List of top Mathematics Questions asked in AP EAPCET

If \[ |z-3i|+|z+5i|=4, \] then the locus of \(z\) is:
If \[ A= \begin{bmatrix} 1 & 1 & a+1 1 & a+1 & 1 a+1 & 1 & 1 \end{bmatrix} \] is not an invertible matrix, then the sum of all the values of \(a\) is:
If \[ (x-iy)^{\frac{1}{3}}=2-i\sqrt{3} \] and the point \(z=(x,y)\) lies on the line \[ \frac{x}{2}+\frac{y}{\sqrt{3}}=k, \] then \(k=\)
If \[ \left|z+\frac{2}{z}\right|=2, \] then the maximum value of \(|z|\) is:
A complex number \(z\) among the following which does not satisfy \[ z^3+27i=0 \] is:
If \[ \begin{pmatrix} 5 & a & -7 \\ b & -7 & c \\ -7 & d & -1 \end{pmatrix} \] is the adjoint of the matrix \[ \begin{pmatrix} 1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2 \end{pmatrix}, \] then \(a+b+c+d=\)
The domain of the real valued function \[ f(x)=\sqrt{\frac{2-|x|}{3-|x|}} \] is:
If \(A\) and \(B\) are \(n\times n\) square matrices such that \[ (2A+B)^2+(A-3B)^2=5A^2-2AB+10B^2, \] then \(ABAB=\)
The rank of the matrix \[ A= \begin{bmatrix} 1 & -1 & 0 & -2 -4 & 4 & 0 & 8 -2 & 1 & 2 & 4 \end{bmatrix} \] is:
If the function \(f:\mathbb{R}\to\mathbb{R}\) is defined by \(f(x)=x|x|\), then \(f\) is:
If \( f(x) \) is the antiderivative of \( g(x) \) and \[ \int f(x) g(x)(1 + f^2(x)) dx = F(x) \], then \( F(x) = \)
Let \( \vec{a}, \vec{b} \) be non-collinear vectors, with \( |\vec{a}| = 2\sqrt{2} \), \( |\vec{b}| = 3 \), and the angle between them is \( 45^\circ \). Then the lengths of the diagonals of the parallelogram whose adjacent sides are \( \vec{5a} + \vec{2b} \) and \( \vec{a} - \vec{3b} \) are:
Let \( A = (1, -2, 3) \), \( B = (3, 1, -3) \), \( C = (-3, 1, 3) \) be the vertices of triangle \( ABC \). If \( \cos \theta = \frac{\vec{AB} \cdot \vec{AC}}{|\vec{AB}||\vec{AC}|} \), then \( \cos A \) is:
If \( y = \tan(3\tan^{-1} x) \), then: \[ (1 - 3x^2)\frac{d^2y}{dx^2} - 12x \frac{dy}{dx} = \]
The standard deviation of first 10 multiples of 4 is
An ellipse has lengths of major and minor axes as 6 and 2 respectively. If the center is at \( (5,6) \) and the major axis lies along the line \( x - y + 1 = 0 \), then the equation of the ellipse is:
For \(n \in N\), If \( I_n = \int \frac{\sin nx}{\sin x} dx = \frac{2}{n-1}\sin((n-1)x) + I_{n-2} \) and \( \int_0^{\pi} \frac{\sin nx}{\sin x} dx = \frac{k\pi}{2} \) then k =
If \( \int \frac{\sin(x-\pi/4)}{2+\sin 2x} dx = -\frac{1}{\sqrt{2}} \tan^{-1}(f(x)) + C \), then \(f(x) = \)
If $ a, b>0 $, then the minimum value of: $$ y = \frac{b^2}{a - x} + \frac{a^2}{x},\quad \text{for } 0<x<a $$
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
The rank of the matrix \( A = \begin{bmatrix} 2 & 1 & 2 \\ 1 & 0 & 1 \\ 4 & 1 & 4 \end{bmatrix} \) is
If the mean deviation of the data: $$ 1, 1 + d, 1 + 2d, \ldots, 1 + 100d $$ from their mean is 255, then find $ d $.
Let $$ G(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix} $$ If $ x + y = 0 $, then evaluate $ G(x)G(y) $
Which of the following quadratic equations whose real roots \( x_1, x_2 \) satisfy the conditions \( x_1^2 + x_2^2 = 5 \), \( 3(x_1^5 + x_2^5) = 11(x_1^3 + x_2^3) \)?