List of top Questions asked in AP EAPCET

Let $ \overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c} $ be non-coplanar vectors. If $ \alpha \overrightarrow{d} = \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} $, $ \beta \overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c} + \overrightarrow{d} $, then $ | \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} + \overrightarrow{d} | = ? $

The radical axis of the circles \[ x^2 + y^2 + 2gx + 2fy + c = 0 \] and \[ 2x^2 + 2y^2 + 3x + 8y + 2c = 0 \] touches the circle \[ x^2 + y^2 + 2x + 2y + 1 = 0. \] Then:

If the equation of the circle whose radius is 3 units and which touches internally the circle $$ x^2 + y^2 - 4x - 6y - 12 = 0 $$ at the point $ (-1, -1) $ is $$ x^2 + y^2 + px + qy + r = 0, $$ then $ p + q - r $ is:

If the function f(x) = $\sqrt{x^2 - 4}$ satisfies the Lagrange’s Mean Value Theorem on $[2, 4]$, then the value of $ C $ is}

If $3A = \begin{bmatrix} 1 & 2 & 2 \\[0.3em] 2 & 1 & -2 \\[0.3em] a & 2 & b \end{bmatrix}$ and $AA^T = I$, then$\frac{a}{b} + \frac{b}{a} =$:

If $ A, B, C $ are the angles of a triangle, then \[ \sin 2A - \sin 2B + \sin 2C = \]

Equation of the circle having its centre on the line $ 2x + y + 3 = 0 $ and having the lines $ 3x + 4y - 18 = 0 $ and $ 3x + 4y + 2 = 0 $ as tangents is:

Evaluate the expression \[ 2 \cot h^{-1}(4) + \sec h^{-1}\left( \frac{3}{5} \right). \]

If the equation of the pair of straight lines passing through the point $ (1, 1) $ and perpendicular to the pair of lines $ 3x^2 + 11xy - 4y^2 = 0 $ is $ ax^2 + 2hxy + by^2 + 2gx + 2fy + 12 = 0 $, then find $ 2(a + h - b - g + f - 12) = ? $

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

Evaluate the integral: $$ I = \int_{\frac{1}{\sqrt[5]{32}}}^{\frac{1}{\sqrt[5]{31}}} \frac{1}{\sqrt[5]{x^{30} + x^{25}}} \, dx. $$

If power of a point $ (4,2) $ with respect to the circle $ x^2 + y^2 - 2x + 6y + a^2 - 16 = 0 $ is 9, then the sum of the lengths of all possible intercepts made by such circles on the coordinate axes is

Assertion (A): If $ B $ is a $ 3 \times 3 $ matrix and $ |B| = 6 $, then $ | \text{Adj}(B) | = 36 $. Reason (R): If $ B $ is a square matrix of order $ n $, then $ |\text{Adj}(B)| = |B|^n $.

If $ x $ is real and $ \alpha, \beta $ are maximum and minimum values of $ \frac{x^2 - x + 1}{x^2 + x + 1} $ respectively, then $ \alpha + \beta = $:

For $ x<0 $, $ \frac{d}{dx} [|x|^x] $ is given by:

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

Then the correct match is