List of top Questions asked in AP EAMCET

The probability that a man failing to hit a target is \(\frac{1}{3}\). If he fires 4 times, then the probability that he hits the target at least thrice 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
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
A box \( P \) contains one white ball, three red balls and two black balls. Another box \( Q \) contains two white balls, three red balls and four black balls. If one ball is drawn at random from each one of the two boxes, then the probability that the balls drawn are of different color is
Two natural numbers are chosen at random from 1 to 100 and are multiplied. If \(A\) is the event that the product is an even number and \(B\) is the event that the product is divisible by 4, then \(P(A \cap \bar B) = \)
If five-digit numbers are formed from the digits 0, 1, 2, 3, 4 using every digit exactly only once, then the probability that a randomly chosen number from those numbers is divisible by 4 is
If the mean deviation about the mean is \(m\) and the variance is \(\sigma^2\) for the following data, then \(m + \sigma^2 =\) % Data table \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 7 & 9 \\ \hline f & 4 & 24 & 28 & 16 & 8 \\ \hline \end{array} \]
The angle between the line with the direction ratios \( (2, 5, 1) \) and the plane \( 8x + 2y - z = 4 \) is given by
If \( \mathbf{a}, \mathbf{b}, \mathbf{c} \) are three vectors such that \( |\mathbf{a}| = |\mathbf{b}| = |\mathbf{c}| = \sqrt{3} \) and \( ( \mathbf{a} + \mathbf{b} - \mathbf{c} )^2 + ( \mathbf{b} + \mathbf{c} - \mathbf{a} )^2 + ( \mathbf{c} + \mathbf{a} - \mathbf{b} )^2 = 36\), then \(|2\mathbf{a} - 3\mathbf{b} + 2\mathbf{c}|^2 =\)
If \( |\mathbf{\bar{f}}| = 10\), \( |\mathbf{\bar{g}}| = 14\) and \( |\mathbf{\bar{f}} - \mathbf{\bar{g}}| = 15\), then \( |\mathbf{\bar{f}} + \mathbf{\bar{g}}| =\)
If the points having the position vectors \( \mathbf{r}_1 = -i + 4j - 4k\), \( \mathbf{r}_2 = 3i + 2j - 5k\), \( \mathbf{r}_3 = -3i + 8j - 5k\) and \( -3i + 2j + \lambda k\) are coplanar, then \(\lambda = \)
The angle between the diagonals of the parallelogram whose adjacent sides are \(2i + 4j - 5k\) and \(i + 2j + 3k\) is
In \(\triangle ABC\), \(r r_1 \cot^ \frac{A}{2} + r r_2 \cot^ \frac{B}{2} + r r_3 \cot^ \frac{C}{2} = \)
In \(\triangle ABC\), if \(4r_1 = 5r_2 = 6r_3\), then \(\sin^2 \frac{A}{2} + \sin^2 \frac{B}{2} + \sin^2 \frac{C}{2} =\)
If \( \theta = \sec^{-1}(\cosh u) \), then \( u = \)
If \( \cos^{-1}(2x) + \cos^{-1}(3x) = \frac{\pi}{3} \) and \( 4x^2 = \frac{a}{b} \), then \( a + b = \):
The general solution of the equation \( \sin^2 \theta + 3 \cos^2 \theta = 5 \sin \theta \) 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 \(540^\circ<A<630^\circ\) and \(|\cos A| = \frac{5}{13}\), then \( \tan\frac{A}{2} \tan A =\)
If \(\sec \theta + \tan \theta = \frac{1}{3}\), then the quadrant in which \(2\theta\) lies is:
If \[ \frac{x^2+3}{x^4+2x^2+9} = \frac{Ax+B}{x^2+ax+b} + \frac{Cx+D}{x^2+cx+d} \] then \( aA + bB + cC + dD = \)
If \( |x| < \frac{2}{3} \), then the fourth term in the expansion of \( (3x - 2)^{2/3} \) is:
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 number of ways in which 17 apples can be distributed among four guests such that each guest gets at least 3 apples 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: