List of top Mathematics Questions asked in AP EAPCET

If \( -3 + ix^2y \) and \( x^2 + y + 4i \) are complex conjugates, then \( x = \):
If \( z = 1 + \cos\theta - i\sin\theta \) and \( 0<\theta<\pi \), then \[ \left[ |z - 1|^2 \cdot \frac{|z|^2}{4} \right]^{1/2} = \]
If \( C \) is a point on the straight line joining the points \( A = -2+i \) and \( B = 3 - 4i \) in the Argand plane and } \[ \frac{AC}{CB} = \frac{1}{2}, \] then the argument of \( C \) is
If \( z_1 = (2, -1) \) and \( z_2 = (6, 3) \), then find the amplitude of the expression \[ \text{amp}\left(\frac{z_1 - z_2}{z_1 + z_2}\right) \]
If \( \left| \frac{z - 2}{z} \right| = 2 \), then the greatest value of \( |z| \) is:
The slope of the tangent at any point $(x,y)$ on the curve is equal to the product of the coordinates of that point. If the equation of the normal to the curve at the point $(\sqrt{2},e)$ is $ax+by=1$, then $\dfrac{b}{a}=$
Evaluate the integral: \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin x \cdot \sin^2 x \cdot \cos x \, dx \]
If \[ \frac{d}{dx}\left( \frac{x^2}{(x+2)(2x+3)} \right) = \frac{-A}{(x+2)^2} + \frac{B}{(2x+3)^2}, \] then the value of \( A + B = \):
If \( f(x) = 3x + \frac{12}{x} \) is continuous on \( \mathbb{R} - \{0\} \) and \( M \) is its maximum value, then \( \displaystyle \lim_{x \to M} f(x) = \):
Let $f:\mathbb{R} \to \mathbb{R}$ be a differentiable function such that $|f(x)-f(y)| \le 2|x-y|^{3/2} \ \forall x,y \in \mathbb{R}$. If $f(0)=1$, then $\int_0^1 f^2(x)dx=$
If the tangent to the curve $x^3y^2 + \dfrac{x^2}{y} = 5$ is parallel to X-axis, then a point on its locus is:
If \[ \lim_{x \to 2} \frac{1 + \sqrt{1 + 4\log_2 x}}{2 + (2x + \sin^2 x + 2\cos x)(2x - 4)} = m, \] then \( m(m - 1) = \):
The curve represented by $x = t^5 + 5t^3 + 20t + 7$ and $y = 4t^3 - 3t^2 - 18t + 3$ is decreasing in the interval
If a normal drawn at a point \( P \) to the curve \( y = \sin x \) passes through the origin, then the locus of \( P \) is:
Evaluate the following integral: \[ \int (x^3 + x^2 m + x^m) (2x^{2m} + 3x^m + 6x^m) \, dx \]

$\displaystyle \int \frac{dx}{\sin(x-a)\cos(x-b)} =$

If $x^3 + y^3 = 3axy$, then at $\left(\frac{3a}{2}, \frac{3a}{2}\right)$ the value of $3a y'' + 40$ is:
The locus of the point on the curve \( y = \sin x \) where the tangent drawn at that point always passes through the point \( (0, \pi) \) is:
The ordinates of the points on the curve \( y = \tan^{-1}(\sin(\sqrt{x})) \), \( 0 \leq x \leq 8\pi^2 \), at which the tangent is parallel to the X-axis are:

$\int \frac{x^2}{(x^2-1)(x^2+1)} dx =$

Let \( f(x) \) be differentiable on \( \mathbb{R} \) and \( f'(m) \ne 0, m \in \mathbb{R} \). If \( \lim\limits_{x \to m} \frac{x f(m) - m f(x)}{x - m} + f'(m) = f(m) \), then \( m = \):

$\displaystyle \int_{\frac{1}{25}}^{1} x^{-2} e^{x^{-1/2}} dx =$

The positive value of \( x \) satisfying the equation \[ \int_0^x (1 - t) \, dt = \frac{1}{2} \] is:

If $f(x) = \frac{1 - x + \sqrt{9x^2 + 10x + 1}}{2x}$, then $\lim_{x \to -1^-} f(x) =$

The area (in sq units) of the triangle formed by the normal at point $(1,0)$ on the curve $x = e^{\sin y}$ with coordinate axes is: