List of top Mathematics Questions asked in AP EAPCET

The coefficient of \( x^r \) in the expansion of \( \frac{1}{\sqrt{(1 - 2x)^3}} \) is
If a seven digit number formed with distinct digits 4, 6, 9, 5, 3, \( x \) and \( y \) is divisible by 3, then the number of such ordered pairs \( (x, y) \) is
In \( \triangle ABC \), if \( \cos A \cos B \cos C = \frac{1}{5} \), then \( \tan A \tan B + \tan B \tan C + \tan C \tan A = \)
If \( \cos(\theta - \alpha), \cos \theta \) and \( \cos(\theta + \alpha) \) are in harmonic progression, then \( 2 \tan^2 \theta = \)
If \( \omega \) is a complex cube root of unity, then \( \cos \left( \sum_{k=1}^{2} (k - \omega)(k - \omega^2) \frac{\pi}{175} \right) = \)
Let the two values of \( z = \frac{1 - i}{\sqrt{1 + i}} \) be \( z_1 \) and \( z_2 \). If \( -\frac{\pi}{2}<\text{Arg}(z_1)<\text{Arg}(z_2)<\pi \), then \( \text{Arg}(z_1) + \text{Arg}(z_2) = \)
If \( \alpha \) and \( \beta \) are the roots of the equation \( x^2 + x + 1 = 0 \), then the quadratic equation whose roots are \( \alpha^{2023} \) and \( \beta^{2012} \) is
If \( 2^n \) divides \( 16! \) and \( 2^{n+1} \) does not divide \( 16! \), then \( n = \)
If the roots of the equation \( 16x^3 - 44x^2 + 36x - 9 = 0 \) are in harmonic progression, then its greatest root is
If \( \alpha \) and \( \beta \) are the roots of the equation \( ax^2 + bx + c = 0 \), then the equation whose roots are \( \alpha + \beta \) and \( \frac{1}{\alpha} + \frac{1}{\beta} \) is
If \( \alpha \) and \( \beta \) are the roots of the equation \( 2x^2 - 4x + 3 = 0 \), then \( \frac{2(\alpha^4 + \beta^4) + 3(\alpha^2 + \beta^2)}{\alpha + \beta} = \)
If \( \sqrt{-3 - 4i} = re^{i\theta} \), then \( r^2 \tan \theta = \)
If \( z_1 = 2 - 3i \) and the roots of the equation \( z^3 + bz^2 + cz + d = 0 \) are \( i, z_1 \) and \( \overline{z_1} \), then \( b + c + d = \)
If there exists a \( k^{th} \) order non-singular sub-matrix in a matrix \( P \) of order \( m \times n \), then the rank \( (\rho) \) of \( P \)
If \( A = \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \end{bmatrix} \) and \( B = \begin{bmatrix} b_{11} & b_{12} & b_{13} \\ b_{21} & b_{22} & b_{23} \end{bmatrix} \), then which one of the following is True?
In a matrix \( A \), if all the sub matrices of \( k^{th} \) order are singular and there is one non-singular sub matrix of order \( r \) \( (r<k) \), then the rank \( (\rho) \) of the matrix \( A \)
Let \( f(x) = |x| \) and \( g(x) = |x| + a \), \( (a>0) \). For \( 0 \le x \le b \), \( \{(x, y) / g(x) \le y \le f(x)\} \) represents all the points in the interior of
Let \( f: \mathbb{R} \rightarrow \mathbb{R} \) be a function defined by \( f(x) = \frac{2x+1}{3} \). If \( \alpha \) is an element in the domain of \( f \) whose image is \( \frac{1}{\alpha} \), then the sum of all possible values of such \( \alpha \) is
Consider the following statements (A) and (B): \[ \text{(A):} \quad \int_a^b \frac{d}{dx} \left( f(x) \right) dx = \frac{d}{dx} \int_a^b f(x) dx \] \[ \text{(B):} \quad \frac{d}{dx} \left( \int f(x) dx \right) = f(x) + C \] Which one of the following is True?
Let $ [t] $ represent the greatest integer not exceeding $ t $. The number of discontinuous points of $ [10^t] $ in $ (0, 10) $ is:

Let $ f(x) = \frac{x}{\sqrt{1- x}}$ + $\frac{\sqrt{1- x}}{x}$. If $ \lim_{x _ 1^-} f(x) = l $ and $ \lim_{x \to m} f(x) = \frac{5}{2} $, then the set of all possible finite values of $ l $ and $ m $ is

Let $ x + y + 1 = 0 $ and $ x - y + 4 = 0 $ be the asymptotes of a hyperbola $ H $. If $ (1, 1) $ is a point on $ H $, then the length of the latus rectum of $ H $ is

If $ P(2, 3) $ and $ Q(-1, 2) $ are conjugate points with respect to the circle $ x^2 + y^2 + 2gx + 3y - 2 = 0 $ then the radius of the circle is

If a straight line is equally inclined at an angle $ \theta $ with all the three coordinate axes, then $ \tan \theta =$

The number of straight lines that can be drawn through the point $ (-3, 4) $, which are at a distance of 5 units from the point $ (2, -8) $, is: