List of top Mathematics Questions asked in AP EAPCET

If $$ ^{10}C_2 = ^{3^{n+1}}C_3 $$ then the value of $ n $ is:

If $ a, b>0 $, then the minimum value of: $$ y = \frac{b^2}{a - x} + \frac{a^2}{x},\quad \text{for } 0<x<a $$

The sum of the real roots of the equation: $$ x^4 - 2x^3 + x - 380 = 0 $$ is:

If variance of a Poisson distribution is 3, find: \[ P(1<X<4) \]

Find the distance between the directrices of the ellipse: \[ \frac{x^2}{36} + \frac{y^2}{20} = 1 \]

In any triangle $ ABC $, evaluate: $$ \frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} $$

Sides passing through vertex $ (\alpha, \beta) $ of a triangle are bisected at right angles by the lines: $$ y^2 - 8xy - ax^2 = 0 $$ Find the coordinates of the centroid of the triangle.

An integrating factor of the differential equation \( (x^2+1)\frac{dy}{dx} + xy = x^3 \) is

\( \int_{-\pi/4}^{\pi/4} \cos^8 x \ dx = \)

If \( f(x) = \sin(\tan^{-1} x) \), then \( \int_0^1 xf''(x)dx = \)

If an open cylinder of given surface area has maximum volume then its radius is

If \(x+y=k, x>0, y>0\) then \(x^2+y^2\) is minimum if

If \( \int \frac{x^8+4}{x^4-2x^2+2} dx = Ax^5+Bx^3+Cx+K \), then \(5A+3B+C = \)

If \( f(x) = \begin{cases 4 & -\infty<x<-\sqrt{5}
x^2-1 & -\sqrt{5} \le x \le \sqrt{5}
4 & \sqrt{5}<x<\infty \end{cases} \). If k is the number of points where f(x) is not differentiable then k -- 2 =}

Assertion (A) : \( f(x)=|x| \) is differentiable at \( x=a \neq 0 \) and continuous but not differentiable at \( x=0 \) Reason (R) : If a function is differentiable at a point then it is continuous at that point. But converse is not true. .

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

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

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

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

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 \(p^2+q^2 = \)

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