List of top Mathematics Questions asked in AP EAPCET

If $x = a \cos^3 t$ and $y = a \sin^3 t$, then the value of $\frac{dy}{dx}$ at $t = \frac{\pi}{4}$ is:

If $y = \tan^{-1}\left(\frac{\sin x + \cos x}{\cos x - \sin x}\right)$, then $\frac{dy}{dx} = $

The value of \[ \lim_{x\to0}\frac{\sin5x-5\sin x}{x^3} \] is:

If \[ f(x)= \begin{vmatrix} 2+\dfrac{\sin x}{x} & 1 & 3
[4pt] 2 & 1+\dfrac{\sin x}{x} & 3
[4pt] 2 & 1 & 3+\dfrac{\sin x}{x} \end{vmatrix}, \] then \[ \lim_{x\to 0} f(x)= \]

If \[ \lim_{x\to\infty} \left(\frac{ax^2+bx+c}{lx^2+mx+n}\right) \left(\frac{lx-1}{lx+a}\right)^{\frac{x}{2}} = \frac{3}{\sqrt{16e}}, \] then \[ \lim_{x\to0} \frac{l+mx+cx^2}{a+bx+nx^2} = \]

Evaluate \[ \lim_{x\to 0}\frac{x\cdot 2^x-x}{1-\cos x}. \]

If $\alpha,\beta$ are the roots of the equation \[ x^2-p(x+1)-c=0, \] then \[ \frac{\alpha^2+2\alpha+1}{\alpha^2+2\alpha+c} + \frac{\beta^2+2\beta+1}{\beta^2+2\beta+c} = \]

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 the roots of the equation \[ x^3-px^2+qx-s=0 \] are in geometric progression, then

Consider the quadratic expression \( f(x) = x^2 + (10-a)x - 10a \). The sum of all values of 'a', such that the roots of \( f(x)=3 \) are integers is:

The expression \( \frac{n(n + 1)^2(n+2)}{12} \) for all \( n \in \mathbb{N} \) is always:

If $\alpha, \beta$ are the roots of the quadratic equation $x^2 - 2x + 4 = 0$, then the value of $\alpha^n + \beta^n$ is:

The quadratic expression having zero's equal to the non-integral roots of \( ||3x-4|-6|=5 \) is:

If $\alpha,\beta$ $(\alpha<\beta)$ are the roots of \[ 2x^2-x-6=0 \] and \[ \alpha x^2+kx-\beta\leq0 \quad \forall x\in\mathbb{R}, \] then the number of integral values $k$ takes is

If the roots of the quadratic equation $x^2 - 2px + q^2 = 0$ are real and distinct, then:

If the roots of the equation $x^3 - 7x^2 + 14x - 8 = 0$ are in geometric progression, then the common ratio can be:

If \( a, b, c \in \mathbb{R} \) and \( -a^{2}x^{2}+bx+c>0 \quad \forall x \in \left(\frac{3-\sqrt{14}}{2},\frac{3+\sqrt{14}}{2}\right) \), then \( c^{2}-\left(\frac{b}{4}\right)^{2} = \)

A positive root of the equation \[ 18x^3-9x^2-5x+2=0 \] is twice another root of it. If among its three roots, the least value is \(a\) and the greatest value is \(b\), then \(2a+3b=\)

If $\alpha \neq \beta$ and $\alpha^2=5\alpha-3,\ \beta^2=5\beta-3$, then the equation whose roots are $\dfrac{\alpha}{\beta}$ and $\dfrac{\beta}{\alpha}$ is

If $\alpha,\beta,\gamma$ are the roots of \[ x^3-10x^2+7x+8=0, \] match List-I with List-II and choose the correct option.

For a quadratic expression \( ax^{2}+bx+c \), if the minimum value \( \frac{49}{12} \) exists at \( x=\frac{-5}{6} \), then \( 12c-5b = \)

If all the roots of the equation \[ x^5-3x^4-5x^3+27x^2-32x+12=0 \] are diminished by $h$ to get a transformed equation in which the constant term is missing, then the sum of the squares of all possible values of $h$ is

If \(\alpha,\beta,\gamma\) are the roots of the equation \[ 24x^3-10x^2-3x+1=0, \] then \[ \frac{1}{\alpha^2}+\frac{1}{\beta^2}+\frac{1}{\gamma^2} = \]

In a triangle \(ABC\), if \[ a=2,\qquad b=4,\qquad \cos C=-\frac{5}{16}, \] then the circumradius \(R\) is

If \[ A= \begin{bmatrix} c & -a & b\\ a & b & -c\\ -b & c & a \end{bmatrix}, \qquad B= \begin{bmatrix} 1 & 0 & 2\\ 0 & 1 & 2\\ 1 & 2 & 0 \end{bmatrix} \] and \[ AB= \begin{bmatrix} 4 & 4 & -2\\ 1 & 1 & 10\\ -1 & 5 & -4 \end{bmatrix}, \] then \(a^2+b^2+c^2=\)