List of top Mathematics Questions asked in TS EAMCET

Let K be the number of rational terms in the expansion of $(\sqrt{2}+\sqrt[6]{3})^{6144}$. If the coefficient of $x^P (P \in N)$ in the expansion of $\frac{1}{(1+x)(1+x^2)(1+x^4)(1+x^8)(1+x^{16})}$ is $a_P$, then $a_K - a_{K+1} - a_{K-1} =$

Numerically greatest term in the expansion of $(3x-4y)^{23}$ when $x=\frac{1}{6}$ and $y=\frac{1}{8}$ is

The number of positive integral solutions of $xyz = 60$ is

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + \frac{a}{2}x + b = 0$ and $(\alpha-\beta)(\alpha-\gamma)$, $(\beta-\alpha)(\beta-\gamma)$, $(\gamma-\alpha)(\gamma-\beta)$ are the roots of the equation $(y+a)^3 + K(y+a)^2 + L = 0$, then $\frac{L}{K}= $

If $1+2i$ is a root of the equation $x^4 - 3x^3 + 8x^2 - 7x + 5 = 0$, then sum of the squares of the other roots is

If local maximum of $f(x) = \frac{ax+b}{(x-1)(x-4)}$ exists at $(2,-1)$, then $a+b=$

If $\omega \neq 1$ is a cube root of unity, then one root among the $7^{th}$ roots of $(1+\omega)$ is

If $Z=r(\cos\theta+i\sin\theta)$, $(\theta \neq -\pi/2)$ is a solution of $x^3 = i$, then $r^9(\cos(9\theta)+i\sin(9\theta)) =$

If $|Z_1 - 3 - 4i| = 5$ and $|Z_2| = 15$ then the sum of the maximum and minimum values of $|Z_1 - Z_2|$ is

If the eight vertices of a regular octagon are given by the complex numbers $\frac{1}{x_j-2i}$ ($j=1,2,3,4,5,6,7,8$), then the radius of the circumcircle of the octagon is

If $2^{4n+3} + 3^{3n+1}$ is divisible by P for all natural numbers $n$, then P is

The domain and range of $f(x) = \frac{1}{\sqrt{|x|-x^2}}$ are A and B respectively. Then $A \cup B = $ ?

The differential equation corresponding to the family of ellipses \( \frac{x^2}{a^2} + \frac{y^2}{4} = 1 \), where 'a' is an arbitrary constant is

If y=f(x) is the solution of the differential equation \( (1+\cos^2 x)f'(x) - 4\sin(2x) - f(x)\sin(2x) = 0 \) when f(0)=0, then \( f(\pi/3) = \)

\( \int_0^{\pi/2} \sqrt{\tan x} \, dx = \)

\( \int_{0}^{\pi/2} \frac{dx}{\cos x - \sqrt{3}\sin x} = \)

\( \int_{-1}^{5} \frac{1}{\sqrt{20+x-x^2}} dx = \)

\( \int \frac{1}{(x+2)\sqrt{x^2+x+2}} dx = \)

\( \int \frac{x+\cos x}{1-\sin x} dx = \)

If \( I_1 = \int \sin^6 x \, dx \) and \( I_2 = \int \cos^6 x \, dx \) then \( I_1 + I_2 = \)

If x and y are two positive real numbers such that xy=4 then the minimum value of \( \sqrt{x+\frac{y^2}{2}} \) is

The real valued function \( f(x) = \frac{x^2}{2} - \log(x^2+x+1) \) is

There is a possible error of 0.02 cm in measuring the base diameter of a right circular cone as 14 cm. If the semi-vertical angle of the cone is 45°, then the approximate error in its volume is (in cu. cm)

A rod of length 41 m with an end A on the floor and another end B on the wall perpendicular to the floor is sliding away horizontally from the wall at the rate of 3 ft/min. When the end B is at the height of 9 ft from the floor, then the rate at which the area of the triangle formed by the rod with wall and floor changes at that instant is (in ft/min)

If the curves \(y^2=12x-3\) and \(y^2=12-kx\) cut each other orthogonally then the length of the sub tangent at (1,b) on the curve \(y^2=12-kx\) is