List of top Questions asked in AP EAMCET

A person is known to speak false once out of 4 times. If that person picks a card at random from a pack of 52 cards and reports that it is a king, then the probability that it is actually a king is
If the line \(2x - 3y + 5 = 0\) is the perpendicular bisector of the line segment joining \(1, -2\) and \((a, b)\), then \(a + b =\)
The circle \(x^2 + y^2 - 8x - 12y + \alpha = 0\) lies in the first quadrant without touching the coordinate axes. If \((6, 6)\) is an interior point to the circle, then the range of \(\alpha\) is:
If the locus of the mid points of the chords of the circle \(x^2 + y^2 = 25\) that subtend a right angle at the origin is given by \( \frac{x^2}{a^2} + \frac{y^2}{a^2} = 1\), then \(|a| =\)
The domain of the real valued function \( f(x) = \sqrt{2 + x} + \sqrt{3 - x} \) is:
Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be defined by \( f(x + y) = f(x) + 12y \), for all \( x, y \in \mathbb{R} \). If \( f(1) = 6 \), then the value of \( \sum_{r=1}^n f(r) \) is:
For any real value of \(x\), if \( \frac{11x^{2}+12x+6}{x^{2}+4x+2} \not\in (a, b) \), then the value for \(x\) for which $$ \frac{11x^{2}+12x+6}{x^{2}+4x+2} = b - a + 3 $$ is: 
If \( A = [a_{ij}]\) where \( 1 \leq i, j \leq n \) with \( n \geq 2 \) and \( a_{ij} = i + j \) is a matrix, then the rank of \( A \) is:
The length of the subnormal at any point on the curve \( y = \left(\frac{x}{2024}\right)^k \) is constant if the value of \( k \) is:
If \( l_1 \) and \( l_2 \) are the lengths of the perpendiculars drawn from a point on the hyperbola \( 5x^2 - 4y^2 - 20 = 0 \) to its asymptotes, then \( \frac{l_1^2 l_2^2}{100} = \)
The range of the real valued function \( f(x) = \frac{x^2 + 2x - 15}{2x^2 + 13x + 15} \) is:
The number of numbers lying between 1000 and 10000 such that every number contains the digits 3 and 7 only once without repetition is:
For a binomial variate \(X \sim B(n, p)\), the difference between the mean and variance is 1 and the difference between their squares is 11. If the probability of \(P(X = 2) = m\left(\frac{5}{6}\right)^n\) and \(n = 36\) then \(m:n\) is
If \( \omega \) is the cube root of unity, then: \[ \frac{a + b\omega + c\omega^2}{c + a\omega + b\omega^2} = \frac{a + b\omega + c\omega^2}{b + c\omega + a\omega^2} \]
Which one of the following is false?
If all chords of the curve \( 2x^2 - y^2 + 3x + 2y = 0 \), which subtend a right angle at the origin, always pass through the point \( (a, \beta) \), then \( (a, \beta) = \):
If \[ \int \frac{1}{1 - \cos x} \, dx = \tan \left( \frac{x}{4} + \beta \right) + c, \] then one of the values of \( \frac{\pi}{4} - \beta \) is:
If \( z_1 = 10 + 6i \), \( z_2 = 4 + 6i \) and \( z \) is any complex number such that the argument of \( \frac{z-z_1}{z-z_2} \) is \( \frac{\pi}{4} \), then the value of \( |z - 7 - 9i| \) is:
If \( |x| < \frac{2}{3} \), then the fourth term in the expansion of \( (3x - 2)^{2/3} \) is:
If \((\alpha + \beta)\) is not a multiple of \(\frac{\pi}{2}\) and \(3 \sin(\alpha - \beta) = 5 \cos(\alpha + \beta)\), then \[ \tan\left(\frac{\pi}{4} + \alpha\right) + 4\tan\left(\frac{\pi}{4} + \beta\right) = \]
If the coefficients of \(x^5\) and \(x^6\) are equal in the expansion of \( \left( a + \frac{x}{5} \right)^{65} \), then the coefficient of \(x^2\) in the expansion of \( \left( a + \frac{x}{5} \right)^4 \) is:
The angle between the diagonals of the parallelogram whose adjacent sides are \(2i + 4j - 5k\) and \(i + 2j + 3k\) is
If a line \( L \) makes angles \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) with the Y-axis and Z-axis respectively, then the angle between \( L \) and another line having direction ratios \( 1,1,1 \) is:
If \( l, m, n \) are the direction cosines of a line that is perpendicular to the lines having the direction ratios \( (1,2,-1) \) and \( (-2,1,1) \), then \( (l+m+n)^2 \) =
The length of the internal bisector of angle A in \( \triangle ABC \) with vertices \( A(4,7,8) \), \( B(2,3,4) \), and \( C(2,5,7) \) is: