List of top Mathematics Questions asked in AP EAPCET

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

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:

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

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

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}

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

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

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 $.

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

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 = $:

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

Then the correct match is

Evaluate the integral \[ I = \int_0^1 \frac{x}{(1 - x)^{3/4}} \, dx \]

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:

A line $ L $ intersects the lines $ 3x - 2y - 1 = 0 $ and $ x + 2y + 1 = 0 $ at the points $ A $ and $ B $. If the point $ (1,2) $ bisects the line segment $ AB $ and $ \frac{a}{b} x + \frac{b}{a} y = 1 $ is the equation of the line $ L $, then $ a + 2b + 1 = ? $

The real valued function $ f: \mathbb{R} \to \left[ \frac{5}{2}, \infty \right) $ defined by $ f(x) = \left| 2x + 1 \right| + \left| x - 2 \right| $ is:

The range of the real valued function $ f(x) =$ $\sin^{-1} \left( \frac{1 + x^2}{2x} \right)$ $+ \cos^{-1} \left( \frac{2x}{1 + x^2} \right)$ is:

The number of positive divisors of 1080 is:

Imaginary part of $ \frac{(1 - i)^3}{(2 - i)(3 - 2i)} $ is:

Suppose the axes are to be rotated through an angle $ \theta $ so as to remove the $ xy $ term from the equation $3 x^2 + 2\sqrt{3}xy + y^2 = 0 $. Then in the new coordinate system, the equation $ x^2 + y^2 + 2xy = 2 $ is transformed to:

The area of the region enclosed by the curves \[ 3x^2 - y^2 - 2xy + 4x + 1 = 0 \] and \[ 3x^2 - y^2 - 2xy + 6x + 2y = 0 \] is:

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

The square root of $ 7 + 24i $ is: