List of top Questions asked in AP EAMCET

Let $[r]$ denote the largest integer not exceeding $r$, and the roots of the equation $ 3z^2 + 6z + 5 + \alpha(x^2 + 2x + 2) = 0 $ are complex numbers whenever $ \alpha > L $ and $ \alpha < M $. If $ (L - M) $ is minimum, then the greatest value of $[r]$ such that $ Ly^2 + My + r < 0 $ for all $ y \in \mathbb{R} $ 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 \( \triangle ABC \), if \( (r_2 - r_1)(r_3 - r_1) = 2r_2r_3 \), then \( 2(r + R) = \):
Given below are two statements
Statement - I: For isothermal irreversible change of an ideal gas, \[ q = -w = P_{\text{ext}}(V_{\text{final}} - V_{\text{initial}}) \] Statement - II: For adiabatic change, \[ \Delta U = W_{\text{adiabatic}} \] The correct answer is:
If the ratio of the absolute temperature of the sink and source of a Carnot engine is changed from 2:3 to 3:4, the efficiency of the engine changes by:
If m and M denote the mean deviations about mean and about median respectively of the data 20, 5, 15, 2, 7, 3, 11, then the mean deviation about the mean of m and M is:
Let \( [P] \) denote the greatest integer \( \leq P \). If \( 0 \leq a \leq 2 \), then the number of integral values of \( a \) such that \( \lim_{x \to a} [x^2] - [x]^2 \) does not exist is:

The descending order of magnitude of the eccentricities of the following hyperbolas is: 
A. A hyperbola whose distance between foci is three times the distance between its directrices. 
B. Hyperbola in which the transverse axis is twice the conjugate axis. 
C. Hyperbola with asymptotes \( x + y + 1 = 0, x - y + 3 = 0 \).

If the line with direction ratios \[ (1, a, \beta) \] is perpendicular to the line with direction ratios \[ (-1,2,1) \] and parallel to the line with direction ratios \[ (\alpha,1,\beta), \] then \( (\alpha, \beta) \) is:
Water of mass \( m \) at \( 30^\circ C \) is mixed with \( 5 \) g of ice at \( -20^\circ C \). If the resultant temperature of the mixture is \( 6^\circ C \), then the value of \( m \) is: (Given: Specific heat capacity of ice = \( 0.5 \) cal \( g^{-1} \) \( ^\circ C^{-1} \), Specific heat capacity of water = \( 1 \) cal \( g^{-1} \) \( ^\circ C^{-1} \), Latent heat of fusion of ice = \( 80 \) cal \( g^{-1} \))
The critical temperature of A, B, C, D gases are 190 K, 630 K, 261 K, 400 K respectively. The quantity of gas adsorbed per gram of charcoal at same pressure is least for the gas
At 300 K, the vapour pressures of A and B liquids are 500 and 400 mm Hg respectively. Equal moles of A and B are mixed to form an ideal solution. The mole fraction of A and B in vapor state is respectively.
A wire of length \(100 \text{ cm}\) and area of cross-section \(2 \text{ mm}^2\) is stretched by two forces of each \(440 \text{ N}\) applied at the ends of the wire in opposite directions along the length of the wire. If the elongation of the wire is \(2 \text{ mm}\), the Young’s modulus of the material of the wire is:
The decrease in each day in the Uranium mass of the material in a Uranium reactor operating at a power of 12 MW is (Energy released in one \(^{92}U\) fission is about 200 MeV)
A compound is formed by atoms of A, B and C. Atoms of C form hcp lattice. Atoms of A occupy 50% of octahedral voids and atoms of B occupy $\frac{2}{3}$ of tetrahedral voids. What is the molecular formula of the solid?
The equation of the circle touching the circle $$ x^2 + y^2 - 6x + 6y + 17 = 0 $$ externally and to which the lines $$ x^2 - 3xy - 3x + 9y = 0 $$ are normal is: 
Consider the reaction: \(C_2H_5Cl(g) \rightarrow 2C(g) + 5H(g) + Cl(g)\), where \(\Delta H = 3047 \, {kJ mol}^{-1}\). The bond dissociation enthalpy (\(\Delta_{{bond}} H\)) values of C–Cl and C=C bonds are 431 and 414 kJ mol\(^{-1}\), respectively. What is the average bond enthalpy of C–H in kJ mol\(^{-1}\)?
If the first ionisation enthalpy of Li, Be and C respectively are 520, 899, 1086 kJ/mol, the first ionisation enthalpy (in kJ/mol) of B will be
If 7 and 8 are the lengths of two sides of a triangle and \( a \) is the length of its smallest side. The angles of the triangle are in AP and \( a \) has two values \( a_1 \) and \( a_2 \) satisfying this condition. If \( a_1<a_2 \), then \( 2a_1 + 3a_2 = \):
For \( \lambda, \mu \in \mathbb{R} \), the lines \[ (x - 2y - 1) + \lambda (3x + 2y - 11) = 0 \] and \[ (3x + 4y - 11) + \mu (-x + 2y - 3) = 0 \] represent two families of lines. If the equation of the line common to both families is given by \[ ax + by - 5 = 0, \] then \( 2a + b = \) ?
If \( 4x - 3y - 5 = 0 \) is a normal to the ellipse \( 3x^2 + 8y^2 = k \), then the equation of the tangent at point (-2,m) is:
Two particles of charges 4 nC and \( Q \) are kept in air with a separation of 10 cm between them. If the electrostatic potential energy of the system is 1.8 μJ, then \( Q \) is:
If all the letters of the word ‘SENSELESSNESS’ are arranged in all possible ways and an arrangement among them is chosen at random, then, the probability that all the E’s come together in that arrangement is:
Consider the following statements:
Statement I: The entropy of pure crystalline solid approaches zero as the temperature approaches absolute zero value.
Statement II: For a reaction at equilibrium, \(\Delta G\) is zero.
Which of the following reactions is not a metal displacement reaction?