List of top Questions asked in AP EAPCET

Evaluate \[ \int_{-a}^{a} f(x)\,dx-\int_{0}^{a} f(-x)\,dx \]

The substitution \[ \frac{dy}{dx}=z, \] reduces the differential equation \[ \frac{d^2y}{dx^2}-\frac{dy}{dx}=0 \] to a differential equation whose solution is \(z=\)

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

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

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 \(m\) 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

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

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 \(3a+b+5c=\)

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:

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

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:

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:

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

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

Suppose two tangents \(PA\) and \(PB\) are drawn to the circle centered at \(C(1,2)\) from the point \(P(16,7)\). If the area of the quadrilateral \(PACB\) is \(75\) square units, then the radius of the circle is