List of top Questions asked in AP EAPCET

\( \int 3^{-\log_3 x^2} dx = \)
If \( q \) is electric charge, \( B \) is magnetic field, \( R \) is the dee radius and \( m \) is the mass of ions, the kinetic energy of the ions in cyclotron is given by:
If \( \sin \theta = \frac{3}{5} \) and \( \theta \) is not in the first quadrant, then \( 15 \sin 2\theta - 20 \cos 2\theta - 7 \tan 2\theta \) is:
If the chord of contact of the point \( P(1, 1) \) with respect to the circle \( S = x^2 + y^2 + 4x + 6y - 3 = 0 \) meet the circle \( S = 0 \) at A and B, then the area of \( \triangle PAB \) is:
The correct order of reactivity of the following towards nucleophilic addition reactions is: \[ \text{I. CH}_3\text{COCH}_3,\quad \text{II. CH}_3\text{CH}_2\text{CHO},\quad \text{III. ClCH}_2\text{CHO} \]
The product of the slopes of the common tangents drawn to the circles $x^2+y^2+2x-2y-2=0$ and $x^2+y^2-2x+2y+1=0$ is
When an external force with angular frequency \( \omega_0 \) acts on a system of natural angular frequency \( \omega \), the system oscillates with angular frequency \( \omega_d \). The condition for the amplitude of oscillations to be maximum is:
What are 'X' and 'Y' respectively in the following reaction sequence? \[ \ce{C6H5CH3→[X] C6H5CO2H →[Y] C6H5CH2OH} \]
Among the following, Ampere’s circuital law is represented by:
One out of 9 ships is likely to sink when they are set on sail. When 6 ships are set on sail, the probability that exactly 3 of them will not arrive safely is:
A truck of mass \( M \) and a car of mass \( \frac{M}{10} \) moving with the same momentum are brought to halt by the application of the same breaking force. The ratio of the distances travelled by the truck and car before they come to stop is:
Positron is the antiparticle of
Two electric dipoles, each of dipole moment ‘P’, are placed at points A (\(a,0\)) and B (\(-a,0\)) as shown in the figure. The work done in rotating both the dipoles through 90° in clockwise direction is (E = Electric field)
Two electric dipoles, each of dipole moment ‘P
The material used in the fabrication of infrared LED's is
In a hydrogen atom, an electron in an orbit with principal quantum number \( n \) jumps to the first excited state, emitting a photon of wavelength \( \lambda \). Then the value of \( n \) is:
If \( -1 \) is a twice repeated root of the equation \( a(x^3 + x^2) + bx + c = 0 \), then the ratio \( a : b : c \) is:
In $ \triangle ABC $, if $ r $ is the inradius and $ r_1, r_2, r_3 $ are the ex-radii, then \[ \frac{1}{4} \left[ b^2 \sin 2C + c^2 \sin 2B \right] = \]
The process which involves the treatment of the ore with a suitable reagent so as to make it soluble but not impurities is called
Observe the following Ellingham diagram, and identify the incorrect statement regarding it:
Above 1673K, Al can reduce MgO to Mg
The major product of the following reaction is
alkyl group
If the numerically greatest term in the expansion of \( (2 - 3x)^9 \) when \( x = 1 \) is \( P_1^q P_2^r P_3^s P_4^t \) (where \( P_1 < P_2 < P_3 < P_4 \) are the first four prime numbers), then \( \alpha + \beta + \gamma + \delta = \):
Satellites which give high value data for remote sensing, meteorology, and environmental studies are
If \( \mathbf{a} = (2x + y)\mathbf{i} + 3\mathbf{j} + 9\mathbf{k} \) and \( \mathbf{b} = 2\mathbf{i} + \mathbf{j} - (x - y)\mathbf{k} \) are two collinear vectors, then \( x^3 + 27y^3 = \)

If $f(x) = \frac{1 - x + \sqrt{9x^2 + 10x + 1}}{2x}$, then $\lim_{x \to -1^-} f(x) =$

If the speed of a wave doubles as it passes from shallow water into deeper water, its wavelength will be