List of top Mathematics Questions asked in AP EAPCET

If a real valued function \(f : A \to B\) defined by \(f(x)=|x|-[x]\) is a bijection, then \(A\) and \(B\) are respectively:

Evaluate \[ \lim_{n\to\infty} \frac{1+2^4+3^4+\cdots+n^4}{n^5} - \lim_{n\to\infty} \frac{1+2^3+3^3+\cdots+n^3}{n^5}. \]

The integral \[ \int \frac{1}{\sqrt[4]{(x-1)^3(x+2)^5}} \, dx \] is equal to:

A vector \( \vec{a} \) has components \( 2p \) and \( 1 \) with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the positive direction. If with respect to the new system, \( \vec{a} \) has components \( p+1 \) and \( 1 \), then the values of \( p \) are:

If \(A(1,1,1)\), \(B(2,3,4)\) and \(C(2,5,7)\) are the vertices of \(\triangle ABC\), then the length of the altitude drawn through the vertex \(A\) is:

The variance of the data \[ 4,\;7,\;8,\;10,\;13,\;16,\;19 \] is

The maximum area of a rectangle inscribed in a circle of radius $r$ is:

The equation of the normal to the curve \( y = \log_e x \) at the point \( P(1,0) \) is ____.

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?

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 value of the integral \( \int_{0}^{32\pi} \sqrt{1 - \cos 4x} \, dx \) is equal to:

The minimum value of the function $f(x) = x^2 + \frac{250}{x}$ for $x > 0$ is:

In a binomial distribution, the mean is 4 and the variance is 3. Then the number of trials $n$ is:

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

If the ends of the major axis \(A'\) and \(A\) of the ellipse \[ \frac{(x-2)^2}{a^2}+\frac{(y-3)^2}{b^2}=1 \] are respectively at distances \(9\) and \(3\) units from a directrix \(L\), then the foci of the ellipse are:

If \[ z=\cos\theta+i\sin\theta, \] then \(|z|\) is equal to:

If $a_n = \sum_{r=0}^n \frac{1}{^{n}C_r}$ and $b_n = \sum_{r=0}^n \frac{r}{^{n}C_r}$, then $\frac{b_n}{a_n} =$

A bag \(P\) contains \(5\) white and \(4\) blue balls. Another bag \(Q\) contains \(4\) white and \(5\) blue balls. One ball is drawn at random from bag \(P\) and transferred to another bag. Then one ball is drawn from bag \(Q\). Find the probability that the ball drawn from bag \(Q\) has the same colour as the ball transferred from bag \(P\).

The minimum value of the function $f(x) = x^2 + \frac{250}{x}$ for $x > 0$ is:

If the circle $x^2 + y^2 - 4x - 6y + \lambda = 0$ touches the x-axis, then the value of $\lambda$ is:

If \[ {}^{n}P_{4}=5040 \] and \[ {}^{15}P_{r}=2730, \] then the value of \(n+r\) is:

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

The equations of the pairs of opposite sides of a parallelogram are \[ x^2-5x+6=0 \] and \[ y^2-6y+5=0. \] Then the equations of its diagonals are

The maximum value of $y = x(\log x)^2$ is:

If \(\sin\theta\neq 0\) and \[ \frac{1}{2}\sin\theta,\quad \cos\theta,\quad \cot\theta \] are in geometric progression, then the number of values of \(\theta\) lying in the interval \((-2\pi,2\pi)\) is