List of top Mathematics Questions asked in AP EAPCET

The function $ y = x^3 - ax^2 + 48x + 7 $ is increasing for all real values of $ x $. Find the interval in which $ a $ lies:
The range of the data set: \( 35, 12, 21, 24, 15, 7, 16, 12, 30, 32, 13, 17 \) is:
Let \( A = \begin{bmatrix} n & 0 & 0 \\ 0 & n & 0 \\ 0 & 0 & n \end{bmatrix} \) and \( B = \begin{bmatrix} 0 & 0 & n \\ 0 & n & 0 \\ n & 0 & 0 \end{bmatrix} \). Then \( A^2 + B^2 + AB = \)
If a matrix A satisfies the equation \( A^3 - 6A^2 + 11A - 6I = 0 \), then \( A^{-1} \) can be
If the point \( (2, \lambda) \) lies inside the circles \( x^2 + y^2 = 13 \) and \( x^2 + y^2 + x - 2y = 14 \), then \( \lambda \) lies in the set:
If $ x = f(\theta) $, $ y = g(\theta) $, then find: $$ \frac{d^2 y}{dx^2} $$
If \(A = \begin{bmatrix}x & 2 & 1 \\ 2 & x & 1 \\ 2 & 1 & 0\end{bmatrix}\) and \(\det(A) = 125\), then \(x =\)
In a triangle \( ABC \), if \( a : b : c = 4 : 5 : 6 \), the ratio of radius of the circumcircle to that of the incircle is:
If \( a^2+b^2+c^2=1, a,b,c \in R \), then the set of extreme values of \(ab+bc+ca\) is
\( \lim_{x \to \frac{\pi}{2}} \frac{1-\tan\frac{x}{2}}{1+\tan\frac{x}{2}} \cdot \frac{1-\sin x}{(\pi-2x)^3 = \)}
Find the values of $ x $ for which the expressions $$ \sin x + i\cos 2x \quad \text{and} \quad \cos x - i\sin 2x $$ are conjugate to each other.
There are 10 points in a plane, out of which 6 are collinear. If $ N $ is the number of triangles that can be formed, then $ N = $ ?
Solve: $$ 4^x - 3^{x - \frac{1}{2}} = 3^{x + \frac{1}{2}} - 2^{2x - 1} $$
Let \( \vec{a} = \hat{i} + x\hat{j} + \hat{k} \), \( \vec{b} = \hat{i} - \hat{j} + \hat{k} \) and \( |\vec{a}+\vec{b}| = |\vec{a}| + |\vec{b}| \) then
If \( \frac{4x^3 + 16x + 7}{(x^2 + 4)^2} = \frac{Ax + B}{x^2 + 4} + \frac{Cx + D}{(x^2 + 4)^2} \), then the number of non-zero values among \( A, B, C, D \) is:
The equation of the family of curves for which the length of the subnormal at any point \((x,y)\) is always a constant \(k\) is
If the differential equation obtained by eliminating \(A, B\) from \(y = (\sin^{-1}x)^2 + A \cos^{-1} x + B\) is \((a-x^2)y'' - xy' = b\), then \(\frac{b+a}{b-a} =\)
The general solution of \(\frac{d^2 y}{dx^2} = 0\) is
Evaluate \[ \int_{\frac{\pi}{11}}^{\frac{9\pi}{22}} \frac{dx}{1+\sqrt{\tan x}} \]
If \(m,n\in \mathbb{Z}\), then \[ \int_0^{2\pi}\cos mx\cos nx\,dx+\int_{-\pi}^{\pi}\sin mx\cos nx\,dx= \]
Evaluate \[ \int_2^5 \sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\,dx \]
Evaluate \(\lim_{n \to \infty} \frac{1}{\sqrt{n}} \left[ 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \cdots + \frac{1}{\sqrt{n}} \right]\)
If \[ \int (1+x)\log(1+x^2)\,dx= \left(x+\frac{x^2}{2}+\frac{1}{2}\right)\log(1+x^2)+g(x)+C, \] then \(g(x)=\)
The minimum value of \[ \left(1+\frac{1}{\sin^n\alpha}\right) \left(1+\frac{1}{\cos^n\alpha}\right) \] is
Evaluate \(\int \tan^{-1}(1-x+x^2) \, dx + \int \tan^{-1}(x) \, dx + \int \tan^{-1}(1-x) \, dx\)