List of top Mathematics Questions asked in AP EAPCET

The value of \(c\) of Lagrange's Mean Value Theorem for \[ f(x)=\sqrt{25-x^2} \] on \([1,5]\) is:

Identify the correct set of molecules with zero dipole moment:

The value of \[ \lim_{n \to \infty} \left\{ \frac{1}{n+m} + \frac{1}{n+2m} + \frac{1}{n+3m} + \dots + \frac{1}{n+nm} \right\} \] is:

In a \(\triangle ABC\), \(a = 1, b = \sqrt{3}\) and \(\angle C = \frac{\pi}{6}\). Then the measure of the third side \(c =\)

If the area of triangle \(ABC\) is \(b^2 - (c - a)^2\), then \(\tan B =\)

In a triangle \(\triangle ABC\), if \(a, b,\) and \(c\) are in arithmetic progression, then \(\cos A + 2 \cos B + \cos C =\)

If \(I = \int \frac{\sin x + \sin^3 x}{\cos 2x} dx = P \cos x + Q \log \left| \frac{\sqrt{2} \cos x - 1}{\sqrt{2} \cos x + 1} \right|\) (where \(c\) is a constant of integration), then values of \(P\) and \(Q\) are respectively

The equation of the normal to the curve \( y = \log_e x \) at the point \( P(1,0) \) is ____.

If the direction ratios of two lines are given by $ l + m + n = 0 $ and $ mn - 2ln + lm = 0 $, then the angle between the lines is:

Let the function $ f(x) $ be defined as $ f(x) = \frac{x - |x|}{x} $, then:

Gas is being pumped into a spherical balloon at the rate of $ 30 \, \text{ft}^3/\text{min} $. Then the rate at which the radius increases when it reaches the value $ 15 \, \text{ft} $ is:

Let \[ f(x)=\int \frac{\sqrt{x}}{(1+x)^2}\,dx \quad (x\geq 0) \] Then \[ f(3)-f(1) \] is equal to:

The value of the definite integral $\int_0^{\pi/2} \ln(\tan x) \, dx$ is:

The solution of the differential equation $x \frac{dy}{dx} + 2y = x^2$ is:

The integral $\int \frac{dx}{x(x^4 + 1)} =$

If $y = \sqrt{\tan x + \sqrt{\tan x + \sqrt{\tan x + \dots \infty}$, then $(2y - 1)\frac{dy}{dx} =$

The value of the limit $\lim_{x \to 0} \frac{e^{3x} - e^{-2x}}{\sin 4x}$ is:

The distance of the point $(1, 2)$ from the line $3x + 4y - 32 = 0$ measured parallel to the line $x - y = 0$ is:

The length of the intercept made by the circle $x^2 + y^2 - 10x + 4y + 9 = 0$ on the x-axis is:

The equation of the tangent to the parabola $y^2 = 8x$ which is parallel to the line $2x - y + 5 = 0$ is:

If the probability that a person suffers a bad reaction from an injection is $0.001$, then the probability that out of $2000$ individuals, exactly $3$ will suffer a bad reaction is:

The number of ways of arranging the letters of the word "EAPCET" is:

If $\vec{a}$, $\vec{b}$, and $\vec{c}$ are three unit vectors such that $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, then the value of $\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}$ is:

If the sum of two roots of the cubic equation $x^3 - 5x^2 - 2x + 24 = 0$ is $2$, then the roots of the equation are:

If $\omega$ is a complex cube root of unity, then $(1 - \omega + \omega^2)^5 + (1 + \omega - \omega^2)^5 =$