List of top Mathematics Questions asked in AP EAMCET

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:
For a dataset, if the coefficient of variation is 25 and the mean is 44, find the variance.
If the vectors \[ \mathbf{a} = 2i - j + k, \quad \mathbf{b} = i + 2j - 3k, \quad \mathbf{c} = 3i + pj + 5k \] are coplanar, find \( p \).
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 \( \mathbf{f}, \mathbf{g}, \mathbf{h} \) are mutually orthogonal vectors of equal magnitudes, then find the angle between the vectors \( \mathbf{f} + \mathbf{g} + \mathbf{h} \) and \( \mathbf{h} \).
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 \( (19a - 6\beta)^2 \).
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: \[ \frac{abc}{xyz} \]
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:
Evaluate the expression: \[ \sin^2 76^\circ + \sin^2 16^\circ - \sin 76^\circ \sin 16^\circ \]
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: \[ \tan^{-1} 2 + \tan^{-1} 3 \]
Evaluate: \[ \cosh^{-1} 2 \]
The coefficient of \( x^5 \) in the expansion of \( (3 + x + x^2)^6 \) is:
The absolute value of the difference of the coefficients of \( x^4 \) and \( x^6 \) in the expansion of \[ \frac{2x^2}{(x^2+1)(x^2+2)} \] is:
The square root of the independent term in the expansion of \[ \left( \frac{2x^2}{5} + \frac{5}{\sqrt{x}} \right)^{10} \] 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 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 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:
For real values of \( x \) and \( a \), if the expression \[ \frac{x+a}{2x^2 - 3x + 1} \] assumes all real values, then:
If the sum of two roots \( \alpha, \beta \) of the equation \[ x^4 - x^3 - 8x^2 + 2x + 12 = 0 \] is zero and \( \gamma, \delta \) (\( \gamma\delta \)) are its other roots, then \( 3\gamma + 2\delta \) is:
If \( f(x + h) = 0 \) represents the transformed equation of \[ f(x) = x^4 + 2x^3 - 19x^2 - 8x + 60 = 0 \] and this transformation removes the term containing \( x^3 \), then \( h \) is: