List of top Mathematics Questions asked in AP EAPCET

It is observed that there will be 25 blood specimens of normal persons, if 100 blood samples are tested. If 10 specimens are sent to a laboratory for testing, then the probability of having at least two specimens of normal persons is:
If a cubical die is thrown, then the mean and variance of the random variable \( X \), giving the number on the face that shows up, are respectively:
The point $ P(2, 1) $ is translated to a point $ Q $ parallel to the line $ L: x - y - 4 = 0 $ by $ 2\sqrt{5} $ units. If the point $ Q $ lies in the third quadrant, then the equation of the line passing through $ Q $ and perpendicular to $ L $ is:
The equation of the pair of tangents drawn from the point \( (1, 1) \) to the circle \( x^2 + y^2 + 2x + 2y + 1 = 0 \) is:
A ray of light incident along a line meets another line $7x - y + 1 = 0$ at the point $(0,1)$ and is then reflected along the line $y + 2x = 1$. Then the equation of the line of inciden is
If \( t \in \mathbb{R} \setminus \{-1\} \), then the locus of the point \[ \left( \frac{3at}{1 + t^3}, \frac{3at^2}{1 + t^3} \right) \] is:
The polar of a point with respect to the circle \( x^2 + y^2 - 10x + 12y - 3 = 0 \), which is not a tangent and not a chord of contact, is:
If $(2,3)$ is the vertex and $(3,2)$ is the focus of a parabola, then its equation is
Let the points $P_1(\frac{\pi}{4}), P_2(\frac{3\pi}{4}), P_3(\frac{5\pi}{4}), P_4(\frac{7\pi}{4})$ lie on the hyperbola $\frac{x^2}{9} - \frac{y^2}{16} = 1$. Then they form:
If the ends of the hypotenuse of a right-angled triangle are $ (0, a) $ and $ (a, 0) $, then the locus of the third vertex is:
If $ O $ is the origin and $ P, Q $ are points on the line $ 3x + 4y + 15 = 0 $ such that $ OP = OQ = 9 $, then the area of $ \triangle OPQ $ is:
The coordinates of the point which divides the line joining the points $ (2, 3, 4) $ and $ (3, -4, 7) $ in the ratio 2 : 4 externally is:
If A(2,3) and B(2,-3) are two points, then the equation of the locus of a point $P$ such that $PA + PB = 8$ is
The equation of the line common to the pair of lines \[ (p^2 - q^2)x^2 + (q^2 - r^2)xy + (r^2 - p^2)y^2 = 0 \] and \[ (l - m)x^2 + (m - n)xy + (n - l)y^2 = 0 \] is:
The lengths of the intercepts made by a circle \(S\) on the \(X\) and \(Y\)-axes are \(\frac{2\sqrt{13}}{3}\) and \(\frac{2\sqrt{17}}{3}\) respectively. Then the equation of the circle is:
Let \(Z\) be the point of intersection of the axis and the directrix of the parabola \(4x^2 - 12x + 4y + 5 = 0\). If \(S\) is its focus, then the point which divides \(SZ\) in the ratio \(2:1\) is:
The line $ x + y + 2 = 0 $ intersects the circle $ x^2 + y^2 + 4x - 4y - 4 = 0 $ in two points $ A $ and $ B $. Let $ S = x^2 + y^2 + 2gx + 2fy + c = 0 $ be a different circle passing through the points $ A $ and $ B $. If the distance of the centre of $ S $ from $ AB $ is $ \sqrt{2} $, then $ g + f + c = $:
Let the transverse axis of a hyperbola \( H \) be parallel to the X-axis and \( x^2 + y^2 - 2x - 4y + 3 = 0 \) be the equation of the auxiliary circle of \( H \). If the asymptotes of \( H \) are at right angles, then the equation of the hyperbola is:
In triangle $\triangle ABC$, $A=(1,2)$ and the equations of medians through $B$ and $C$ are $x+y=5$ and $x=4$. Find area of triangle ABC.
Let the locus of the point of intersection of the perpendicular tangents drawn to the circle \[ x^2 + y^2 + 6x - 4y - 12 = 0 \] be the circle \( S \). Then the equation of the tangent drawn to \( S \) which is perpendicular to the line \( 6x - 4y + k = 0 \) is:
The equation of a tangent to the circle \(x^2 + y^2 + 2x - 12y - 132 = 0\) which is perpendicular to the line \(12x + 5y + k = 0\) is:
If the area of the triangle formed by the lines \( y = x + c \) and \( 2x^2 + 5xy + 3y^2 = 0 \) is \( \frac{1}{20} \) sq. units, then \( c = \)
If the line passing through the points \( (5,1,a) \) and \( (3,b,1) \) crosses the YZ plane at the point \( \left( 0, \frac{17}{2}, \frac{-13}{2} \right) \), then \( a + b = \):
If the lines joining the origin to the points of intersection of a line $L$ and $x^2 + y^2 = 4$ are the coordinate axes, then the equation of the line $L$ is
If \(2x^2 - 5xy + 2y^2 = 0\) represents two sides of a triangle whose centroid is \((1,1)\), then the equation of the third side is: