List of top Questions asked in AP EAMCET

The absolute value of the difference of the coefficients of $x^4$ and $x^6$ in the expansion of  
$\frac{2x^2}{(x^2+1)(x^2+2)}$ 
is:

When a convex lens is immersed in a liquid of refractive index equal to 80% of the refractive index of the material of the lens, the focal length of the lens increases by 100%. The refractive index of the liquid is:
While solving a system of linear equations \( AX = B \) using Cramer’s rule, if \includegraphics[]{6.png}

In a Carnot engine, the absolute temperature of the source is 25% more than the absolute temperature of the sink. The efficiency of the engine is

5 boys and 6 girls are arranged in all possible ways. Let \(X\) denote the number of linear arrangements in which no two boys sit together, and \(Y\) denote the number of linear arrangements in which no two girls sit together. If \(Z\) denotes the number of ways of arranging all of them around a circular table such that no two boys sit together, then \(X:Y:Z\) = ?
If the number of real roots of \( x^9 - x^5 + x^4 - 1 = 0 \) is \( n \), the number of complex roots having argument on imaginary axis is \( m \), and the number of complex roots having argument in the second quadrant is \( k \), then \( m.n.k \) is:
If \( \alpha \) and \( \beta \) are two distinct negative roots of the equation \( x^5 - 5x^3 + 5x^2 - 1 = 0 \), then the equation of least degree with integer coefficients having \( \sqrt{-\alpha} \) and \( \sqrt{-\beta} \) as its roots is:
If \( \alpha, \beta \) are the roots of the equation \( x^2 - 6x - 2 = 0 \), \( \alpha > \beta \), and \( a_n = \alpha^n - \beta^n, n \geq 1 \), then the value of \( \frac{a_{10} - 2 a_8}{2 a_9} \) is:
One second after projection, a projectile is travelling in a direction inclined at \( 45^\circ \) to horizontal. After two more seconds it is travelling horizontally. Then the magnitude of velocity of the projectile is ( \( g = 10 \) ms\(^{-2}\)):
If \( (\alpha, \beta, \gamma) \) are the direction cosines of an angular bisector of two lines whose direction ratios are (2,2,1) and (2,-1,-2), then \( (\alpha + \beta + \gamma)^2 \) is:
Find the general solution of the differential equation \( ( \sin y \cos^2 y - x \sec^2 y ) dy = (\tan y) dx \).
Which of the following, on thermal decomposition, form both acidic and basic oxides along with O\(_2\)?
(i) NaNO3
(ii) Ca(NO3)2
(iii) Be(NO3)2
(iv) LiNO3
Impure silver ore + CN⁻ + H₂O → [X]⁻ + OH⁻
[X]⁻ + Zn → [Y]²⁺ + Ag (pure)
The co-ordination numbers of the metals in [X], [Y] are respectively:
Carrot and curd are sources for the vitamins respectively.
Number of deactivating groups among: \( -Cl, -SO_3H, -OH, -NHC_2H_5, -COOCH_3, -CH_3 \)
The number of 5-digit odd numbers greater than 40,000 that can be formed by using 3, 4, 5, 6, 7, 0 such that at least one of its digits must be repeated is:
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:
If the pair of tangents drawn to the circle \( x^2 + y^2 = a^2 \) from the point \( (10, 4) \) are perpendicular, then \( a \) is:
The perimeter of the locus of the point \( P \) which divides the line segment \( QA \) internally in the ratio 1:2, where \( A = (4, 4) \) and \( Q \) lies on the circle \( x^2 + y^2 = 9 \), is:
The general solution of \( 4 \cos 2x - 4 \sqrt{3} \sin 2x + \cos 3x - \sqrt{3} \sin 3x + \cos x - \sqrt{3} \sin x = 0 \) is:
216 small identical liquid drops each of surface area \( A \) coalesce to form a bigger drop. If the surface tension of the liquid is \( T \), the energy released in the process is
In \( \triangle ABC \), prove the identity: $$ a^2 \sin 2B + b^2 \sin 2A = $$ 
The \( n^{th} \) term of the series \[ 1 + (3+5+7) + (9+11+13+15+17) + \dots \] is:
If \( (r, \theta) \) denotes \( r (\cos \theta + i \sin \theta) \). If \[ x = (1, \alpha), \quad y = (1, \beta), \quad z = (1, \gamma) \] and \( x + y + z = 0 \), then \[ \sum \cos (2\alpha - \beta - \gamma) = \]
If the ratio of the terms equidistant from the middle term in the expansion of \( (1 + x)^{12} \) is \( \frac{1}{256} \), then the sum of all the terms of the expansion \( (1 + x)^{12} \) is: