List of top Mathematics Questions asked in AP EAPCET

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

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

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

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

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

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

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 one of the roots of the equation \(x^2-5x-14=0\) is the length of the semi-conjugate axis of the hyperbola \[ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 \] and the square of the other root is the semi-transverse axis, then the focus of the hyperbola that lies on the positive \(x\)-axis is

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

Let \(A = (-3, -2, 7)\) and \(B = (3, 1, -2)\). Let a plane perpendicular to the line segment AB divide AB in the ratio 2:1. Then the intercept made by the plane on y-axis is

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 \(2d_2^2+d_3^2+1=\)

Let \[ E_1=\frac{x^2}{9}+\frac{y^2}{4}=1 \] and \[ E_2=\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \] be two ellipses and \(R\) be a rectangle with sides parallel to the coordinate axes. Let \(E_1\) be inscribed ellipse in \(R\) and \(E_2\) be circumscribed ellipse on \(R\). If \(E_2\) passes through \((0,4)\), then

The equation of directrix of parabola \(x^2 + 8x + 12y + 4 = 0\) is

The ratio of the areas of the concentric circles \(x^2 + y^2 - 6x + 12y + 15 = 0\) and \(x^2 + y^2 - 6x + 12y - 15 = 0\) is

For any real number \(\lambda \neq 1\), the centre of the circle that passes through \(A(1, \lambda)\), \(B(\lambda, 1)\), and \(C(\lambda, \lambda)\) is

The shortest distance from the line \(3x + 4y = 25\) to the circle \(x^2 + y^2 - 6x + 8y = 0\) is

The straight line \(x \cos \alpha + y \sin \alpha = p\) cuts the circle \(x^2 + y^2 - a^2 = 0\) at A and B. Then the equation of circle having AB as diameter is

Given two points \(Q(3,4)\) and \(R(1,2)\). What is the point \(P(x,y)\) on the line \(2x - y - 1 = 0\) for which \(PQ + PR = QR\) holds?

Suppose the vertices of a triangle are given by \(A(0,3)\), \(B(-2,0)\), and \(C(6,1)\). For \((\alpha, \alpha + 1)\) to lie inside the triangle, \(\alpha\) should lie in the interval