List of top Mathematics Questions asked in AP EAPCET

If \[ \cos\alpha+\cos\beta+\cos\gamma=0 \] and \[ \sin\alpha+\sin\beta+\sin\gamma=0, \] then which of the following is true?

If \[ z=\frac{(1-i)^3}{(\sqrt{3}-i)^2}, \] then the complex conjugate of \(z\) is:

The locus of the point \(z=x+iy\) satisfying \[ \left|\frac{z-(2+i)}{z+(2-i)}\right|=2 \] is:

Let \(A\) be a \(3\times3\) matrix such that \[ AA^{T}=I_3. \] Then \(A\) is:

Let \(\alpha\) and \(\beta\) be the roots of \[ x^2+bx+c=0. \] If \[ \alpha^2+\beta^2=14 \] and \[ \alpha\beta=3, \] then the value of \(b^2\) is:

If \[ a_n= \sqrt{7+\sqrt{7+\sqrt{7+\cdots}}} \] (\(n\) radicals), then which of the following is true?

Let \(f,g,h\) be differentiable functions such that \[ \begin{vmatrix} f(x) & g(x) & h(x)\\ f'(x) & g'(x) & h'(x)\\ f''(x) & g''(x) & h''(x) \end{vmatrix} =0. \] Then which of the following statements is correct?

The function \[ f(x)=\sin\left(\log\left(x+\sqrt{x^2+1}\right)\right) \] is

Consider the system of linear equations \[ x+y+z=6, \] \[ x+2y+3z=10, \] \[ 3x+2y+\lambda z=\mu. \] If the system has infinitely many solutions, then the value of \(\mu+\lambda\) is:

The domain of the real-valued function \[ f(x)=\cos^{-1}\left(\frac{2-x}{4}\right)+[\log(3-x)]^{-1} \] is:

The general solution of the differential equation \( \frac{dy}{dx} + y \tan x = - \tan x \log(\cos x) \) (\(0 < x < \pi/2\)) is:

Among the following differential equations, the equation having order 2 and degree 3 is:

A circle passes through the ends of the latus rectum of parabola \( y^2=12x \) and has its centre at the vertex. The area inside the circle and outside the parabola in the \( 1^{st} \) quadrant is:

The integral \( \int_{0}^{\pi} |x \cos 2x| dx \) is equal to:

The integral \( \int_{\sqrt{2}}^{2} \frac{x}{(x^3 - x^2 + x - 1)(x+1)} dx \) is equal to:

Consider the differential equations \(\frac{dy}{dx}(x+y+1)=1\) and \(\frac{dx}{dy}=3y+2x^2\).
Which of the following is correct regarding these two differential equations?

The integral \( \int_{0}^{1} x^{5/2} (1-x)^{3/2} dx \) is equal to:

The integral \( \int \frac{\cos x - \sin x}{10 + \sin 2x} dx \) is equal to:

The length of the tangent drawn at the point \(P(1, 3\sqrt{3})\) on the curve is \(\frac{x^2}{3} + \frac{y^2}{27} = 4\):

The function \(f(x) = \frac{x}{2} + \frac{2}{x}\) has a local minimum at

The surface area of a cube is 150 sq. cm. If it is increased by 0.025 sq. cm, then the approximate increase in its volume (in c.c.) is:

If \(x > 0\), then \(\int \frac{1}{\sqrt{x^4 + 2x^3 + 2x^2}} dx =\)

The value of the integral \(\int \frac{dx}{\cos 2x + \sin 2x + 2\sin^2 x}\) is:

The integral \( \int \frac{\cos^3 x}{(1+\sin x)^4} dx \) is equal to:

If a cylindrical tank of radius 3 m is filled with water at the rate of \(\frac{3}{2} \, m^3/sec \), then the rate of change of its water level in (m/sec) is: