List of top Mathematics Questions asked in TS EAMCET

If the line $ 4x - 3y + p = 0 $ (where $ p + 3>0 $) touches the circle $ x^2 + y^2 - 4x + 6y + 4 = 0 $ at the point $ (h,k) $, then the value of $ h - 2k $ is:

Evaluate the integral: \[ \int \frac{\sec x}{3(\sec x + \tan x) + 2} \,dx \]

If the line \[ 2x + by + 5 = 0 \] forms an equilateral triangle with \[ ax^2 - 96bxy + ky^2 = 0, \] then $ a + 3k $ is: \

If all the numbers which are greater than 6000 and less than 10000 are formed with the digits $ 3,5,6,7,8 $ without repetition of the digits, then the difference between the number of odd numbers and the number of even numbers among them is:

The mean and variance of a binomial variate $X$ are $\frac{16}{5}$ and $\frac{48}{25}$ respectively. Given that $P(X \geq 1) = 1 - K \left(\frac{3}{5}\right)^7$, find $5K$:

If the focus of an ellipse is $(-1,-1)$, equation of its directrix corresponding to this focus is $x + y + 1 = 0$ and its eccentricity is $\frac{1}{\sqrt{2}}$, then the length of its major axis is:

The set of all real values of $x$ for which the expansion of: $$ \left( 125x^2 - \frac{27}{x} \right)^{-23} $$ is valid, is:

Given a square matrix $A$ where $A^2 + I = 2A$, find $A^9$.

If $ (2, -1) $ is the point of intersection of the pair of lines \[ 2x^2 + axy + 3y^2 + bx + cy - 3 = 0 \quad \text{then} \quad 3a + 2b + c = \]

If the angle between the pair of lines given by the equation $ax^2 + 4xy + 2y^2 = 0$ is $45^\circ$, then the possible values of 'a' are

f is a real valued function satisfying the relation $f\bigl(3x + \tfrac{1}{2x}\bigr) \;=\; 9x^2 + \tfrac{1}{4x^2}$. If $f\bigl(x + \tfrac{1}{x}\bigr) = 1$ then $x =$ ?

Suppose $ \theta_1 $ and $ \theta_2 $ are such that $ (\theta_1 - \theta_2) $ lies in the 3rd or 4th quadrant. If \[ \sin\theta_1 + \sin\theta_2 = \frac{21}{65} \quad \text{and} \quad \cos\theta_1 + \cos\theta_2 = \frac{27}{65} \] then \[ \cos\left(\frac{\theta_1 - \theta_2}{2}\right) = \]

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with the name of his own wife is ?

If 2 cards drawn at random from a well shuffled pack of 52 playing cards are from the same suit, then the probability of getting a face card and a card having a prime number is:

If the tangents $ x + y + k = 0 $ and $ x + ay + b = 0 $ drawn to the circle $ S : x^2 + y^2 + 2x - 2y + 1 = 0 $ are perpendicular to each other and $ k, b $ are both greater than 1, then find $ b - k $.

If $2\,\tan^{-1}x = 3\,\sin^{-1}x$ and $x \neq 0$, then $8x^2 +1 =\;?$

If \[ \frac{x^4}{(x^2+1)(x-2)} = f(x) + \frac{Ax+B}{x^2+1} + \frac{C}{x-2} \] then $ f(14) + 2A - B = $ ?

For $ n \in \mathbb{N} $, the largest positive integer that divides $ 81^n + 20n - 1 $ is $ k $. If $ S $ is the sum of all positive divisors of $ k $, then find $ S - k $.

Evaluate the integral: \[ \int \frac{dx}{9\cos^2 2x + 16\sin^2 2x} \]

The slope of a common tangent to the circles $ x^2 + y^2 - 4x - 8y + 16 = 0 $ and $ x^2 + y^2 - 6x - 16y + 64 = 0 $ is:

If the ratio of the distances of a variable point $P$ from the point $(1,1)$ and the line $x - y + 2 = 0$ is $1/\sqrt{2}$, then the equation of the locus of $P$ is: