List of top Questions asked in AP EAMCET

The probability that a person goes to college by car,\(\frac{1}{5}\) bus,\(\frac{2}{5}\) or train \(\frac{3}{5}\) is given. If he reaches college on time, find the probability he traveled by car.
For a dataset, if the coefficient of variation is 25 and the mean is 44, find the variance.
Let \( \mathbf{a}, \mathbf{b} \) be two unit vectors. If \( \mathbf{c} = \mathbf{a} + 2\mathbf{b} \) and \( \mathbf{d} = 5\mathbf{a} - 4\mathbf{b} \) are perpendicular to each other, find the angle between \( \mathbf{a} \) and \( \mathbf{b} \).
If 5 letters are to be placed in 5-addressed envelopes, then the probability that at least one letter is placed in the wrongly addressed envelope is:
If the vectors \[ \mathbf{a} = 2i - j + k, \quad \mathbf{b} = i + 2j - 3k, \quad \mathbf{c} = 3i + pj + 5k \] are coplanar, find \( p \).
In a regular hexagon \( ABCDEF \), if \( \overrightarrow{AB} = \mathbf{a} \) and \( \overrightarrow{BC} = \mathbf{b} \), then find \( \overrightarrow{FA} \).
In \( \triangle ABC \), evaluate: \[ \cos A + \cos B + \cos C \]
In \( \triangle ABC \), given: \[ a = 26, \quad b = 30, \quad \cos C = \frac{63}{65} \] Find \( c \).
If \( H \) is the orthocenter of \( \triangle ABC \) and \( AH = x \), \( BH = y \), \( CH = z \), then evaluate: \[ \frac{abc}{xyz} \]
If the points with position vectors \[ (\mathbf{a}i + 10j + 13k), \quad (6i + 11j + 11k), \quad \left(\frac{9}{2}i + \beta j - 8k\right) \] are collinear, then evaluate \( (19a - 6\beta)^2 \).
Find the value of \( x \) satisfying: \[ 1 + \sin x + \sin^2 x + \sin^3 x + \dots = 4 + 2\sqrt{3} \] where \( 0x\pi, x \neq \frac{\pi}{2} \).
Evaluate: \[ \cosh^{-1} 2 \]
Evaluate: \[ \tan^{-1} 2 + \tan^{-1} 3 \]
Evaluate the expression: \[ \sin^2 76^\circ + \sin^2 16^\circ - \sin 76^\circ \sin 16^\circ \]
Evaluate the expression: \[ \tan 6^\circ \tan 42^\circ \tan 66^\circ \tan 78^\circ \]
The maximum value of \[ 12 \sin x - 5 \cos x + 3 \] is:
The number of different ways of preparing a garland using 6 distinct white roses and 6 distinct red roses such that no two red roses come together is:
The coefficient of \( x^5 \) in the expansion of \( (3 + x + x^2)^6 \) is:
If all the letters of the word CRICKET are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word CRICKET is:
The number of ways a committee of 8 members can be formed from a group of 10 men and 8 women such that the committee contains at most 5 men and at least 5 women is:
If \( Z = x + iy \) is a complex number, then the number of distinct solutions of the equation \[ z^3 + \bar{z} = 0 \] is:
While solving a system of linear equations \( AX = B \) using Cramer’s rule, if \includegraphics[]{6.png}
The set of all real values of \( c \) for which the equation \[ zz' + (4 - 3i)z + (4+3i)z + c = 0 \] represents a circle is:
If the determinant of a 3rd order matrix \( A \) is \( K \), then the sum of the determinants of the matrices \( (AA^T) \) and \( (A - A^T) \) is:
For all positive integers \( n \), if \( 3(5^{2n+1}) + 2^{3n+1 \) is divisible by \( k \), then the number of prime numbers less than or equal to \( k \) is:}