List of top Questions asked in AP EAMCET- 2024

A Circle S passes through the points of intersection of the circles \( x^2 + y^2 - 2x + 2y - 2 = 0 \) and \( x^2 + y^2 + 2x - 2y + 1 = 0 \). If the centre of this circle S lies on the line \( x - y + 6 = 0 \), then the radius of the circle S is:
Find the equation of a line passing through the intersection of \( 3x + y - 4 = 0 \) and \( x - y = 0 \), and making a \( 45^\circ \) angle with \( x - 3y + 5 = 0 \).

If the area of the circum-circle of the triangle formed by the line 2x + 5y + a = 0 and the positive coordinate axes is \(\frac{29\pi}{4}\) sq. units, then |a| =

If the circle S = 0 cuts the circles x2 + y2 - 2x + 6y = 0, x2 + y2 - 4x - 2y + 6 = 0, and x2 + y2 - 12x + 2y + 3 = 0 orthogonally, then the equation of the tangent at (0, 3) on S = 0 is:

The equation of a line which makes an angle of \( 45^\circ \) with each of the pair of lines \[ xy - x - y + 1 = 0 \] is:
The equation of one side of an equilateral triangle is \( x + y = 2 \), and one vertex is \( (2,-1) \). The length of the side is:
If a variable straight line passing through the point of intersection of the lines x - 2y + 3 = 0 and 2x - y - 1 = 0 intersects the X and Y axes at A and B respectively, then the equation of the locus of a point which divides the segment AB in the ratio -2 : 3 is:
In a triangle ABC, if \( (r_1 + r_2) \csc^2 \frac{C}{2} = \)
In \( \triangle ABC \), given: \[ a = 26, \quad b = 30, \quad \cos C = \frac{63}{65} \] Find \( c \).
If \( H \) is the orthocenter of \( \triangle ABC \) and \( AH = x \), \( BH = y \), \( CH = z \), then evaluate: \[ \frac{abc}{xyz} \]
If a running track of 500 ft. is to be laid out enclosing a playground, the shape of which is a rectangle with a semicircle at each end, then the length of the rectangular portion such that the area of the rectangular portion is maximum is (in feet).
In a triangle ABC, if \( r : R = 1 : 3 : 7 \), then \( \sin(A + C) + \sin B = \)
In a triangle ABC, if \( a = 13, b = 14, c = 15 \), then \( r_1 = \)
If the direction cosines of two lines are given by \[ l + m + n = 0 \quad \text{and} \quad mn - 2lm - 2nl = 0, \] then the acute angle between those lines is:
In \(\Delta ABC\) if \(B = 90^\circ\) then \(2(r + R) = \)
If the angle \( \theta \) between the line \( \frac{x + 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{2} \) and the plane \( 2x - y + \sqrt{\lambda}z + 4 = 0 \) is such that \( \sin \theta = \frac{1}{3} \), then the value of \( \lambda \) is:
Find the locus of points satisfying the equation \( axy + byz = cy \).
In a triangle ABC, if \( (a-b)(s-c) = (b-c)(s-a) \), then \( r_1 + r_3 = \):
What are X, Y, Z in the following reaction sequence respectively?
Gattermann-Koch reaction

What are X and Y respectively in the following reaction sequence? 

Some substances are given below Ag: CO\(_2\) (s); SiO\(_2\) (s); ZnS (s) SO\(_2\) (s); A/N: HCl (s); H\(_2\)O (s) The number of molecular solids and network solids in the above list is respectively.
In the Wurtz-Fitting reaction, a compound \(X\) reacts with an alkyl halide. What is \(X\)?
The product (C) in the given reaction sequence is:
bromination step with Br2
60 cm\(^3\) of SO\(_2\) gas diffused through a porous membrane in \( x \) minutes. Under similar conditions, 360 cm\(^3\) of another gas (molar mass 4 g mol\(^{-1}\)) diffused in \( y \) minutes. The ratio of \( x \) and \( y \) is:
In water, which of the following gases has the highest Henry’s law constant at 293 K?