List of top Questions asked in AP EAMCET

Equation of the normal to the curve \( y = x^2 + x \) at the point \( (1,2) \) is:
The number of unit cells present in 5.85 g of a cube-shaped crystal of sodium chloride is \( x \times 10^y \). \( x \) and \( y \) respectively are (Na = 23 u, Cl = 35.5 u) \[ (N_A = 6 \times 10^{23} { mol}^{-1}) \]

Let a and b be two non-collinear vectors of unit modulus. If u = a − (a · b)b and v = a × b, then ∥v∥ = ?

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: 
If \( A = (1,2,3), B = (3,4,7) \) and \( C = (-3,-2,-5) \) are three points then the ratio in which the point C divides AB externally is
Size of the antenna for a carrier wave of frequency 3 MHz is:
If \( 1 \cdot 3 \cdot 5 + 3 \cdot 5 \cdot 7 + 5 \cdot 7 \cdot 9 + \dots \) (n terms) = \( n(n + 1)f(n) - 3n \), then \( f(1) = \):
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:
If \( m, n \) are respectively the least positive and greatest negative integer values of such that \( (\frac{1-i}{1+i})^k = -i\), then \( m - n = \):
The rms velocity (\( u_{\text{rms}} \)), mean velocity (\( u_{\text{av}} \)), and most probable velocity (\( u_{\text{mp}} \)) of a gas differ from each other at a given temperature. Which of the following ratios regarding them is correct?
Evaluate the integral: \[ I = \int_{-\pi}^{\pi} \frac{x \sin x}{1 + \cos^2 x} \,dx. \]
The equation \( 2x^2 - 3xy - 2y^2 = 0 \) represents two lines \( L_1 \) and \( L_2 \). The equation \( 2x^2 - 3xy - 2y^2 - x + 7y - 3 = 0 \) represents another two lines \( L_3 \) and \( L_4 \). Let \( A \) be the point of intersection of lines \( L_1 \) and \( L_3 \), and \( B \) be the point of intersection of lines \( L_2 \) and \( L_4 \). The area of the triangle formed by the lines \( AB \), \( L_3 \), and \( L_4 \) is: .
The \(\Delta T_b\) value for 0.01 m KCl solution is 0.01 K. What is the Van’t Hoff factor? (Kb for water = 0.52 K kg mol\(^{-1}\))
Identify the correct equation relating \( \Delta H \), \( \Delta U \), and \( \Delta T \) for 1 mole of an ideal gas (R = gas constant):
Match the complexes in list-I with their hybridization in list-II.
complexes in list-I with their hybridization
Identify the correct set from the following.
Force is given by the expression \( F = A \cos(Bx) + C \cos(Dt) \), where 'x' is displacement and 't' is time. The dimensions of \( \frac{D}{B} \) are the same as that of:
Two persons A and B throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as 4 and the person who gets this result first is declared as the winner. If A starts the game, then the probability that B wins the game is:
The de Broglie wavelength of a particle of mass 1 mg moving with a velocity of \( 10 \) ms\(^{-1}\) is (h = \( 6.63 \times 10^{-34} \) Js)
If \[ 3f(x) - 2f\left(\frac{1}{x}\right) = x, \] then \( f'(2) \) is:
If \( y = \frac{ax + \beta}{\gamma x + \delta} \), then \( 2y_1 y_3 = \) ?
In Young’s double-slit experiment with monochromatic light of wavelength 6000 Å, the fringe width is 3 mm. If the distance between the screen and slits is increased by 50\% and the distance between the slits is decreased by 10\%, then the fringe width is
If two numbers \(x\) and \(y\) are chosen one after the other at random with replacement from the set of numbers \( \{1, 2, 3, \ldots, 10\} \), then the probability that \( |x^2 - y^2| \) is divisible by 6 is:
An inductor of inductive reactance 80 \(\Omega\) and a resistor of resistance 60 \(\Omega\) are connected in series to an ac source. The impedance and the power factor of the circuit are respectively:
A piston divides a closed gas cylinder into two parts. Initially, the piston is kept pressed such that one part has pressure P and volume 5V and the other part has pressure 8P and volume V. The piston is now left free. The new pressure if the process is isothermal: