List of top Mathematics Questions asked in AP EAPCET

Evaluate \[ \int_{0}^{\pi}\frac{x}{\sin x}\left(3\cos^2x+2\sin x+\sin^3x-3\right)\,dx \] is equal to:

If \([\,\cdot\,]\) represents greatest integer function, then \[ \int_{\frac{3\pi}{4}}^{\pi} \left[\sin x+\left[\frac{4x}{\pi}\right]\right]\,dx = \] is equal to:

Evaluate \[ \int_{0}^{\pi} \left( \cos^2\left(\frac{3\pi}{8}-\frac{x}{4}\right) - \cos^2\left(\frac{11\pi}{8}+\frac{x}{4}\right) \right)\,dx \] is equal to:

If \[ \int \frac{\sin^3x\left(\tan^{-1}(\sec x+\cos x)\right)^{-1}}{\cos^4x+3\cos^2x+1}\,dx=f(x)+C, \] then \[ e^{f(x)}= \]

Evaluate \[ \int \frac{1}{\left(\sin x+\cos x+\sqrt{2\sin 2x}\right)^2}\,dx= \]

If \[ \int e^x\{f(x)-f'(x)\}=g(x)+C, \] then \[ \int e^x f'(x)\,dx= \]

The maximum area of a right angled triangle with hypotenuse \(h\) is:

The value of \(a\) for which the function \[ f(x)=a\sin x+\frac{1}{3}\sin 3x \] has an extremum value at \(x=\dfrac{\pi}{3}\) is:

If \(m\) is the slope of a tangent to the curve \(e^y=1+x^2\) at \(x=1\), then \(m=\)

\(V\) is the set of points on the curve \(y^3-3xy+2=0\) where the tangent is vertical, then \(V=\)

The equation of tangent of the curve \[ y=\sqrt{9-2x^2} \] at the point where the ordinate and abscissa are equal is

If \[ \frac{d}{dx} \left[ A\log\left(\frac{\sqrt{1-x^3}+B}{\sqrt{1-x^3}+1}\right) \right] = \frac{1}{x\sqrt{1-x^3}}, \] then \(AB=\)

If \[ \frac{y}{x}\cos^4\alpha+\frac{x}{y}\sin^4\alpha = 2\sin^2\alpha\cos^2\alpha, \] then \[ \frac{dy}{dx}= \]

If \[ f(x)=\frac{1-\sin x}{\log(1+\pi^2-4\pi x+4x^2)} \] is continuous at \(x=\frac{\pi}{2}\), then \(f\left(\frac{\pi}{2}\right)=\)

Evaluate \[ \lim_{x\to \frac{\pi}{6}} \frac{3\sin x-\sqrt{3}\cos x}{6x-\pi} \]

If \(a,b,c\) are the direction ratios of a line \(L\) and \(\ell,m,n\) are its direction cosines, then \[ \frac{a^2}{b^2+c^2}= \] is equal to:

Evaluate \[ \lim_{n\to \infty}\sum_{r=1}^{n}\frac{r+2}{r(r+1)(r+3)} \] is equal to:

If \(a\gt 0,\ b\gt 0\), then \[ \lim_{n\to\infty} \left( \frac{a+b^{1/n}-1}{a} \right)^n = \] is equal to:

If \(a,b,c\) are the intercepts made by the plane passing through the point \((1,2,3)\) parallel to the plane \(3x+4y-5z=0\) on \(X,Y,Z\)-axes respectively, then \(3a+b+5c=\)

The parabola with focus at \((4,-3)\) and vertex at \((4,-1)\) is

Let \(L(x_1,4)\) be the end of the latus rectum of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] lying in the first quadrant and let \(S(8,y_1)\) be the focus of the given hyperbola. Then the length of its transverse axis is:

If the line \(3x-my+5=0\) is a tangent to the hyperbola \(3x^2-4y^2=300\), then the square of the \(Y\)-intercept made by this tangent line is

If the latus rectum of an ellipse is equal to half of the minor axis, then its eccentricity is:

If the vertices of a triangle \(ABC\) are \(A(1,2,3)\), \(B(h,-3,0)\) and \(C(-4,k,-1)\) and the centroid of the triangle is \(\left(5,-1,\dfrac{2}{3}\right)\), then triangle \(ABC\) is:

The midpoint of the diagonal of a rectangle formed by \(x^2+5x-6=0\) and \(y^2-8y-20=0\) is