List of top Mathematics Questions asked in TS EAMCET

The general solution of the differential equation \[ \frac{dy}{dx} + \frac{\sin(2x + y)}{\cos x} + 2 = 0 \] is:
Evaluate the integral: \[ \int 4\cos^2 x - 5\sin^2 x \cos x \, dx. \]
Evaluate the integral: \[ \int \frac{4\tan^4 x + 3 \tan^2 x - 1}{\tan^2 x + 4} \, dx. \]
Evaluate the integral: \[ \int \left( \sin^3 x + \cos^2 x \right)^2 \, dx \]
Evaluate the integral: \[ I = \int_{-\frac{\pi}{8}}^{\frac{\pi}{8}} \frac{\sin^4(4x)}{1 + e^{4x}} \, dx \]
The area of the region enclosed by the curves \( y^2 = 4(x+1) \) and \( y^2 = 5(x-4) \) is:
If \(\theta\) is the angle between the vectors \(4\mathbf{i} - \mathbf{j} + 2\mathbf{k}\) and \( \mathbf{i} + 3\mathbf{j} - 2\mathbf{k}\), then \(\sin 2\theta\) is:
If the probability that a randomly selected student from a college is good at mathematics is 0.6, then the probability of having exactly two students who are good at mathematics in a group of 8 students standing in front of the college is:
If the focal chord of the parabola \( x^2 = 12y \) drawn through the point \( (3, 0) \) intersects the parabola at the points P and Q, then the sum of the reciprocals of the abscissae of the points P and Q is:
(a,b) is the point of concurrency of the lines \(x-3y+3=0\), \(Kx+y+k=0\) and \(2x+y-8=0\). If the perpendicular distance from the origin to the line \(L: ax-by+2k=0\) is \(p\), then the perpendicular distance from the point \((2,3)\) to \(L=0\) is:
If the normal drawn at the point \( P(9, 9) \) on the parabola \( y^2 = 9x \) meets the parabola again at \( Q(a, b) \), then \( 2a + b = \text{?} \)
The length of the latus rectum of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) \( (a>b) \) is \( \frac{8}{3} \). If the distance from the center of the ellipse to its focus is \( \sqrt{5} \), then \( \sqrt{a^2 + 6ab + b^2} = \text{?} \)
If \( (h, k) \) is the internal center of similitude of the circles \( x^2 + y^2 + 2x - 6y + 1 = 0 \) and \( x^2 + y^2 - 4x + 2y + 4 = 0 \), then find \( 4h \).
A circle \( S \equiv x^2 + y^2 + 2gx + 2fy + 6 = 0 \) cuts another circle \[ x^2 + y^2 - 6x - 6y - 6 = 0 \] orthogonally. If the angle between the circles \( S = 0 \) and \[ x^2 + y^2 + 6x + 6y + 2 = 0 \] is 60°, then the radius of the circle \( S = 0 \) is:
If \( \sin^{-1}(4x) - \cos^{-1}(3x) = \frac{\pi}{6} \), then \( x = \):
If \( \frac{2x^3 + 1}{2x^2 - x - 6} = ax + b + \frac{A}{px - 2} + \frac{B}{2x + q} \), then \( 51apB = \):
If a circle passing through the point \((1,1)\) cuts the circles \(x^2 + y^2 + 4x - 5 = 0\) and \(x^2 + y^2 - 4x + 3 = 0\) orthogonally, then the center of that circle is:
In triangle ABC, if \( a = 4, b = 3, c = 2 \), then \( 2(a - b \cos C)(a - c \sec B) = \):
If \( \tan A = -\frac{60}{11} \) and A does not lie in the 4th quadrant. \( \sec B = \frac{41}{9} \) and B does not lie in the 1st quadrant. If \( \csc A + \cot B = K \), then \( 24K = \):
If \( \tan A + \tan B + \cot A + \cot B = \tan A \tan B - \cot A \cot B \) and \( 0^\circ<A + B<270^\circ \), then \( A + B = \):
The equation that is satisfied by the general solution of the equation \( 4 - 3 \cos \theta = 5 \sin \theta \cos \theta \) is:
In triangle ABC, if \( A = 45^\circ \), \( C = 75^\circ \), and \( R = \sqrt{2} \), then the value of \( r \) is:
If \[ 2x^2 - 3xy + 4y^2 + 2x - 3y + 4 = 0 \] then \[ \left( \frac{dy}{dx} \right)_{(3,2)} = \]
If \[ x = \frac{9t^2}{1 + t^4}, \quad y = \frac{16t^2}{1 - t^4} \] then \[ \frac{dy}{dx} = \]
A plane \(\pi\) passes through the points \( (5,1,2) \), \( (3,-4,6) \), and \( (7,0,-1) \). If \( p \) is the perpendicular distance from the origin to the plane \(\pi\) and \([l, m, n]\) are the direction cosines of a normal to the plane \(\pi\), then \([3l + 2m + 5n] =\)