List of top Questions asked in AP EAPCET

Evaluate the integral: \[ I = \int_{-3}^{3} |2 - x| dx. \]

Evaluate the integral: \[ I = \int \frac{\cos x + x \sin x}{x (x + \cos x)} dx =\]

If a tangent to the hyperbola $ x^2 - \frac{y^2}{3} = 1 $ is also a tangent to the parabola $ y^2 = 8x $, then the equation of such tangent with the positive slope is:

Evaluate the infinite series: \[ 1 + \frac{1}{3} + \frac{1.3}{3.6} + \frac{1.3.5}{3.6.9} + \dots \text{ to } \infty = \]

If the solution of the system of simultaneous linear equations: $$ x + y - z = 6, $$ $$ 3x + 2y - z = 5, $$ $$ 2x - y - 2z + 3 = 0 $$ is $ x = \alpha, y = \beta, z = \gamma $, then $ \alpha + \beta = ?$

Two digits are selected at random from the digits 1 through 9. If their sum is even, then the probability that both are odd is:

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

If $ T = 2\pi \sqrt{\frac{L}{g}} $, $ g $ is a constant and the relative error in $ T $ is $ k $ times to the percentage error in $ L $, then $ \frac{1}{k} = $ ?

In $ \triangle ABC $, if $ r_1 = 4 $, $ r_2 = 8 $, $ r_3 = 24 $, then find $ a $=

If the equation of the circle passing through the points of intersection of the circles \[ x^2 - 2x + y^2 - 4y - 4 = 0, \quad x^2 + y^2 + 4y - 4 = 0 \] and the point $ (3,3) $ is given by \[ x^2 + y^2 + \alpha x + \beta y + \gamma = 0, \] then $ 3(\alpha + \beta + \gamma) $ is:

A common tangent to the circle $ x^2 + y^2 = 9 $ and the parabola $ y^2 = 8x $ is

Let $ a $ be an integer multiple of 8. If $ S $ is the set of all possible values of $ a $ such that the line $ 6x + 8y + a = 0 $ intersects the circle $ x^2 + y^2 - 4x - 6y + 9 = 0 $ at two distinct points, then the number of elements in $ S $ is:

If $ A(1,0,2) $, $ B(2,1,0) $, $ C(2,-5,3) $, and $ D(0,3,2) $ are four points and the point of intersection of the lines $ AB $ and $ CD $ is $ P(a,b,c) $, then $ a + b + c = ? $

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 = ? $

The distance of the point $ O(0,0,0) $ from the plane $ \overrightarrow{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 5 $ measured parallel to $ 2\hat{i} + 3\hat{j} - 6\hat{k} $ is?

Evaluate the expression: \[ \frac{\sin 1^\circ + \sin 2^\circ + \dots + \sin 89^\circ}{2(\cos 1^\circ + \cos 2^\circ + \dots + \cos 44^\circ) + 1} =\]

If $ \overrightarrow{a}, \overrightarrow{b} $ are two non-collinear vectors, then $ |\overrightarrow{b}| \overrightarrow{a} + |\overrightarrow{a}| \overrightarrow{b} $ represents

The general solution of the differential equation \[ (x + y)y \,dx + (y - x)x \,dy = 0 \] is:

Let $ \overline{X} $ and $ \overline{Y} $ be the arithmetic means of the runs of two batsmen A and B in 10 innings respectively, and $ \sigma_A, \sigma_B $ are the standard deviations of their runs in them. If batsman A is more consistent than B, then he is also a higher run scorer only when

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) = $ ?

The general solution of the differential equation $$ (y^2 + x + 1) \, dy = (y + 1) \, dx $$ is:

If the origin is shifted to a point $ P $ by the translation of axes to remove the $ y $-term from the equation $ x^2 - y^2 + 2y - 1 = 0 $, then the transformed equation of it is:

Match the items of List-I with those of List-II (Here $ \Delta $ denotes the area of $ \triangle ABC $).

Then the correct match is

Given the equation: $$ \frac{A}{x-a} + \frac{Bx + C}{x^2 + b^2} = \frac{1}{(x-a)(x^2 + b^2)} $$ then $ C $=

If a polygon of $ n $ sides has 275 diagonals, then $ n $ is: