List of top Mathematics Questions asked in AP EAPCET

Evaluate \[ \sum_{r=1}^{\infty} \frac{1\cdot3\cdot5\cdots(2r-1)} {2^{2r}r!} (\sqrt{3})^r : \]

The number of skew symmetric matrices of order \( 3 \times 3 \) that can be formed by using all the elements 0, \( \pm a, \pm b, \pm c \) is:

Consider the quadratic expression \( f(x) = x^2 + (10-a)x - 10a \). The sum of all values of 'a', such that the roots of \( f(x)=3 \) are integers is:

The modulus of the product of all the values of \( (2+3i)^{3/5} \) is:

If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 - 3x + 1 = 0 \), then \( \frac{\alpha}{1-\alpha} + \frac{\beta}{1-\beta} + \frac{\gamma}{1-\gamma} = \)

The quadratic expression having zero's equal to the non-integral roots of \( ||3x-4|-6|=5 \) is:

If \( x^5 + ax^4 + bx^3 + cx^2 + 5x + d = 0 \) is an odd order reciprocal equation of second type and \( \frac{1+\sqrt{3}i}{2} \) is a root, then \( b-c = \)

For a \( 3 \times 3 \) non singular matrix A, if \( \text{Adj}(\text{Adj}(\text{Adj}(\text{Adj}(A)))) = |A|^n A \), then \( n = \)

On a matrix A when three elementary operations namely interchange of \( R_1 \) and \( R_2 \), \( R_2 \rightarrow R_2 - 2R_1 \), \( R_3 \rightarrow R_3 - 3R_1 \) are applied successively, A is transformed to \( \begin{bmatrix} 1 & 3 & 4 \\ 2 & 1 & 5 \\ 6 & 1 & 2 \end{bmatrix} \). Then \( \text{Tr}(A) = \)

Among the solutions of the equation \( x^6 = 64 \), the sum of all those solutions whose real part is negative is:

If \( \text{Arg}(\frac{z-1}{z+5}) = \pi/3 \) and \( |z-1|=|z+5| \), then \( |z|^2 = \)

If the two systems of equations \( x+y-2z=0, 4x+4y-8z=0, 3x+3y-6z=0 \) and \( x+y+z=3, 2x+2y-z=\lambda, x+y-\mu z=1 \) have the same set of solutions, then \( \lambda+\mu = \)

The complete range of the function \( f(x) = [x]^2 + 5[x] + 6 \), where \([x]\) is the greatest integer function, is:

If a real valued function \( f:(1, 2] \rightarrow B \) defined by \( f(x) = \log_{10}(x-1) \) is a bijection, then \( B = \)

If \( x_1+x_2+x_3+\dots+x_n=pn(n-1) \forall n \in \mathbb{N} \) and \( x_{j+1}-x_j = \text{constant} \, (j=1,2,\dots,n-1) \), then \( (\frac{x_n}{n-1})^2 = \)

The differential equation among the following, whose general solution is \( y=A e^{5x}+B e^{-4x} \) is

The substitution required to reduce the differential equation \( \frac{dy}{dx}+\sin y \cos y \sin x = \sin 2x \cos^{2}y \) to a linear differential equation in z is

If \( \int \frac{2x+5}{(x-1)(x+1)(x+4)(x+6)} \, dx = \frac{1}{10}\log\left(\frac{f(x)}{g(x)}\right)+c \) and \( \frac{f(-2)}{g(-2)}=6 \), then \( \frac{f(10)}{g(10)} = \)

The area (in sq. units) of the region bounded between the curve \( y=x^{2}+5x+1 \) and the line \( 7x-y+1=0 \) is

If \( \int_{0}^{3} x\left(\sqrt[5]{9-x^{2}}\right) \, dx = k \cdot 3^{1/k} \), then \( k = \)

\( \lim_{n \rightarrow \infty} \frac{1}{n}\sum_{r=1}^{n}\sin^{k}\left(\frac{\pi r}{2n}\right)\cos\left(\frac{\pi r}{2n}\right) = \)

If \( \int_{\pi/4}^{3\pi/4} \frac{x \sin x}{1+3\cos 2x} \, dx = k \int_{\pi/4}^{3\pi/4} \frac{\sin x}{1+3\cos 2x} \, dx \), then \( \int_{0}^{k} \sin^{\pi/k}x \, dx = \)

The general solution of the differential equation \( \frac{dy}{dx}=x^{2}y(x+y+xy+1) \) is \( y = \)

The length of the normal drawn to the curve \( 2x^{3}+2y^{3}=9xy \) at the point (2, 1) is

If \( \int e^{x}\left(\frac{1}{n}+\tan nx\right)\sec nx \, dx = \frac{1}{n}(g(x)+k) = F(x) \) and \( F(0)=1 \), then \( k = \)