List of top Questions asked in TS EAMCET- 2025

If $a=3, b=5, c=7$ are the sides of a triangle ABC, then its circumradius is

If $\frac{x^2+1}{(x^2+2)(x^2+3)} = \frac{Ax+B}{x^2+2} + \frac{Cx+D}{x^2+3}$, then $A+B+C+D=$

If $x \in (-\pi,\pi)$ then the number of solutions of the equation $2 \sin x \sin 3x \sin 5x + \sin 5x \cos 4x = 0$ is

The number of values of x satisfying the equation $\text{Tan}^{-1}(x+\frac{\sqrt{2}}{x}) + \text{Tan}^{-1}(x-\frac{\sqrt{2}}{x}) = \text{Tan}^{-1}(x)$ is

$4 \cos\frac{70}{2}\cos\frac{30}{2} - \sin 50 =$

If $\sin A = -\frac{24}{25}$, $\cos B = \frac{15}{17}$, A does not belong to 4\textsuperscript{th} quadrant and B does not belong to 1\textsuperscript{st} quadrant then $(A + B)$ lies in the quadrant

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

The number of ways in which 6 boys and 4 girls can be arranged in a row such that between any two girls there must be exactly 2 boys is

If all the letters of the word ACADEMICIAN are permuted in all possible ways then the number of permutations in which no two A's are together and all the consonants are together is

If $C_0, C_1, C_2, \dots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$ then the value of $\sum r^3 \cdot C_r$ when $n = 5$ is

The coefficient of $x^{12}$ in the expansion of $(x^2+2x+2)^8$ is

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $12x^4-56x^3+89x^2-56x+12=0$ such that $\alpha\beta = \gamma\delta = 1$ and $\frac{\alpha+\beta}{\gamma+\delta}>1$, then $\frac{\alpha+\beta}{\gamma+\delta} =$

If the quotient and remainder obtained when the expression $3x^5-6x^4+2x^3+4x^2-5x+8$ is divided by the expression $x^2-2x+3$ are $ax^3+bx^2+cx+d$ and $px+q$ respectively, then $ab+cd =$

Sum of all the roots of the equation $||2x-3|-4| = 2$ is

If a complex number $z = x+iy$ represents a point $P(x, y)$ in the Argand plane and z satisfies the condition that the imaginary part of $\frac{z-3}{z+3i}$ is zero, then the locus of the point P is

Number of real values of $(-1-\sqrt{3}i)^{3/4}$ is

If $\tan\theta$ and $\cot\theta$ are two distinct roots of the equation $ax^2+bx+c=0, a\neq0, b\neq0$, then

If the system of simultaneous linear equations $x - 2y + z = 0$, $2x + 3y + z = 6$ and $x + 2y + pz = q$ has infinitely many solutions, then

The amplitude of the complex number is:
\[\frac{(\sqrt{3}+i)(1-\sqrt{3}i)}{(-1+i)(-1-i)}\]

If $A = \begin{pmatrix} 1 & 5 & 2 \\ 4 & 1 & 3 \\ 2 & 6 & 3 \end{pmatrix}$, then $|(\text{Adj A})^{-1}| =$

The value of the greatest integer k satisfying the inequation $2^{n+4} + 12 \geq k(n+4)$ for all $n \in N$ is

If the system of linear equations $(\sin\theta)x - y + z = 0$, $x - (\cos\theta)y + z = 0$, $x + y + (\sin\theta)z = 0$ has a non-trivial solution, then the least positive value of $\theta$ is

Let $f: R \rightarrow R$ be defined by $f(x) = 5^{|x|} + \text{sgn}(5^{-x})$, where sgn x denotes signum function of x. Then f is

The product of all the values of \( (\sqrt{3}-i)^{\frac{3}{7}} \) is

If the moment of inertia of a uniform solid cylinder about the axis of the cylinder is \( \frac{1}{n} \) times its moment of inertia about an axis passing through its midpoint and perpendicular to its length, then the ratio of the length and radius of the cylinder is