List of top Questions asked in AP EAMCET

The sum of the rational terms in the binomial expansion of \( \left( \sqrt{2} + 3^{1/5} \right)^{10} \) is:
If the eleventh term in the binomial expansion of \( (x + a)^n \) is the geometric mean of the eighth and twelfth terms, then the greatest term in the expansion is:
If a committee of 10 members is to be formed from 8 men and 6 women, then the number of different possible committees in which the men are in majority is:
The number of ways in which 3 men and 3 women can be arranged in a row of 6 seats, such that the first and last seats must be filled by men is:
If the roots of the equation \( 4x^3 - 12x^2 + 11x + m = 0 \) are in arithmetic progression, then \( m = {?} \)
The algebraic equation of degree 4 whose roots are the translates of the roots of the equation \( x^4 + 5x^3 + 6x^2 + 7x + 9 = 0 \) by \( -1 \) is:
If \( (3 + i) \) is a root of \( x^2 + ax + b = 0 \), then \( a = {?} \)
Roots of the equation \( a(b - c)x^2 + b(c - a)x + c(a - b) = 0 \) are:
If \( \omega \) is the cube root of unity, then: \[ \frac{a + b\omega + c\omega^2}{c + a\omega + b\omega^2} = \frac{a + b\omega + c\omega^2}{b + c\omega + a\omega^2} \]
If the amplitude of \( (Z - 2) \) is \( \frac{\pi}{2} \), then the locus of \( Z \) is:
The complex conjugate of \( (4 - 3i)(2 + 3i)(1 + 4i) \) is:
The system \( x + 2y + 3z = 4, \, 4x + 5y + 3z = 5, \, 3x + 4y + 3z = \lambda \) is consistent and \( 3\lambda = n + 100 \), then \( n = ? \)
Let \( A \) be a \( 4 \times 4 \) matrix and \( P \) be its adjoint matrix. If \( |P| = \left| \frac{A}{2} \right| \), then \( |A^{-1}| = ? \)
If \( A = \begin{bmatrix} 2 & 3 \\ 1 & k \end{bmatrix} \) is a singular matrix, then the quadratic equation having the roots \( k \) and \( \frac{1}{k} \) is:
The sum of the series \( \frac{1}{1.5} + \frac{1}{5.9} + \frac{1}{9.13} + \cdots \) up to \( n \) terms is:
The range of the real valued function \( f(x) = \frac{x^2 + 2x - 15}{2x^2 + 13x + 15} \) is:
The domain of the real-valued function \( f(x) = \log_2 \log_3 \log_5 (x^2 - 5x + 11) \) is:
A car sounding a horn of frequency 1000 Hz passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing of the car is 11:9. The speed of the car is (Speed of sound \( v = 340 \, {ms}^{-1} \)):
If \( \vec{a} = i\hat{i} + j\hat{j} + 3k\hat{k} \), \( \vec{b} = i\hat{i} + 2k\hat{k} \), \( \vec{c} = -3i\hat{i} + 2j\hat{j} + k\hat{k} \) are linearly dependent vectors and the magnitude of \( \vec{a} \) is \( \sqrt{14} \), then if \( \alpha, \beta \) are integers, find \( \alpha + \beta \):
The line \( 21x + 5y = k \) touches the hyperbola \( 7x^2 - 5y^2 = 232 \), then \( k \) is:
Angle between the circles \( x^2 + y^2 - 4x - 6y - 3 = 0 \) and \( x^2 + y^2 + 8x - 4y + 11 = 0 \) is:
The triangle \( PQR \) is inscribed in the circle \[ x^2 + y^2 = 25. \] If \( Q = (3,4) \) and \( R = (-4,3) \), then \( \angle QPR \) is:
If the slope of one of the lines in the pair of lines \( 8x^2 + axy + y^2 = 0 \) is thrice the slope of the second line, then \( a = \) ?
A line \( L \) passing through the point \( P(-5,-4) \) cuts the lines \( x - y - 5 = 0 \) and \( x + 3y + 2 = 0 \) respectively at \( Q \) and \( R \) such that \[ \frac{18}{PQ} + \frac{15}{PR} = 2, \] then the slope of the line \( L \) is:
If a random variable \( X \) has the following probability distribution, then its variance is nearly: 
random variable