List of top Mathematics Questions asked in AP EAMCET

If the origin is shifted to remove the first degree terms from the equation \(2x^2 - 3y^2 + 4xy + 4x + 4y - 14 = 0\), then with respect to this new co-ordinate system, the transformed equation of \(x^2 + y^2 - 3xy + 4y + 3 = 0\) is
The angle between the line with the direction ratios \( (2, 5, 1) \) and the plane \( 8x + 2y - z = 4 \) is given by
The equation of the straight line passing through the point of intersection of the lines represented by \(x^2 + 4xy + 3y^2 - 4x - 10y + 3 = 0\) and the point \((2,2)\) is:
Equation of a tangent line of the parabola \(y^2 = 8x\), which passes through the point \((1, 3)\) is:
If \( L_1 \) and \( L_2 \) are two lines which pass through origin and have direction ratios \( (3, 1, -5) \) and \( (2, 3, -1) \) respectively, then the equation of the plane containing \( L_1 \) and \( L_2 \) is:
Let \( A(2, 3), B(1, -1) \) be two points. If \( P \) is a variable point such that \( \angle APB = 90^\circ \), then the locus of \( P \) is
In the interval \([0, 3]\), the function \(f(x) = |x - 1| + |x - 2|\) is:
If the mean deviation about the mean is \(m\) and the variance is \(\sigma^2\) for the following data, then \(m + \sigma^2 =\) % Data table \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 5 & 7 & 9 \\ \hline f & 4 & 24 & 28 & 16 & 8 \\ \hline \end{array} \]
Evaluate the integral \( \int_0^{\frac{\pi}{2}} \frac{1}{1 + \sqrt{\tan x}} \, dx \):
A box \( P \) contains one white ball, three red balls and two black balls. Another box \( Q \) contains two white balls, three red balls and four black balls. If one ball is drawn at random from each one of the two boxes, then the probability that the balls drawn are of different color is
Two natural numbers are chosen at random from 1 to 100 and are multiplied. If \(A\) is the event that the product is an even number and \(B\) is the event that the product is divisible by 4, then \(P(A \cap \bar B) = \)
If a complex number \( z \) is such that \( \frac{z-2i}{z-2} \) and the locus of \( z \) is a closed curve, then the area of the region bounded by that closed curve and lying in the first quadrant is:
\(\int\left(\frac{x}{x\cos x - \sin x}\right)^2 dx = \)
If $$ y = (1 + a + a^2 + \dots)e^{nx} $$ then the relative error in $y$ is:

 If the equation of the tangent at (2, 3) on y2 = ax3 + b is y = 4x - 5, then the value of a2 + b2 is:

If a tangent of slope 2 to the ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) touches the circle \(x^2 + y^2 = 4\), then the maximum value of ab is:

If \( y = f(x) \) is a thrice differentiable function and a bijection, then \[ \frac{d^2x}{dy^2} \left(\frac{dy}{dx}\right)^3 + \frac{d^2y}{dx^2} = ? \]
The normal drawn at a point \( (2, -4) \) on the parabola \( y^2 = 8x \) cuts again the same parabola at \( (\alpha, \beta) \). Then \( \alpha + \beta \) is:
The locus of the midpoints of the chords of the hyperbola \( x^2 - y^2 = a^2 \) which touch the parabola \( y^2 = 4ax \) is:
The solution of the differential equation \[ x dy - y dx = \sqrt{x^2 + y^2} dx \] when \( y(\sqrt{3}) = 1 \) is:
If the product of the eccentricities of the ellipse \( \frac{x^2}{16} + \frac{y^2}{b^2} = 1 \) and the hyperbola \( \frac{x^2}{9} - \frac{y^2}{16} = 1 \) is 1, then the value of \( b^2 \) is:
While solving a system of linear equations \( AX = B \) using Cramer’s rule, if \includegraphics[]{6.png}
A point moves on the curve \( y = x^3 - 3x^2 + 2x - 1 \) and its y-coordinate increases at a rate of 6 units per second. When the point is at (2,-1), the rate of change of its x-coordinate is:
The length of the tangent drawn at the point \( P \left( \frac{\pi}{4} \right) \) on the curve \( x^{2/3} + y^{2/3} = 2^{2/3} \) is:
The set of all real values of \( a \) such that the function \( f(x) = x^3 + 2ax^2 + 3(a+1)x + 5 \) is strictly increasing in its entire domain is: