 =$

The slope of the normal to the curve $y = 2x^2 + 3\sin x$ at $x = 0$ is:

The minimum value of the function $f(x) = x^2 + \frac{250}{x}$ for $x > 0$ is:

A balloon, which always remains spherical, has a variable radius. The rate at which its volume is increasing with respect to its radius $r$ when $r = 5$ cm is:

If $x = a \cos^3 t$ and $y = a \sin^3 t$, then the value of $\frac{dy}{dx}$ at $t = \frac{\pi}{4}$ is:

If $y = \tan^{-1}\left(\frac{\sin x + \cos x}{\cos x - \sin x}\right)$, then $\frac{dy}{dx} = $

The value of $\lim_{x \to \infty} \left(\frac{x+6}{x+1}\right)^{x+4}$ is:

If $f(x) = \frac{k \cos x}{\pi - 2x}$ for $x \neq \frac{\pi}{2}$ and $f\left(\frac{\pi}{2}\right) = 3$ is continuous at $x = \frac{\pi}{2}$, then the value of $k$ is:

The line $y = mx + c$ touches the ellipse $9x^2 + 16y^2 = 144$ if the value of $c^2$ is:

The ratio in which the $xy$-plane divides the line segment joining the points $(2, 4, 5)$ and $(3, 5, -4)$ is:

If a line makes angles $45^\circ$ and $60^\circ$ with the positive $x$ and $y$ axes respectively, then the acute angle it makes with the $z$-axis is:

The acute angle between the planes $2x - y + z = 6$ and $x + y + 2z = 3$ is:

If the eccentricity of a hyperbola is $\sqrt{3}$, then the eccentricity of its conjugate hyperbola is:

If the circle $x^2 + y^2 + 2x - 2y + c = 0$ cuts the circle $x^2 + y^2 - 4x - 6y + 11 = 0$ orthogonally, then the value of $c$ is:

The equation of the common chord of the circles $x^2 + y^2 - 4x - 4y = 0$ and $x^2 + y^2 - 6x - 8y + 10 = 0$ is:

If the circle $x^2 + y^2 - 4x - 6y + \lambda = 0$ touches the x-axis, then the value of $\lambda$ is:

If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is:

The equation of the parabola with focus at $(3, 0)$ and directrix $x + 3 = 0$ is:

If the angle between the pair of lines $x^2 - 2cxy - 7y^2 = 0$ is $\frac{\pi}{3}$, then the value of $c^2$ is:

If the lines joining the origin to the points of intersection of the line $y = mx + 1$ and the circle $x^2 + y^2 = 1$ are perpendicular to each other, then the value of $m^2$ is:

If the straight lines $x + 2y - 9 = 0$, $3x + 5y - 5 = 0$ and $ax + by - 1 = 0$ are concurrent, then the straight line $22x - 35y = 1$ passes through the point:

The distance between the parallel lines $5x + 12y - 3 = 0$ and $5x + 12y + 10 = 0$ is:

If the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ passes through the origin, has radius 3, and its center lies on the line $x + y = 4$, then $g + f =$

A random variable $X$ has the following probability distribution:
$X = x$: 0, 1, 2, 3, 4, 5
$P(X=x)$: $k$, $3k$, $5k$, $7k$, $9k$, $11k$
Then the value of $k$ is: