List of top Mathematics Questions asked in TS EAMCET

Two ships leave a port at the same time. One of them moves in the direction of E50$^\circ$N with a speed of 8 kmph and the other moves in the direction of S20$^\circ$E with a speed of 12 kmph. Then the distance between the ships at the end of 2 hours is (in km)

A and B are two non-square matrices. If \( P = A + B \), \( Q = A^TB \), \( R = AB^T \), then the matrices whose order is equal to the order of A are

Let P be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$ and let the perpendicular drawn through P to the major axis meet its auxiliary circle at Q. If the normals drawn at P and Q to the ellipse and the auxiliary circle respectively meet in R, then the equation of the locus of R is

\(P(5,2)\) is a point on the curve \(y=f(x)\) and \(\frac{7}{2}\) is the slope of the tangent to the curve at P. The area of the triangle formed by the tangent and the normal to the curve at P with x-axis is

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

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 $a_K - a_{K+1} - a_{K-1} =$

A plane $\pi_1$ contains the vectors $\vec{i}+\vec{j}$ and $\vec{i}+2\vec{j}$. Another plane $\pi_2$ contains the vectors $2\vec{i}-\vec{j}$ and $3\vec{i}+2\vec{k}$. $\vec{a}$ is a vector parallel to the line of intersection of $\pi_1$ and $\pi_2$. If the angle $\theta$ between $\vec{a}$ and $\vec{i}-2\vec{j}+2\vec{k}$ is acute, then $\theta=$

If \( \cos\theta + \sin\theta = \sqrt{2}\cos\theta \) and \( 0<\theta<\frac{\pi}{2} \), then \( \sec(2\theta) + \tan(2\theta) = \)

If $\vec{a}=\hat{i}-2\hat{j}+2\hat{k}$ and $\vec{b}=9\hat{i}+6\hat{j}-18\hat{k}$ are two vectors, then $\frac{\text{Projection of } \vec{b} \text{ on } \vec{a}}{\text{Projection of } \vec{a} \text{ on } \vec{b}} =$

\( \int_{0}^{\pi / 4} x^{2} \sin 2 x d x= \)

If $D \subset \mathbb{R}$ and $f : D \to \mathbb{R}$ defined by $f(x) = \frac{x^2+x+a}{x^2-x+a}$ is a surjection then '$a$' lies in the interval

A real valued function
$f:[4, \infty) \to \mathbb{R}$ is defined as $f(x) = (x^2+x+1)^{(x^2-3x-4)}$, then f is

If a number x is drawn randomly from the set of numbers \{1, 2, 3, ..., 50\}, then the probability that number x that is drawn satisfies the inequation $x + \frac{10}{x} \le 11$ is

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 $\lambda_1 + \lambda_2 =$

Find the value of \( k \) such that \( 5 \cdot 2^n - 48n + k \) is divisible by 24.

If are the roots of the equation \[ 2x^3 \;-\; 5x^2 \;+\; 4x \;-\; 3 \;=\; 0, \] then \[ \sum \alpha\beta(\alpha+\beta) \;=\;? \]

The solution set of the inequality \[ 3^x + 3^{1-x} - 4 <0 \] contained in \( \mathbb{R} \) is:

The common solution set of the inequalities \[ x^2 - 4x \leq 12 \quad \text{and} \quad x^2 - 2x \geq 15 \] taken together is:

If \( \alpha, \beta \) are the real roots of the equation \( x^2 + ax + b = 0 \). If \( \alpha + \beta = \frac{1}{2} \) and \( \alpha^3 + \beta^3 = \frac{37}{8} \), then \( {a}-{\frac{1}{b}} =\)

The solution set of the inequality \( \sqrt{x^2 + x - 2}>(1 - x) \) is:

If \( \alpha, \beta, \gamma \) are the roots of the equation \( 4x^3 - 3x^2 + 2x - 1 = 0 \), then \( \alpha^3 + \beta^3 + \gamma^3 = \)