List of top Mathematics Questions asked in TS EAMCET

The probability distribution of a random variable X is given below. Then, the standard deviation of X is.

Urn A contains 6 white and 2 black balls; urn B contains 5 white and 3 black balls and urn C contains 4 white and 4 black balls. If an urn is chosen at random and a ball is drawn at random from it, then the probability that the ball drawn is white is

If \( f(x)=\sqrt{\cos ^{-1} \sqrt{1-x^{2}}} \), then \( f^{\prime}\left(\frac{1}{2}\right)= \)

If all the letters of the word 'HANDLE' are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word 'HELAND' is

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

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

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

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

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

If \( x = \frac{t^2}{1+t^5} \), \( y = \frac{2t^3}{1+t^5} \) and \( t \neq -1 \) is a parameter then \( \frac{dy}{dx} = \)

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

If \( y = f(\cosh x) \) and \( f'(x) = \log(x + \sqrt{x^2-1}) \) then \( \frac{d^2 y}{dx^2} = \)

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 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 A, B are the points of contact of the tangents drawn from the point (-3,1) to the circle \( x^2+y^2-4x+2y-4=0 \), then the equation of the circumcircle of the triangle PAB is

1+(1+3)+(1+3+5)+(1+3+5+7)+... to 10 terms =

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

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

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

5 boys and 5 girls have to sit around a table. The number of ways in which all of them can sit so that no two boys and no two girls are together is

Consider the following statements
Statement-I: $\cosh^{-1}x = \tanh^{-1}x$ has no solution
Statement-II: $\cosh^{-1}x = \coth^{-1}x$ has only one solution
The correct answer is

If a=3, b=5, c=7 are the sides of a triangle ABC, then \( \cot A + \cot B + \cot C = \)

If $x = \sin 2\theta \cos 3\theta$, $y = \sin 3\theta \cos 2\theta$, then $\frac{dy}{dx} =$