List of top Mathematics Questions asked in AP EAMCET

If \( m, n \) are respectively the least positive and greatest negative integer values of such that \( (\frac{1-i}{1+i})^k = -i\), then \( m - n = \):
Evaluate the integral \[ \int_{0}^{\frac{\pi}{4}} \frac{x^2}{(x \sin x + \cos x)^2} dx. \]
If the plane \[ x - y + z + 4 = 0 \] divides the line joining the points \[ P(2,3,-1) \quad {and} \quad Q(1,4,-2) \] in the ratio \( l:m \), then \( l + m \) is:
Let \( \vec{a} \times \vec{b} = 7\hat{i} - 5\hat{j} - 4\hat{k} \) and \( \vec{a} = \hat{i} + 3\hat{j} - 2\hat{k} \), if the length of projection of \( \vec{b} \) on \( \vec{a} \) is \( \frac{8}{\sqrt{14}} \), then \( |\vec{b}| \) is:
If \( (a, b) \) is the stationary point of the curve \( y = 2x - x^2 \), then the area bounded by the curves \( y = 2x - x^2 \), \( y = x^2 - 2x \), and \( x = a \) is:
Evaluate \( \int_{1}^{2} \frac{x^4 - 1}{x^6 - 1} dx \):
The real values of \( x \) that satisfy the equation \[ \tan^{-1}x + \tan^{-1}2x = \frac{\pi}{4} \] is:
If a committee of 10 members is to be formed from 8 men and 6 women, then the number of different possible committees in which the men are in majority is:

The circle S = x2 + y2 − 2x − 4y + 1 = 0 cuts the y-axis at A, B (OA: OB). If the radical axis of S ≡ 0 and S′ = x2 + y2 − 4x − 2y + 4 = 0 cuts the y-axis at C, then the ratio in which C divides AB is:

In a class consisting of 40 boys and 30 girls, 30% of the boys and 40% of the girls are good at Mathematics. If a student selected at random from that class is found to be a girl, then the probability that she is not good at Mathematics is:
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:
The equation of a circle which touches the straight lines \[ x + y = 2, \quad x - y = 2 \] and also touches the circle \[ x^2 + y^2 = 1 \] is:
If \( \vec{a}, \vec{b}, \vec{c}, \vec{d} \) are position vectors of 4 points such that \( 2\vec{a} + 3\vec{b} + 5\vec{c} - 10\vec{d} = 0 \), then the ratio in which the line joining \( \vec{c} \) divides the line segment joining \( \vec{a} \) and \( \vec{b} \) is:
In each of the following options, a function and an interval are given. Choose the option containing the function and the interval for which Lagrange’s Mean Value Theorem is not applicable.
P is a point on \( x + y + 5 = 0 \), whose perpendicular distance from \( 2x + 3y + 3 = 0 \) is \( \sqrt{13} \), then the coordinates of P are:
If \( O(0, 0, 0), A(3, 0, 0), B(0, 4, 0) \) form a triangle then the incenter of triangle OAB 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:
If \(540^\circ<A<630^\circ\) and \(|\cos A| = \frac{5}{13}\), then \( \tan\frac{A}{2} \tan A =\)
A is a point on the circle with radius 8 and center at O. A particle P is moving on the circumference of the circle starting from A. M is the foot of the perpendicular from P on OA and \( \angle POM = \theta \). When \( OM = 4 \) and \( \frac{d\theta}{dt} = 6 \) radians/sec, then the rate of change of PM is (in units/sec):
Evaluate the integral: \[ I = \int_{-5\pi}^{5\pi} \left(1 - \cos 2x \right)^{\frac{5}{2}} dx. \]
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 the roots of the equation \(x^3 + ax^2 + bx + c = 0\) are in arithmetic progression, then:
If \( \frac{3 - 2i \sin \theta}{1 + 2i \sin \theta}\) is a purely imaginary number, then \( \theta \) is:
If \[ x = 3 \left[ \sin t - \log \left( \cot \frac{t}{2} \right) \right], \quad y = 6 \left[ \cos t + \log \left( \tan \frac{t}{2} \right) \right] \] then find \( \frac{dy}{dx} \).
The differential equation of the family of hyperbolas having their centers at origin and their axes along the coordinate axes is: