List of top Questions asked in AP EAPCET

Find the derivative of the function \( f(x) = \sin^{-1} \big( 2x \sqrt{1 - x^2} \big) \) with respect to \( x \), for \( x \in \left(-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right) \).
If vectors \( \vec{a} = 2\hat{i} + 3\hat{j} + \hat{k} \) and \( \vec{b} = \hat{i} - \hat{j} + 2\hat{k} \), then the magnitude of the projection of \( \vec{a} \) on \( \vec{b} \) is:
Consider the quadratic equation \( ax^2 + bx + c = 0 \), where \( 2a + 3b + 6c = 0 \) and let \[ g(x) = \frac{a x^3}{3} + \frac{b x^2}{2} + c x \] Statement-I: The given quadratic equation \( ax^2 + bx + c = 0 \) has at least one root in \( (0, 1) \). Statement-II: Rolle's theorem is applicable to \( g(x) \) on \( [0, 1] \). Then:
If the rms value of the electric field of electromagnetic waves at a distance of 3 m from a point source is \( 3 \, \text{N C}^{-1} \), then the power of the source is
If the lines \( 3x - 4y + 4 = 0 \) and \( 6x - 8y - 7 = 0 \) are the tangents to the same circle, then the area of that circle (in sq. units) is
If the formation of a real image using a biconvex lens of material of refractive index 1.5 is shown in the figure. If this setup is immersed in water (refractive index = $\frac{4}{3}$), then
formation of a real image using
If \(x^2 + y^2 = 25\) and \(xy = 12\), then what is the value of \(x^4 + y^4\)?
The sum of bond order values of \( C_2 \) and \( O_2^{2-} \) is \( x \), which is equal to the sum of bond order values of \( a, b, \) and \( c \). What are \( a, b, \) and \( c \)?
A short bar magnet of magnetic moment \( 10^4 \, \text{J T}^{-1} \) is free to rotate in a horizontal plane. The work done in rotating the magnet slowly from the direction parallel to a horizontal magnetic field of \( 4 \times 10^{-5} \, \text{T} \) to a direction \( 60^\circ \) to the direction of the field is
To get an output value $ 1 $ from the given circuit, the input values of $ A $, $ B $, and $ C $ are:
output value 1 from the given circuit,
The number of solutions of the system of equations \(2x+y-z=7\), \(x-3y+2z=1\), \(x+4y-3z=5\) is
A solution of urea in water has a boiling point of \( 100.18^\circ C \). What is the freezing point of the same solution, if \( K_f \) and \( K_b \) of water are \( 1.86 \) and \( 0.52 \) K kg mol\(^{-1} \), respectively? (Boiling point of water = \( 100^\circ C \))
The cubic equation whose roots are the squares of the roots of the equation \( x^3 - 2x^2 + 3x - 4 = 0 \) is
If \( \int \frac{x}{x \tan x + 1} \, dx = \log f(x) + k \), then \( f\left(\frac{\pi}{4}\right) = \)
Which of the following will give a white precipitate with \( \text{AgNO}_3 \) solution?
When a wire made of material with Young's modulus Y is subjected to a stress S, the elastic potential energy per unit volume stored in the wire is
If $\sin x - \sin y = \frac{27{65}$ and $\cos x - \cos y = -\frac{21}{65}$, then $\sin(x+y)= $}
A solid sphere of mass 2 kg and radius 10 cm is rolling down on an inclined plane without slipping. If the rotational kinetic energy of the sphere is 40 J, then its total kinetic energy is
The mean of 6 numbers is 15, and the standard deviation is 2. If each number is increased by 5, what is the new standard deviation?
The function \( f(x) = \frac{x^2 - 4x + 3}{x^2 - 5x + 6} \) is defined for all real values of \( x \) except:
What is the number of moles in 88 grams of carbon dioxide (CO2)?
Area of the region (in sq. units) bounded by the curve $ y = x^2 - 5x + 4 $, $ x = 0 $, $ x = 2 $, and the X-axis is
A point P divides the line joining points $A(2, 3)$ and $B(10, 7)$ in the ratio 3:1 internally. What are the coordinates of point P?
If \( \tan(\theta - \phi) = \frac{3}{4} \) and \( \theta + \phi = \frac{\pi}{2} \), then the value of \[ \tan \left( \frac{\pi}{4} - \theta \right) + \tan \left( \frac{\pi}{4} - \phi \right) \] is:
Evaluate the infinite series: \[ \left|\begin{array}{ccc} 2 & 1 & \frac{1}{3}
3 & 1 & 1
\end{array}\right| + \left|\begin{array}{ccc} 1 & \frac{1}{3} & \frac{1}{2}
3 & 1 & 1
\end{array}\right| + \left|\begin{array}{ccc} 1 & \frac{1}{4} & \frac{1}{9}
3 & 1 & 1
\end{array}\right| + \left|\begin{array}{ccc} 1 & \frac{1}{4} & \frac{1}{27}
3 & 1 & 1
\end{array}\right| + \cdots = ? \]