List of top Mathematics Questions asked in AP EAPCET

The origin is shifted to (2, 3) and axes are rotated through angle \(\theta\). If \(3x^2+2xy+3y^2-18x-22y+50=0\) transforms to \(4x^2+2y^2-1=0\), then \(\theta =\)

A variable circle passes through the fixed point \(A(p,q)\) and touches the X-axis. The locus of the other end of the diameter through A is

A random variable X takes values 0, 1, 2, 3 and its mean is 1.3. If $P(X=3)=2P(X=1)$ and $P(X=2)=0.3$, then find $P(X=0)$.

A hunter is firing at a target. He has only 10% chance of hitting it in one round. The number of rounds he must fire in order to have at least 50% chance of hitting the target at least once, is

$\overline{b}$ and $\overline{c}$ are non-collinear vectors and $\overline{a}$ is a vector such that $(\overline{c}\cdot\overline{c})\overline{a}=\overline{c}$. If $\overline{a}\times(\overline{b}\times\overline{c})+(\overline{a}\cdot\overline{b})\overline{b}=(4-2\beta-sin~\alpha)\overline{b}+(\beta^{2}-1)\overline{c}$, then the values of the scalars $\alpha$ and $\beta$ are

$\overline{V}=2\overline{i}+\overline{j}-\overline{k}$ and $\overline{W}=\overline{i}+3\overline{k}$. If $\overline{U}$ is a unit vector, then the maximum value of the scalar triple product $[\overline{U}\overline{V}\overline{W}]$ is

For a biased die, the probabilities for different faces are given by P(1)=0.1, P(2)=0.32, P(3)=0.21, P(4)=0.15, P(5)=0.05, P(6)=0.17. The die is tossed and it is known that either face 1 or 2 turned up. The probability that it is face 1 is:

Two symmetric cubical dice are rolled once. Match the items of Column-I with the items of Column-II. center tabular|l|l|l|l| 2|c|Column-I & 2c|Column-II
A & Probability that the numbers appearing are equal & I & 1/12
B & Probability that the numbers are all distinct & II & 5/36
C & Probability that the sum of numbers is 10 & III & 1/6
D & Probability that the sum of numbers is 6 & IV & 4/36
tabular center

The mean of 5 observations is 5. If three of the observations are 1, 2, 6 and the other two observations are such that each is greater than 5, then the mean deviation from the mean of the observations is

In a \(\triangle ABC\), let \(r\) be the inradius and \(r_1,r_2,r_3\) be the exradii opposite to vertices \(A,B,C\) respectively. Match the items of List-I with List-II. \[ \begin{array}{|c|c|} \hline \text{List-I} & \text{List-II}\\ \hline \text{A. } rr_1=r_2r_3 & \text{I. } \Delta^2\\ \text{B. } r_1+r_2=r_3-r & \text{II. } \angle A=90^\circ\\ \text{C. } \dfrac1{r_1}+\dfrac1{r_2}+\dfrac1{r_3} & \text{III. } \angle C=90^\circ\\ \text{D. } rr_1r_2r_3 & \text{IV. } s^2\\ & \text{V. } \dfrac1r\\ \hline \end{array} \]

Let $\overline{a}=x\overline{i}-2\overline{j}+3\overline{k}$, $\overline{b}=-2\overline{i}+x\overline{j}-\overline{k}$ and $\overline{c}=7\overline{i}-2\overline{j}+x\overline{k}$. If $x=x_0$ is the point of the local maxima of $f(x)=\overline{a}\cdot(\overline{b}\times\overline{c})$, then at $x=x_0$, $\overline{a}\cdot\overline{b}+\overline{b}\cdot\overline{c}+\overline{c}\cdot\overline{a}=$

OABCD is a pentagon in which \(OA\) and \(CB\) are parallel and \(OD\) and \(AB\) are parallel. If \[ \overrightarrow{OA}=\overrightarrow{a}, \qquad \overrightarrow{OD}=\overrightarrow{d}, \] and \[ \frac{OA}{CB}=2, \qquad \frac{OD}{AB}=\frac13, \] then \[ \overrightarrow{AD}+\overrightarrow{OC}+\overrightarrow{DC} \] is equal to:

If the median AD of \(\Delta ABC\) is bisected at the point E and BE is produced to meet the side AC at F. Then the vector \( \overline{BF} = \)

In a \(\Delta ABC\) if \( a:b:c = 5:6:7 \), then the ratio of the radius of the circumcircle to that of the incircle is:

If the angles of triangle ABC are in arithmetic progression and the sides a, b and c satisfy \( \frac{\sqrt{3}}{2} < \frac{b}{a} < 1 \) and \( c < b \), then the possible values of the side c are:

If \( \sinh^{-1}(2) + \sinh^{-1}(3) = \alpha \), then \( \cosh \alpha = \)

All the values of \(\alpha\) satisfying the equations \( 2\cos^2 \alpha - 3\cos \alpha = 32\tan^8 \theta \) and \( 3\cos 2\theta = 1 \) are:

Calculate \[ \sin\frac{8\pi}{9}\, \sin\frac{7\pi}{9}\, \sin\frac{2\pi}{3}\, \sin\frac{5\pi}{9}. \]

If \( A+B+C=\pi \) and \( \cos A = \cos B \cos C \), then \( \tan A - \tan B - \tan C = \)

If \( 7\sin x + 15\sin y = 17 \), then the maximum value of \( 7\cos x + 15\cos y \) is:

The domain of \( f(x) = \cos^{-1}[\log_2(x^2+5x+8)] \) is:

If \[ \frac{3x^2+x+2} {(3x^2+x+4)(3x^2+x+1)} = \frac{Ax+B}{3x^2+x+4} + \frac{Cx+D}{3x^2+x+1}, \] then \((A+B)+(C+D)\) is:

All the solutions \((n,r)\) of the equation \( \frac{{}^nC_r}{{}^{n+1}C_r} = \frac{1}{3} \) can be obtained from one of the following equations given in the options for \( k=1,2,3, \dots \):

The number of skew symmetric matrices of order \( 3 \times 3 \) that can be formed by using all the elements 0, \( \pm a, \pm b, \pm c \) is:

Let the numerical values of the coefficients of a polynomial belong to the set \( \{0, 1, 2, \dots, 9\} \). Then the number of reciprocal polynomials of third degree with the leading coefficient 1 that can be formed is: