List of top Questions asked in TS EAMCET

$\int_{0}^{\pi/4} \frac{\sec x}{3\cos x + 4\sin x} dx =$

$\int_0^{\pi/2} \frac{1}{5\cos^2 x + 16\sin^2 x + 8\sin x \cos x} dx =$

$\int \frac{x\text{Tan}^{-1}x}{(1+x^2)^2}dx =$

$\int \frac{\log x}{(1+x)^2}dx = $

$\int \frac{3^x(x\log 3 - 1)}{x^2} dx =$

$\int_{-2}^{4} |2-x^2| dx =$

$\int_4^{18} \frac{1}{(x+2)\sqrt{x-3}}dx = $

The area of the region bounded by $y=x^3$, x-axis, $x=-2$ and $x=4$ is

$\lim_{n \to \infty} \frac{(2n(2n-1)...(n+2)(n+1))^{1/n}}{n} =$

If $I_1 = \int \frac{e^x}{e^{4x}+e^{2x}+1}dx$, $I_2 = \int \frac{e^{-x}}{e^{-4x}+e^{-2x}+1}dx$, then $I_2-I_1=$

If $\int \frac{3x+2}{4x^2+4x+5}dx = A\log(4x^2+4x+5)+B\tan^{-1}(\frac{2x+1}{2})+c$, then $A+B=$

Consider the following
Assertion (A): $\int \sqrt{x-3}(\sin^{-1}(\log x) + \cos^{-1}(\log x))dx = \frac{\pi}{3}(x-3)^{3/2}+c$
Reason (R): $\sin^{-1}(f(x))+\cos^{-1}(f(x))=\frac{\pi}{2}$, $|f(x)|\le 1$
The correct answer is

$\int \frac{1}{(2\cos x + \sin x)^2} dx =$

$\int x\text{Tan}^{-1}\sqrt{\frac{1+x^2}{1-x^2}}dx=$

If $[\cdot]$ denotes the greatest integer function, then $\int_1^2 [x^2] dx =$

$\int(1+\tan^2 x)(1+2x\tan x)dx =$

$\int_{-1}^{1} \frac{\log 2 - \log(1+x)}{\sqrt{1-x^2}} dx =$

If $\frac{5\pi}{4}<x<\frac{7\pi}{4}$, then $\int \sqrt{\frac{1-\sin 2x}{1+\sin 2x}} dx =$

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

The locus of a point which divides the line segment joining the focus and any point on the parabola \(y^2 = 12x\) in the ratio \(m:n\) (\(m+n \ne 0\)) is a parabola. Then the length of the latus rectum of that parabola is

A circle C passing through the point (1,1) bisects the circumference of the circle \( x^2+y^2-2x=0 \). If C is orthogonal to the circle \( x^2+y^2+2y-3=0 \) then the centre of the circle C is

If the line x+y=2 cuts the circle \(x^2+y^2+2x-4y+4=0\) at two points A and B then the radius of the circle passing through A, B and orthogonal to \(x^2+y^2-2x-4y-4=0\) is

If L is a line common to the planes \(3x + 4y + 7z = 1\), \(x - y + z = 5\) then the direction ratios of the line L are

If \( 4x^2+12xy+9y^2+2gx+2fy-1=0 \) represent a pair of parallel lines then

If P is any point on the ellipse \( \frac{x^2}{25} + \frac{y^2}{9} = 1 \) and S, S' are its foci, then the maximum area (in sq. units) of \(\Delta SPS' = \)