List of top Mathematics Questions asked in AP EAPCET

If two numbers $x$ and $y$ are chosen one after the other at random with replacement from the set of numbers $ \{1, 2, 3, \ldots, 10\} $, then the probability that $ |x^2 - y^2| $ is divisible by 6 is:

If $ a $ is a common root of $ x^2 - 5x + \lambda = 0 $ and $ x^2 - 8x - 2\lambda = 0 $ ($ \lambda \neq 0 $) and $ \beta, \gamma $ are the other roots of them, then $ a + \beta + \gamma + \lambda = $:

If $ 5 \sinh x - \cosh x = 5 $, then one of the values of $ \tanh x $ is:

If \[ \int \frac{2}{1+\sin x} dx = 2 \log |A(x) - B(x)| + C \] and $ 0 \leq x \leq \frac{\pi}{2} $, then $ B(\pi/4) = $ ?

If $ 1 \cdot 3 \cdot 5 + 3 \cdot 5 \cdot 7 + 5 \cdot 7 \cdot 9 + \dots $ (n terms) = $ n(n + 1)f(n) - 3n $, then $ f(1) = $:

Evaluate the sum: \[ \frac{1}{3 \cdot 7} + \frac{1}{7 \cdot 11} + \frac{1}{11 \cdot 15} + \dots \text{ up to 50 terms=} \]

Evaluate the integral $$ \int_{0}^{\frac{\pi}{4}} \frac{x^2}{(x \sin x + \cos x)^2} dx. $$

If $ y = \tan(\log x) $, then $ \frac{d^2y}{dx^2} $ is given by:

The angle between the planes $ \vec{r} \cdot (12\hat{i} + 4\hat{j} - 3\hat{k}) = 5 $ and $ \vec{r} \cdot (5\hat{i} + 3\hat{j} + 4\hat{k}) = 7 $ is:

Sum of the positive roots of the equation: \[ \begin{vmatrix} x^2 + 2x + 2 & x + 2 & 1 \\ 2x + 1 & x - 1 & 1 \\ x + 2 & -1 & 1 \end{vmatrix} = is \; 0. \]

Let $ a>1 $ and $ 0<b<1 $. -∞$ f : \mathbb{R} \to [0, 1] $ is defined by $ f(x) = \begin{cases} a^x & \text{if } x<0 b^x & \text{if } 0 \leq x \leq 1 \end{cases} $, then $ f(x) $ is:

Let $ f(x) = 3 + 2x $ and $ g_n(x) = (f \circ f \circ \dots \text{n times}) (x) $. If for all $ n \in \mathbb{N} $, the lines $ y = g_n(x) $ pass through a fixed point $ (a, \beta) $, then $ \alpha + \beta = ? $

If the sum of two roots of $ x^3 + px^2 + qx - 5 = 0 $ is equal to its third root, then $ p(q^2 - 4q) = $ ?

If $ 2x^2 + 3x - 2 = 0 $ and $ 3x^2 + \alpha x - 2 = 0 $ have one common root, then the sum of all possible values of $ \alpha $ is:

If $ a_n = \sum_{r=0}^{n} \frac{1}{\binom{n}{r}} $, then $ \sum_{r=0}^{n} r \binom{n}{r} = $:

If $n$ is an integer and $Z = \cos \theta + i \sin \theta$, $\theta \neq (2n + 1)$ $\frac{\pi}{2}$, then: $\frac{1 + Z^{2n}}{1 - Z^{2n}}$ = ?