List of top Mathematics Questions asked in AP EAPCET

If the mean deviation of the numbers $1, 1+d, 1+2d, \dots, 1+100d$ from their mean is 255, then $d =$

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

The value of the integral \( \int_{0}^{\pi/2} \sin^6 x \cos^4 x \, dx \) is equal to:

If \(O\) is the origin and \(H\) is the orthocenter of a triangle formed by the lines \[ x+y=1, \] \[ 6x^2-13xy+6y^2=0, \] then \[ OH= \]

The value of the integral \( \int_{-2\pi}^{2\pi} \sin^4 x \cos^6 x \, dx \) is equal to:

If \[ A(0,1,-2),\quad B(-1,2,-3),\quad C(2,-3,4) \] and \[ D(3,4,5) \] are the vertices of a tetrahedron \(ABCD\), then the volume of the tetrahedron is

The value of the definite integral $\int_0^{\pi/2} \ln(\tan x) \, dx$ is:

If the unit vector which is perpendicular to the normals drawn to the planes \[ \vec r\cdot(2\hat{i}+\hat{j}-\hat{k})=3 \] and \[ \vec r\cdot(6\hat{i}+3\hat{j}+2\hat{k})=4 \] is \[ x\hat{i}+y\hat{j}+z\hat{k}, \] then \(x+y+z=\)

If \( A(1,0,1) \), \( B(0,1,-1) \), \( C(-1,1,0) \) are the vertices of a triangle ABC, then \( \cos^{2}A+\cos^{2}B = \)

If the equation \[ x^4-10x^3+37x^2-60x+36=0 \] has two distinct real roots, where each one of them is a repeated root, then the sum of squares of all the roots of the given equation is

In \(\triangle ABC\), if \[ \overrightarrow{AB}=2\hat{i}-\hat{j}+2\hat{k} \] and \[ \overrightarrow{AC}=3\hat{i}-3\hat{j}+4\hat{k}, \] then the triangle \(ABC\) is

A dice is thrown twice. If getting a number greater than four is considered a success, the variance of the probability distribution of the number of successes is

Let A be the resulting point after the point (4, 1) undergoes the following transformations successively:
i. reflection in the line \( y=x \)
ii. translation through a distance of 2 units along the positive direction of X-axis.
If the axes are rotated through an angle of \( \frac{\pi}{4} \) about origin in the positive direction, then the coordinates of the point A are

When the origin is shifted to $(2, 3)$ by translation of axes, the coordinates of a point $P$ become $(1, -2)$. The original coordinates of $P$ are:

The area (in square units) of the region bounded by the parabola $y^2 = 4x$ and the line $y = 2x$ is:

Let \[ A= \begin{bmatrix} 1 & 2\\ 2 & 1 \end{bmatrix}. \] Then the determinant of \(A^2\) is:

For \(n\in\mathbb{N}\), \[ 1^2+2^2+3^2+\cdots+n^2 > \]

If the axes are rotated about the origin in positive direction through an angle of \(30^\circ\), then the transformed equation of \[ x^2+2\sqrt{3}xy-y^2=2a^2 \] is

The determinant \[ \det \begin{bmatrix} \frac{a^2 + b^2}{c} & c & c a & \frac{b^2 + c^2}{a} & a b & b & \frac{c^2 + a^2}{b} \end{bmatrix} \] is equal to:

The area (in square units) of the region bounded by the parabola $y^2 = 4x$ and the line $y = 2x$ is:

If \[ A= \begin{bmatrix} 1&2\\ 3&4 \end{bmatrix}, \] then \(\det(A)\) is equal to:

If the tangent drawn at \((\sqrt2,1)\) on the circle \[ x^2+y^2=3 \] is also a tangent to the two circles of equal radius \(2\sqrt3\) with centres at \[ (0,\beta_1) \quad \text{and} \quad (0,\beta_2), \] then \[ |\beta_1-\beta_2|= \]

The domain of the function $f(x) = \sqrt{\log_{10} \left(\frac{5x - x^2}{4}\right)}$ is:

If the straight lines $x + 2y - 9 = 0$, $3x + 5y - 5 = 0$ and $ax + by - 1 = 0$ are concurrent, then the straight line $22x - 35y = 1$ passes through the point: