List of top Questions asked in TS EAMCET- 2025

Let ABC be a triangle right angled at B. If a = 13 and c = 84, then r + R =

In a triangle ABC, if $c^2 - a^2 = b(\sqrt{3}c - b)$ and $b^2 - a^2 = c(c-a)$, then $\angle ACB =$

If $\text{Sinh}^{-1}x = \text{Cosh}^{-1}y = \log(1+\sqrt{2})$ then $\text{Tan}^{-1}(x+y) =$

Number of solutions of the equation $\sin^2\theta + 2\cos^2\theta - \sqrt{3}\sin\theta\cos\theta = 2$ lying in the interval $(-\pi, \pi)$ is

$\frac{\cos 15^\circ \cos^2 22\frac{1}{2}^\circ - \sin 75^\circ \sin^2 52\frac{1}{2}^\circ}{\cos^2 15^\circ - \cos^2 75^\circ} =$

If $3\sin\theta + 4\cos\theta = 3$ and $\theta \neq (2n+1)\frac{\pi}{2}$, then $\sin 2\theta =$

If $\frac{x+3}{(x+1)(x^2+2)} = \frac{a}{x+1} + \frac{bx+c}{x^2+2}$ then $a-b+c =$

If $C_0, C_1, C_2, \dots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$ then $\sum_{r=1}^{n} \frac{r C_r}{C_{r-1}} =$

Numerically greatest term in the expansion of $(2x-3y)^n$ when $x=\frac{7}{5}, y=\frac{3}{7}$ and $n=13$ is

The equation having the multiple root of the equation $x^4 + 4x^3 - 16x - 16 = 0$ as its root is

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4 - 4x^3 + 3x^2 + 2x - 2 = 0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers, then $\alpha + 2\beta + \gamma^2 + \delta^2 =$

If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed 1, then the range of 'a' is

If the equations $x^2 + px + 2 = 0$ and $x^2 + x + 2p = 0$ have a common root then the sum of the roots of the equation $x^2 + 2px + 8 = 0$ is

If $\alpha$ is a root of the equation $x^2-x+1=0$ then $(\alpha + \frac{1}{\alpha}) + (\alpha^2 + \frac{1}{\alpha^2}) + (\alpha^3 + \frac{1}{\alpha^3}) + \dots$ to 12 terms =

If $\cos\alpha+\cos\beta+\cos\gamma = 0 = \sin\alpha+\sin\beta+\sin\gamma$, then $\sin 2\alpha + \sin 2\beta + \sin 2\gamma =$

The set of all values of $\theta$ such that $\frac{1-i\cos\theta}{1+2i\sin\theta}$ is purely imaginary is

One of the values of $\sqrt{24-70i} + \sqrt{-24+70i}$ is

The sum of all the roots of the equation $\begin{vmatrix} x & -3 & 2 \\ -1 & -2 & x-1 \\ 1 & x-2 & 3 \end{vmatrix} = 0$ is

If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, then Adj(Adj(Adj A)) =

If the system of simultaneous linear equations $x+\lambda y-2z=1$, $x-y+\lambda z=2$ and $x-2y+3z=3$ is inconsistent for $\lambda = \lambda_1$ and $\lambda_2$, then $\lambda_1 + \lambda_2 =$

If $\frac{1}{2.7} + \frac{1}{7.12} + \frac{1}{12.17} + \dots$ to 10 terms = k, then k =

Study the following and identify the correct combinations:

Turbinals support this part of the nasal chamber

Volume of air remained in lungs even after forcible expiration: