List of top Mathematics Questions asked in AP EAPCET

If a tangent to the hyperbola \( x^2 - \frac{y^2}{3} = 1 \) is also a tangent to the parabola \( y^2 = 8x \), then the equation of such tangent with the positive slope is:

If a circle of radius 4 cm passes through the foci of the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) and is concentric with the hyperbola, then the eccentricity of the conjugate hyperbola of that hyperbola is:

Let \( F \) and \( F' \) be the foci of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) (where \( b<2 \)), and let \( B \) be one end of the minor axis. If the area of the triangle \( FBF' \) is \( \sqrt{3} \) sq. units, then the eccentricity of the ellipse is:

A common tangent to the circle \( x^2 + y^2 = 9 \) and the parabola \( y^2 = 8x \) is

If the equation of the circle passing through the points of intersection of the circles \[ x^2 - 2x + y^2 - 4y - 4 = 0, \quad x^2 + y^2 + 4y - 4 = 0 \] and the point \( (3,3) \) is given by \[ x^2 + y^2 + \alpha x + \beta y + \gamma = 0, \] then \( 3(\alpha + \beta + \gamma) \) is:

If the circles \( x^2 + y^2 - 8x - 8y + 28 = 0 \) and \( x^2 + y^2 - 8x - 6y + 25 - a^2 = 0 \) have only one common tangent, then \( a \) is:

Let \( a \) be an integer multiple of 8. If \( S \) is the set of all possible values of \( a \) such that the line \( 6x + 8y + a = 0 \) intersects the circle \( x^2 + y^2 - 4x - 6y + 9 = 0 \) at two distinct points, then the number of elements in \( S \) is:

If power of a point \( (4,2) \) with respect to the circle \( x^2 + y^2 - 2x + 6y + a^2 - 16 = 0 \) is 9, then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is

Equation of the circle having its centre on the line \( 2x + y + 3 = 0 \) and having the lines \( 3x + 4y - 18 = 0 \) and \( 3x + 4y + 2 = 0 \) as tangents is:

If the equation of the pair of straight lines passing through the point \( (1, 1) \) and perpendicular to the pair of lines \( 3x^2 + 11xy - 4y^2 = 0 \) is \( ax^2 + 2hxy + by^2 + 2gx + 2fy + 12 = 0 \), then find \( 2(a + h - b - g + f - 12) = ? \)

If the slope of one line of the pair of lines \( 2x^2 + hxy + 6y^2 = 0 \) is thrice the slope of the other line, then \( h \) = ?

A line \( L \) passing through the point \( (2,0) \) makes an angle \( 60^\circ \) with the line \( 2x - y + 3 = 0 \). If \( L \) makes an acute angle with the positive X-axis in the anticlockwise direction, then the Y-intercept of the line \( L \) is?

A line \( L \) intersects the lines \( 3x - 2y - 1 = 0 \) and \( x + 2y + 1 = 0 \) at the points \( A \) and \( B \). If the point \( (1,2) \) bisects the line segment \( AB \) and \( \frac{a}{b} x + \frac{b}{a} y = 1 \) is the equation of the line \( L \), then \( a + 2b + 1 = ? \)

If the origin is shifted to a point \( P \) by the translation of axes to remove the \( y \)-term from the equation \( x^2 - y^2 + 2y - 1 = 0 \), then the transformed equation of it is:

If the line segment joining the points \( (1,0) \) and \( (0,1) \) subtends an angle of \( 45^\circ \) at a variable point \( P \), then the equation of the locus of \( P \) is:

For the probability distribution of a discrete random variable \( X \) as given below, the mean of \( X \) is:

A, B, C are mutually exclusive and exhaustive events of a random experiment and E is an event that occurs in conjunction with one of the events A, B, C. The conditional probabilities of E given the happening of A, B, C are respectively 0.6, 0.3 and 0.1. If \( P(A) = 0.30 \) and \( P(B) = 0.50 \), then \( P(C \mid E) = \):

Two digits are selected at random from the digits 1 through 9. If their sum is even, then the probability that both are odd is:

S is the sample space and A, B are two events of a random experiment. Match the items of List A with the items of List B.

Then the correct match is:

If \( \overrightarrow{a}, \overrightarrow{b} \) are two non-collinear vectors, then \( |\overrightarrow{b}| \overrightarrow{a} + |\overrightarrow{a}| \overrightarrow{b} \) represents

Let \( O(0) \), \( A(\hat{i} + \hat{j} + \hat{k}) \), \( B(-2\hat{i} + 3\hat{k}) \), \( C(2\hat{i} + \hat{j}) \), and \( D(4\hat{k}) \) be the position vectors of the points \( O, A, B, C, \) and \( D \). If a line passing through \( A \) and \( B \) intersects the plane passing through \( O, C, \) and \( D \) at the point \( R \), then the position vector of \( R \) is:

Match the items of List-I with those of List-II (Here \( \Delta \) denotes the area of \( \triangle ABC \)).

Then the correct match is

In \( \triangle ABC \), if \( r_1 = 4 \), \( r_2 = 8 \), \( r_3 = 24 \), then find \( a \)=

An urn contains 3 black and 5 red balls. If 3 balls are drawn at random from the urn, the mean of the probability distribution of the number of red balls drawn is:

Evaluate: \[ 4 \tan^{-1} \frac{1}{5} - \tan^{-1} \frac{1}{70} + \tan^{-1} \frac{1}{99}= \]