List of top Questions asked in AP EAPCET- 2025

If the area of a right angled triangle with hypotenuse 5 is maximum, then its perimeter is
If the point of contact of the circles \( x^2+y^2-6x-4y+9=0 \) and \( x^2+y^2+2x+2y-7=0 \) is \( (\alpha, \beta) \), then \( 7\beta = \)
If Q \( (\alpha, \beta, \gamma) \) is the harmonic conjugate of the point P(0,-7,1) with respect to the line segment joining the points (2,-5,3) and (-1,-8,0), then \( \alpha - \beta + \gamma = \)
If \(3x+2\sqrt{2}y+k=0\) is a normal to the hyperbola \(4x^2-9y^2-36=0\) making positive intercepts on both the axes, then \(k=\) Options :
If the equation of the pair of lines passing through (1, 1) and perpendicular to the pair of lines \(2x^2 + xy - y^2 - x + 2y - 1 = 0\) is \(ax^2 + 2hxy + by^2 + 2gx + 3y = 0\). then \(\frac{b}{a} =\)
If \( ax^2 + 2hxy - 2ay^2 + 3x + 15y - 9 = 0 \) represents a pair of lines intersecting at (1,1), then ah =
If the lines \(x+y-2=0\), \(3x-4y+1=0\) and \(5x+ky-7=0\) are concurrent at \((\alpha, \beta)\), then equation of the line concurrent with the given lines and perpendicular to \(kx+y-k=0\) is
If the four points (6,2,4), (1,3,5), (1,-2,3), and (6,k,2) are coplanar, then \(k =\)
The area (in square units) of the triangle formed by the X-axis, the tangent and the normal drawn at (1, 1) to the curve $x^3 + y^3 = 2xy$ is
Identify the correct option from the following:
If the equation of the circle lying in the first quadrant, touching both the coordinate axes and the line \( \frac{x}{3} + \frac{y}{4} = 1 \) is \( (x-c)^2+(y-c)^2=c^2 \), then c =
The value of $c$ of Rolle's theorem for the function $f(x) = 2 \sin x + \sin 2x$ in the interval $[0, \pi]$ is
Identify the correct option from the following:
If a circle S passes through the origin and makes intercept 4 units on line \(x = 2\), then the equation of curve on which center of S lies is
The lengths of the two focal chords of the parabola \( y^2 = 16x \) is 25 units each. If these two chords cut the parabola at \( A, B, C, D \), then the area (in sq. units) of the quadrilateral formed by \( A, B, C, D \) is:
A line segment \( PQ \) has the length 63 and direction ratios \( (3, -2, 6) \). If this line makes an obtuse angle with the X-axis, then the components of the vector \( \vec{PQ} \) are:
If the tangents drawn from a point \( P \) to the ellipse \( 4x^2+9y^2-16x+54y+61=0 \) are perpendicular, then the locus of \( P \) is:
Let \( A_1 \) be the area of the given ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \). Let \( A_2 \) be the area of the region bounded by the curve which is the locus of mid point of the line segment joining the focus of the ellipse and a point P on the given ellipse, then \( A_1 : A_2 = \)
If the perpendicular distances from the points \( (2,3) \), \( (4,a) \), and \( (\alpha, \beta) \) onto the line \( 3x + 4y - 3 = 0 \) are equal and \( 4\alpha - 3\beta + 1 = 0 \), then the sum of all possible values of \( \alpha \), \( \alpha \) and \( \beta \) is:
Which one of the following functions is monotonically increasing in its domain?
A circle passing through origin cuts the coordinate axes at \(A\) and \(B\). If the straight line \(AB\) passes through a fixed point \((x_1,y_1)\), then the locus of the centre of the circle is?
If the circle \(S_1 = x^2 + y^2 + 2gx + 4y + 1 = 0\) bisects the circumference of circle \(x^2 + y^2 - 2x - 3 = 0\), then the radius of circle \(S_1\) is
The equation of the normal drawn at the point \((\sqrt{2}+1, -1)\) to the ellipse \(x^2 + 2y^2 - 2x + 8y + 5 = 0\) is
If \( \int \frac{5 \tan x}{\tan x - 2} \, dx = a x + b \log |\sin x - 2 \cos x| + c \), then \( a + b = \)
The lengths of the two focal chords of the parabola \( y^2 = 16x \) is 25 units each. If these two chords cut the parabola at \( A, B, C, D \), then the area (in sq. units) of the quadrilateral formed by \( A, B, C, D \) is:
\(\operatorname{Tanh}^{-1}(\sin\theta) =\)
The angle between the tangents drawn from point (1, 4) to parabola \(y^2 = 4x\) is