List of top Mathematics Questions asked in AP EAPCET

If the product of the lengths of the perpendiculars drawn from the ends of a diameter of the circle \( x^2 + y^2 = 4 \) onto the line \( x + y + 1 = 0 \) is maximum, then the two ends of that diameter are:

If the intercepts made by a variable circle on the X-axis and Y-axis are 8 and 6 units respectively, then the locus of the center of the circle is:

The slope of the non-vertical tangent drawn from the point $(3,4)$ to the circle $x^2 + y^2 = 9$ is:

Point \(P(6,4)\) lies on the line \(x - y - 2 = 0\). If \(A(\alpha, \beta)\) and \(B(\gamma, \delta)\) are two points on this line lying on either side of \(P\) at a distance of 4 units from \(P\), then find \(\alpha^2 + \beta^2 + \gamma^2 + \delta^2\).

If the transformed equation of the equation \[ 2x^2 + 3xy - 2y^2 - 17x + 6y + 8 = 0 \] after translating the coordinate axes to a new origin \((\alpha, \beta)\) is \[ aX^2 + 2h XY + bY^2 + c = 0, \] then find \(3\alpha + c\).

A random variable \(X\) follows a binomial distribution in which the difference between its mean and variance is 1. If \(2P(x=2) = 3P(x=1)\), then \(n^2 P(x>1)\) is:

70% of the total employees of a factory are men. Among the employees of that factory, 30% of men and 15% of women are technical assistants. If an employee chosen at random is found to be a technical assistant, then the probability that this employee is a man is:

Two cards are drawn at random from a pack of 52 playing cards. If both the cards drawn are found to be black in colour, then the probability that at least one of them is a face card is:

A person is known to speak the truth in 3 out of 4 occasions. If he throws a die and reports that it is six, then the probability that it is actually six is:

If \(A\) and \(B\) are events of a random experiment such that \[ P(A \cup B) = \frac{3}{4}, \quad P(A \cap B) = \frac{1}{4}, \quad P(\overline{A}) = \frac{2}{3}, \] then \(P(\overline{A} \cap B)\) is:

If \(\vec{a} = \vec{i} + p \vec{j} - 3 \vec{k}, \vec{b} = p \vec{i} - 3 \vec{j} + \vec{k}, \vec{c} = -3 \vec{i} + \vec{j} + 2 \vec{k}\) are three vectors such that \[ |\vec{a} \times \vec{b}| = |\vec{a} \times \vec{c}|, \] then \(p =\)

If \(\vec{a} = 2 \vec{i} - 3 \vec{j} + 4 \vec{k}, \vec{b} = \vec{i} + 2 \vec{j} - \vec{k}, \vec{c} = -3 \vec{i} - \vec{j} + 2 \vec{k}\) and \(\vec{d} = \vec{i} + \vec{j} + \vec{k}\) are four vectors, then evaluate \[ (\vec{a} \times \vec{b}) \times (\vec{c} \times \vec{d}) = ? \]

The variance of the ungrouped data \(2, 12, 3, 11, 5, 10, 6, 7\) is:

In \(\triangle ABC\), if \(r_1 = 2r_2 = 3r_3\), then find the ratio \(a : b\).

If \(\vec{a}, \vec{b}, \vec{c}\) are three unit vectors such that \[ |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2 = 15, \] then \[ |\vec{a} - \vec{b} - \vec{c}|^2 - 4(\vec{b} \cdot \vec{c}) = ? \]

Let \(\vec{a}\), \(\vec{b}\) be position vectors of points \(A\) and \(B\) respectively. \(C\) and \(D\) are points on the line \(AB\) such that \(\overrightarrow{AB}, \overrightarrow{AC}\) and \(\overrightarrow{BD}, \overrightarrow{BA}\) are two pairs of like vectors. If \(\overrightarrow{AC} = 3 \overrightarrow{AB}\) and \(\overrightarrow{BD} = 2 \overrightarrow{BA}\), then \(\overrightarrow{CD} =\)

If the area of triangle \(ABC\) is \(4\sqrt{5}\) sq. units, length of the side \(CA\) is 6 units and \(\tan \frac{B}{2} = \frac{\sqrt{5}}{4}\), then its smallest side is of length:

Let \( H(x) = 3x^4 + 6x^3 - 2x^2 + 1 \) and \( g(x) \) be a linear polynomial. If \[ \frac{H(x)}{(x-1)(x+1)(x-2)} = f(x) + \frac{g(x)}{(x-1)(x+1)(x-2)}, \] then find \( H(-1) + 2H(2) - 3H(1) \).

If \(630^\circ<\theta<810^\circ\) and \(\tan \theta = -\frac{7}{24}\), then find \(\cos \left(\frac{\theta}{4}\right)\).

For \(\theta \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\), if \(2\cos \theta + \sin \theta = 1\), and \(7\cos \theta + 6 \sin \theta = k\), then the possible values of \(k\) are:

Evaluate \[ \sum_{k=0}^{12} \sin\left( (k+1) \frac{\pi}{6} + \frac{\pi}{4} \right) \sin \left( \frac{k \pi}{6} + \frac{\pi}{4} \right) \]

Number of solutions of the equation \[ 2 \sin^2 \theta - 3 \cos^2 \theta = \sin \theta \cos \theta \] in the interval \((- \pi, \pi)\) is:

Evaluate \[ \tan^{-1} \frac{\sqrt{8} - 2\sqrt{15}}{\sqrt{15} + 1} + \tan^{-1} \frac{1}{\sqrt{5}} \]

The number of ways of arranging all the letters of the word PERFECTION such that there must be exactly two consonants between any two vowels is:

If \(\alpha\) and \(\beta\) (\(\alpha>\beta\)) are the multiple roots of the equation \[ 4x^4 + 4x^3 - 23x^2 - 12x + 36 = 0, \] then find \(2\alpha - \beta\).