List of top Questions asked in AP EAMCET

In Kolbe's electrolysis of sodium propanoate, products formed at anode and cathode are respectively:
Suppose the axes are to be rotated through an angle \( \theta \) so as to remove the \( xy \) term from the equation \(3 x^2 + 2\sqrt{3}xy + y^2 = 0 \). Then in the new coordinate system, the equation \( x^2 + y^2 + 2xy = 2 \) is transformed to:
A 4 kg stone is attached to a steel wire being whirled at a constant speed of \( 12 \) m/s in a horizontal circle. The wire is 4 m long with a diameter of 2 mm, and Young’s modulus is \( 2 \times 10^{11} \) Nm\(^2\). The strain in the wire is:
If \(540^\circ<A<630^\circ\) and \(|\cos A| = \frac{5}{13}\), then \( \tan\frac{A}{2} \tan A =\)
The molecular formula of a crystalline solid is X\( _3 \)Y\( _2 \). Atoms of Y form ccp lattice, and atoms of X occupy 50% octahedral voids and x% of tetrahedral voids. What is the percentage of unoccupied tetrahedral voids?
A diatomic gas does a work of \( \frac{Q}{4} \) when a heat of \( Q \) is supplied to it. Then the molar heat capacity of the gas is:
A is a point on the circle with radius 8 and center at O. A particle P is moving on the circumference of the circle starting from A. M is the foot of the perpendicular from P on OA and \( \angle POM = \theta \). When \( OM = 4 \) and \( \frac{d\theta}{dt} = 6 \) radians/sec, then the rate of change of PM is (in units/sec):
Evaluate the integral: \[ I = \int_{-5\pi}^{5\pi} \left(1 - \cos 2x \right)^{\frac{5}{2}} dx. \]
The area of the region enclosed by the curves \[ 3x^2 - y^2 - 2xy + 4x + 1 = 0 \] and \[ 3x^2 - y^2 - 2xy + 6x + 2y = 0 \] is:
If the roots of the equation \(x^3 + ax^2 + bx + c = 0\) are in arithmetic progression, then:
If \( \frac{3 - 2i \sin \theta}{1 + 2i \sin \theta}\) is a purely imaginary number, then \( \theta \) is:
If \[ x = 3 \left[ \sin t - \log \left( \cot \frac{t}{2} \right) \right], \quad y = 6 \left[ \cos t + \log \left( \tan \frac{t}{2} \right) \right] \] then find \( \frac{dy}{dx} \).
The relation between time \( t \) and displacement \( x \) is \( t = \alpha x^2 + \beta x \), where \(\alpha\) and \(\beta\) are constants. If \( \nu \) is the velocity, the retardation is:
In which of the following metals extraction, impurities are removed as slag?
The differential equation of the family of hyperbolas having their centers at origin and their axes along the coordinate axes is:
Find the differential equation representing the family of circles having their centers on the Y-axis. Given that \( y_1 = \frac{dy}{dx} \) and \( y_2 = \frac{d^2y}{dx^2} \).

Choose the incorrect statements regarding definition of Living:
(A) Cell division replaces lost cells in certain tissues
(B) In living organisms, growth is from outside
(C) Metabolism is the sum total of all chemical reactions occurring in the living organism
(D) In unicellular organisms, reproduction is not synonymous with the growth

The point (a, b) is the foot of the perpendicular drawn from the point (3, 1) to the line x + 3y + 4 = 0. If (p, q) is the image of (a, b) with respect to the line 3x - 4y + 11 = 0, then $\frac{p}{a} + \frac{q}{b} = $

Choose the incorrect combination among the following: 


 

Evaluate the limit: \[ \lim\limits_{x \to 2} \frac{\sqrt{1 + 4x} - \sqrt{3} + 3x}{x^3 - 8}. \]

If the potential difference across \(PQ\) is 4V, the potential difference across \(A\) and \(B\) in the given figure is:


 

Toluene on reaction with the reagent X gave Y, which dissolves in NaHCO\( _3 \) and when reacted with Br\( _2 \)/Fe gave Z. What are X and Z?
The motion of a particle is given by \(X = a \cos t\), \(Y = a \sin t\) and \(Z = t\). The trajectory traced by the particle as a function of time is:
A basket contains 12 apples in which 3 are rotten. If 3 apples are drawn at random simultaneously from it, then the probability of getting at most one rotten apple is:
If \[ \int \log \left( 6\sin^2x + 17\sin x + 12 \right)^{\cos x} \, dx = f(x) + c \] then, \[ f\left(\frac{\pi}{2}\right) = \]