List of top Mathematics Questions asked in AP EAPCET

If the differential equation obtained by eliminating \(A, B\) from \(y = (\sin^{-1}x)^2 + A \cos^{-1} x + B\) is \((a-x^2)y'' - xy' = b\), then \(\frac{b+a}{b-a} =\)

The equation of the family of curves for which the length of the subnormal at any point \((x,y)\) is always a constant \(k\) is

The general solution of \(\frac{d^2 y}{dx^2} = 0\) is

If \[ \int (1+x)\log(1+x^2)\,dx= \left(x+\frac{x^2}{2}+\frac{1}{2}\right)\log(1+x^2)+g(x)+C, \] then \(g(x)=\)

Evaluate \[ \int_{\frac{\pi}{11}}^{\frac{9\pi}{22}} \frac{dx}{1+\sqrt{\tan x}} \]

If \(m,n\in \mathbb{Z}\), then \[ \int_0^{2\pi}\cos mx\cos nx\,dx+\int_{-\pi}^{\pi}\sin mx\cos nx\,dx= \]

Evaluate \[ \int_2^5 \sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\,dx \]

Evaluate \(\lim_{n \to \infty} \frac{1}{\sqrt{n}} \left[ 1 + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \cdots + \frac{1}{\sqrt{n}} \right]\)

If \(0 \lt x \lt 1, \int \frac{dx}{\sqrt{x^2 - x^5}} = \frac{1}{3} \log |f(x)| + C\), then \(f(1/2) =\)

The minimum value of \[ \left(1+\frac{1}{\sin^n\alpha}\right) \left(1+\frac{1}{\cos^n\alpha}\right) \] is

Evaluate \[ \int \frac{dx}{\sin\left(x-\frac{\pi}{3}\right)\cos x} \]

Evaluate \(\int \tan^{-1}(1-x+x^2) \, dx + \int \tan^{-1}(x) \, dx + \int \tan^{-1}(1-x) \, dx\)

At \(x = 0\), \(f(x) = \cos x - 1 + \frac{x^2}{2} - \frac{x^3}{3}\)

The sum of the intercepts made by a tangent drawn to the curve \((x/a)^n + (y/b)^n = 2\) at \((a,b)\) on the coordinate axes is

Maximum area of the rectangle inscribed in a circle of radius 10 cm is

The angle between the curve \(2y = e^{-x/2}\) and the y-axis is \(\tan^{-1}(k)\). Then \(k =\)

If \(x = a \cos^3 \theta, y = a \sin^3 \theta\), then \(\frac{d^2y}{dx^2}\) at \(\theta = \pi/4\) is

If \[ f(x)= \begin{cases} \tan^{-1}x, & |x|\leq 1\\[2mm] \frac{1}{2}\left(|x|-1\right), & |x|\gt 1 \end{cases} \] then the domain of \[ \frac{d}{dx}f(x) \] is

If \(\lim_{n \to \infty} x_n\) exists and is finite, \(x_1 = 2\), \(x_{n+1} = \frac{a + b x_n}{b + c x_n}\) \(\forall n \in \mathbb{N}\) and \(c \gt b \gt a \gt 0\), then \(\lim_{n \to \infty} x_n =\)

Evaluate \(\lim_{x \to 0} \frac{x^2 \log(\cos x)}{\log(1+x^2)}\)

The integral value of \(n\) for which \[ \lim_{x\to 0}\frac{(\cos x-1)(\cos x-e^x)}{x^n} \] is a finite non-zero real number is

If \[ y=\frac{ax+b}{cx+d} \] and \[ \frac{dx}{dy}=\frac{ad-bc}{Py^2+Qy+R} \] then \(P+Q+R=\)

If the chord of contact of a point \(P\) w.r.t. the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) passes through a fixed point \((\alpha, \beta)\), then the locus of \(P\) is a straight line. The sum of the squares of the intercepts made by this line on the coordinate axes is

If \(d_1,d_2,d_3\) are the distances of the point \((1,2,3)\) from the \(X,Y,Z\)-coordinate axes respectively, then \(2d_2^2+d_3^2+1=\)

If \(P = (3, 12, 4)\) and \(Q\) is a point on the line \(OP\) such that \(OQ = 3\), then the sum of all the coordinates of \(Q\) is