List of top Questions asked in TS EAMCET

The equation of the locus of a point which is at a distance of 5 units from a fixed point (1,4) and also from a fixed line 2x+3y-1=0 is

Let $\pi_1$ be the plane determined by the vectors $\hat{i}+\hat{j}, \hat{i}+\hat{k}$ and $\pi_2$ be the plane determined by the vectors $\hat{j}-\hat{k}, \hat{k}-\hat{i}$. Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the planes $\pi_1$ and $\pi_2$. If $\vec{b} = \hat{i}+\hat{j}-\hat{k}$ then the angle between the vectors $\vec{a}$ and $\vec{b}$ is

The variance of the discrete data 3, 4, 5, 6, 7, 8, 10, 13 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 a coin is tossed seven times, then the probability of getting exactly three heads such that no two heads occur consecutively is

Two cards are drawn randomly from a pack of 52 playing cards one after the other with replacement. If A is the event of drawing a face card in the first draw and B is the event of drawing a clubs card in the second draw, then $P\left(\frac{B}{A}\right)=$

If X is a random variable with probability distribution $P(X=k) = \frac{(2k+3)c}{3^k}$, $k=0,1,2,\dots,\infty$, then $P(X=3) =$

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

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

If $\vec{a} = (x+2y-3)\hat{i} + (2x-y+3)\hat{j}$ and $\vec{b} = (3x-2y)\hat{i} + (x-y+1)\hat{j}$ are two vectors such that $\vec{a} = 2\vec{b}$, then $y-5x=$

If $\vec{a} = \hat{i} + \sqrt{11}\hat{j} - 2\hat{k}$ and $\vec{b} = \hat{i} + \sqrt{11}\hat{j} - 10\hat{k}$ are two vectors then the component of $\vec{b}$ perpendicular to $\vec{a}$ is

Let $\vec{a} = \hat{i} + 2\hat{j} + 2\hat{k}$ and $\vec{b} = 2\hat{i} - \hat{j} + p\hat{k}$ be two vectors. If $(\vec{a}, \vec{b}) = 60^\circ$, then $p =$

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

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

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

$16 \sin 12^\circ \cos 18^\circ \sin 48^\circ =$

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

If $0 \le x \le \frac{3}{4}$, then the number of values of $x$ satisfying the equation $\text{Tan}^{-1}(2x-1) + \text{Tan}^{-1}2x = \text{Tan}^{-1}4x - \text{Tan}^{-1}(2x+1)$ is

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

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

There are 15 stations on a train route and the train has to be stopped at exactly 5 stations among these 15 stations. If it stops at at least two consecutive stations, then the number of ways in which the train can be stopped is

Number of all possible ways of distributing eight identical apples among three persons is

Number of all possible words (with or without meaning) that can be formed using all the letters of the word CABINET in which neither the word CAB nor the word NET appear is

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

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