List of top Mathematics Questions asked in AP EAPCET

If $I_n = \int \tan^n x \, dx \quad (n>1)$, then $I_4 + I_6 =$
The slope of the tangent at any point $(x,y)$ on the curve is equal to the product of the coordinates of that point. If the equation of the normal to the curve at the point $(\sqrt{2},e)$ is $ax+by=1$, then $\dfrac{b}{a}=$
The curve represented by $x = t^5 + 5t^3 + 20t + 7$ and $y = 4t^3 - 3t^2 - 18t + 3$ is decreasing in the interval

Given \( f(x) = \begin{cases} \frac{1}{2}(b^2 - a^2), & 0 \le x \le a \\[6pt] \frac{1}{2}b^2 - \frac{x^2}{6} - \frac{a^3}{3x}, & a<x \le b \\[6pt] \frac{1}{3} \cdot \frac{b^3 - a^3}{x}, & x>b \end{cases} \). Then:

If the tangent drawn to the curve $(x^2+1)(y-3)=x$ at a point P, lying in the first quadrant, is a horizontal line, then the equation of the normal at the point P is
The area (in sq units) of the triangle formed by the normal at point $(1,0)$ on the curve $x = e^{\sin y}$ with coordinate axes is:
If $x^3 + y^3 = 3axy$, then at $\left(\frac{3a}{2}, \frac{3a}{2}\right)$ the value of $3a y'' + 40$ is:
The equation of the pair of asymptotes of the hyperbola $x^2 - 2y^2 - 8x + 8y + 4 = 0$ is
If the tangent to the curve $x^3y^2 + \dfrac{x^2}{y} = 5$ is parallel to X-axis, then a point on its locus is:
Let the points $P_1(\frac{\pi}{4}), P_2(\frac{3\pi}{4}), P_3(\frac{5\pi}{4}), P_4(\frac{7\pi}{4})$ lie on the hyperbola $\frac{x^2}{9} - \frac{y^2}{16} = 1$. Then they form:
If $f(g(x+y)) = f(g(x)) + f(g(y))$, $g(1)=2$, $f(2)=1$, then $g(f(x))$ is discontinuous on:
If $(2,3)$ is the vertex and $(3,2)$ is the focus of a parabola, then its equation is
If the circles $x^2+y^2 - 4x + 2fy + 1 = 0$ and $x^2+y^2 + 2gx - 4y - 1 = 0$ cut orthogonally, then $r_1^2 + r_2^2 - 8=$
The length of the chord of contact from point $(2,1)$ to the circle $x^2+y^2+4x+2y+1=0$ is
Let A, A' be the end points of major axis, S, S' be the foci and B, B' be the end points of minor axis of an ellipse E. If $\angle \text{BAB}' = 60^\circ$, then $\angle \text{SBS}' =$
The product of the slopes of the common tangents drawn to the circles $x^2+y^2+2x-2y-2=0$ and $x^2+y^2-2x+2y+1=0$ is
If $x+y-1=0$ and $2x - y + 1=0$ are conjugate lines with respect to the circle $x^2 + y^2 - 4x + 2fy - 1 = 0$, then $f=$
The line $3x+y-5=0$ touches a circle S at $(1,2)$. If $(h,k)$ is the ntre of the circle S such that $h^2+hk+k^2=37$ and radius is $\sqrt{10}$, then $k=$
If the foot of the perpendicular drawn from $(0,0,0)$ to a plane is $(1,2,3)$, then the equation of the plane is
If the chord through $(1,-2)$ cuts the curve $3x^2 - y^2 - 2x + 4y = 0$ at P and Q, then the angle subtended by PQ at the origin is
If a point R$(4,y,z)$ lies on the line joining $P(2,-3,4)$ and $Q(8,0,10)$, then distan of R from origin is
The transformed equation of $2x^2 + 3y^2 - z^2 - 8x + 18y + 2z + 9 = 0$ when the axes are translated to the point $(2,-3,1)$ is
If the lines joining the origin to the points of intersection of a line $L$ and $x^2 + y^2 = 4$ are the coordinate axes, then the equation of the line $L$ is
If $X_1, X_2, ..., X_n$ are $n$ independent events such that $P(X_r) = \frac{1}{r+1}$, for $r=1, 2, ..., n$, then the probability that none of the $n$ events occur is
If the mean and varian of a binomial variable $X$ are 2 and 1 respectively, then $P(X>1) = $