List of top Questions asked in AP EAPCET- 2024

Bag A contains 3 white and 4 red balls, bag B contains 4 white and 5 red balls, and bag C contains 5 white and 6 red balls. If one ball is drawn at random from each of these three bags, then the probability of getting one white and two red balls is:

If \( P(A \cap B) + P(B \mid A \cap B) = \), then:

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:

In a random experiment, two dice are thrown and the sum of the numbers appeared on them is recorded. This experiment is repeated 9 times. If the probability that a sum of 6 appears at least once is \( P_1 \) and a sum of 8 appears at least once is \( P_2 \), then \( P_1 : P_2 = \):

If two numbers \(x\) and \(y\) are chosen one after the other at random with replacement from the set of numbers \( \{1, 2, 3, \ldots, 10\} \), then the probability that \( |x^2 - y^2| \) is divisible by 6 is:

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

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:

Two persons A and B throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as 4 and the person who gets this result first is declared as the winner. If A starts the game, then the probability that B wins the game is:

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:

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 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 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

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 \( a + 2b + 1 = ? \)

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 \( 2(a + h - b - g + f - 12) = ? \)

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:

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:

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

The perimeter of the locus of the point \( P \) which divides the line segment \( QA \) internally in the ratio 1:2, where \( A = (4, 4) \) and \( Q \) lies on the circle \( x^2 + y^2 = 9 \), is:

P is a point on \( x + y + 5 = 0 \), whose perpendicular distance from \( 2x + 3y + 3 = 0 \) is \( \sqrt{13} \), then the coordinates of P are:

If a circle is inscribed in an equilateral triangle of side \( a \), then the area of any square inscribed in this circle (in square units) is: