List of top Mathematics Questions asked in TS EAMCET

\( \tan^{-1}\frac{3}{5} + \tan^{-1}\frac{6}{41} + \tan^{-1}\frac{9}{191} = \)

If \( \sin A = -\frac{60}{61} \), \( \cot B = -\frac{40}{9} \) and neither A nor B is in \( 4^{\text{th}} \) quadrant then \( 6\cot A + 4\sec B = \)

A real valued function \( f(x)=\left|x^{2}-3x+2\right|+2x-3 \) is defined on \( [-2,1] \). If m and M are absolute minimum and absolute maximum values of \( f \) respectively then \( M-4m= \)

If \( f(x)=x+\log \left(\frac{x-1}{x+1}\right) \) is a well-defined real valued function then \( f \) is

Let 'a' be a positive real number. If a real valued function \( f(x) = \begin{cases}\frac{6^x - 3^x - 2^x + 1}{1 - \cos\left(\frac{x}{a}\right)} & \text{if } x \neq 0 \\ \log 3 \log 4 & \text{if } x = 0 \end{cases} \) is continuous at \( x=0 \), then \( a = \)

If [x] is the greatest integer function then \( \lim_{x \to 3^-} \frac{(3-|x| + \sin|3-x|) \cos(9-3x)}{|3-x|[3x-9]} = \)

One of the foci of an ellipse is \( (2,-3) \) and its corresponding directrix is \( 2x+y=5 \). If the eccentricity of the ellipse is \( \frac{\sqrt{5}}{3} \) then the coordinates of the other focus are

A line L perpendicular to the line \( 5x-12y+6=0 \) makes positive intercept on the Y-axis. If the distance from the origin to the line L is 2 units and the angle made by the perpendicular drawn from the origin to the line L with positive X-axis is \( \theta \), then \( \tan \theta + \cot \theta = \)

If \( X \sim B(7, p) \) is a binomial variate and \( P(X=3) = P(X=5) \) then \( p = \)

If \( \begin{vmatrix} 9 & 25 & 16 \\ 16 & 36 & 25 \\ 25 & 49 & 36 \end{vmatrix} = K \), then \( K, K+1 \) are the roots of the equation

If the augmented matrix corresponding to the system of equations \( x+y-z=1 \), \( 2x+4y-z=0 \) and \( 3x+4y+5z=18 \) is transformed to \( \begin{bmatrix} 1 & a & 0 & -1 \\ 0 & 2 & 1 & b \\ 0 & 0 & c & 32 \end{bmatrix} \), then

If the equation of the plane passing through the points (2,1,2), (1,2,1) and perpendicular to the plane \( 2x-y+2z=1 \) is \( ax+by+cz+d=0 \) then \( \frac{a+b}{c+d} = \)

The shortest distance between the lines \( \bar{r} = (3\bar{i} - 5\bar{j} + 2\bar{k}) + t(4\bar{i} + 3\bar{j} - \bar{k}) \) and \( \bar{r} = (\bar{i} + 2\bar{j} - 4\bar{k}) + s(6\bar{i} + 3\bar{j} - 2\bar{k}) \) is

If \( \bar{a} = \bar{i} - 2\bar{j} - 2\bar{k} \) and \( \bar{b} = 2\bar{i} + \bar{j} + 2\bar{k} \) are two vectors then \( (\bar{a} + 2\bar{b}) \times (3\bar{a} - \bar{b}) = \)

The general solution of the differential equation \( 2dx + dy = (6xy + 4x - 3y)dx \) is

If \( \cos x \frac{dy}{dx} = y \sin x - 1, x \neq (2n+1)\frac{\pi}{2}, n \in \mathbb{Z} \) is the differential equation corresponding to the curve \( y = f(x) \) and \( f(0)=1 \) then \( f(x)= \)

\( \int_{-2 \pi}^{2 \pi} \sin ^{4} x \cos ^{6} x d x= \)

\( \int_{0}^{\pi / 4} x^{2} \sin 2 x d x= \)

\( \int_{0}^{2} \sqrt{(x+3)(2-x)} d x= \)

If \( \int(x+2) \sqrt{x^{2}-x+2} d x=\frac{1}{3} f(x)+\frac{5}{8} g(x)+\frac{35}{16} h(x)+c \) then \( f(-1)+g(-1)+h\left(\frac{1}{2}\right)= \)

\( \int \left( \frac{1-\log x}{1+(\log x)^2} \right)^2 dx = \)

\( \int e^{4x}(\sin 3x - \cos 3x) dx = \)

\( \int \frac{2\sin x - 3\cos x}{4\cos x - 3\sin x} dx = \)

If \( 1^\circ = 0.0175 \) radians, then the approximate value of \( \sec 58^\circ \) is