List of top Questions asked in AP EAPCET

If all the letters of the word ‘SENSELESSNESS’ are arranged in all possible ways and an arrangement among them is chosen at random, then, the probability that all the E’s come together in that arrangement is:

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:

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:

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:

If $ X \sim B(5, p) $ is a binomial variate such that $ p(X = 3) = p(X = 4) $, then $ P(|X - 3| < 2) = \dots $

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:

Suppose the axes are to be rotated through an angle $ \theta $ so as to remove the $ xy $ term from the equation $3 x^2 + 2\sqrt{3}xy + y^2 = 0 $. Then in the new coordinate system, the equation $ x^2 + y^2 + 2xy = 2 $ is transformed to:

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:

For $ \lambda, \mu \in \mathbb{R} $, the lines \[ (x - 2y - 1) + \lambda (3x + 2y - 11) = 0 \] and \[ (3x + 4y - 11) + \mu (-x + 2y - 3) = 0 \] represent two families of lines. If the equation of the line common to both families is given by \[ ax + by - 5 = 0, \] then $ 2a + b = $ ?

If the pair of lines represented by $$ 3x^2 - 5xy + P y^2 = 0 $$ and $$ 6x^2 - xy - 5y^2 = 0 $$ have one line in common, then the sum of all possible values of $ P $ is:

The area of the region enclosed by the curves \[ 3x^2 - y^2 - 2xy + 4x + 1 = 0 \] and \[ 3x^2 - y^2 - 2xy + 6x + 2y = 0 \] is:

If the equation of the circle whose radius is 3 units and which touches internally the circle $$ x^2 + y^2 - 4x - 6y - 12 = 0 $$ at the point $ (-1, -1) $ is $$ x^2 + y^2 + px + qy + r = 0, $$ then $ p + q - r $ is:

The equation of the circle touching the circle \[ x^2 + y^2 - 6x + 6y + 17 = 0 \] externally and to which the lines \[ x^2 - 3xy - 3x + 9y = 0 \] are normal is:

The pole of the straight line \[ 9x + y - 28 = 0 \] with respect to the circle \[ 2x^2 + 2y^2 - 3x + 5y - 7 = 0 \] is:

The equation of a circle which touches the straight lines $x + y = 2$, $x - y = 2$ and also touches the circle $x^2 + y^2 = 1$ is:

The radical axis of the circles \[ x^2 + y^2 + 2gx + 2fy + c = 0 \] and \[ 2x^2 + 2y^2 + 3x + 8y + 2c = 0 \] touches the circle \[ x^2 + y^2 + 2x + 2y + 1 = 0. \] Then:

If the ordinates of points $ P $ and $ Q $ on the parabola \[ y^2 = 12x \] are in the ratio 1:2, then the locus of the point of intersection of the normals to the parabola at $ P $ and $ Q $ is:

The product of perpendiculars from the two foci of the ellipse $$ \frac{x^2}{9} + \frac{y^2}{25} = 1 $$ on the tangent at any point on the ellipse is:

The value of $ c $ such that the straight line joining the points \[ (0,3) \quad \text{and} \quad (5,-2) \] is tangent to the curve \[ y = \frac{c}{x+1} \] is:

The descending order of magnitude of the eccentricities of the following hyperbolas is: A. A hyperbola whose distance between foci is three times the distance between its directrices. B. Hyperbola in which the transverse axis is twice the conjugate axis. C. Hyperbola with asymptotes $ x + y + 1 = 0, x - y + 3 = 0 $.

If the plane \[ x - y + z + 4 = 0 \] divides the line joining the points \[ P(2,3,-1) \quad \text{and} \quad Q(1,4,-2) \] in the ratio $ l:m $, then $ l + m $ is:

If the line with direction ratios \[ (1, a, \beta) \] is perpendicular to the line with direction ratios \[ (-1,2,1) \] and parallel to the line with direction ratios \[ (\alpha,1,\beta), \] then $ (\alpha, \beta) $ is:

The equation of the plane which bisects the angle between the planes $$ 3x - 6y + 2z + 5 = 0 \quad \text{and} \quad 4x - 12y + 3z - 3 = 0 \quad \text{which contains the origin is:} $$

Evaluate the limit: \[ \lim_{x \to 0} \frac{\sin(\pi \cos^2 x)}{x^2}. \]