List of top Questions asked in TS EAMCET

If

\[ \cosh^{-1}\left(\frac{5}{3}\right) + \sinh^{-1}\left(\frac{3}{4}\right) = k, \]

then \( e^k \) is:

Arrange the following halides in decreasing order of their reactivity towards dehydrohalogenation: 

A circle passes through the points \( (2, 0) \) and \( (1, 2) \). If the power of the point \( (0, 2) \) with respect to this circle is 4, then the radius of the circle is
The general solution of the differential equation $$ \frac{dy}{dx} = \frac{2y^2 + 1}{2y^3 - 4xy + y}. $$ 

The wavelength of an electron is \( 10^3 \) nm. What is its momentum in kg m s\(^{-1}\)?

A 31.4 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter of 2 cm. The pressure exerted by the heel on the horizontal floor is (Acceleration due to gravity = 10 m/s\(^2\)):
If \( 3^{2n+2} - 8n - 9 \) is divisible by \( 2^p \) \(\forall n \in \mathbb{N}\), then the maximum value of \( p \) is
If \( \int x^3 \sin 3x \,dx = f(x) \cos 3x + g(x) \sin 3x + c \), then evaluate \( 27(f(x) + xg(x)) \):
A circle passing through the points \( (1, 1) \) and \( (2, 0) \) touches the line \( 3x - y - 1 = 0 \). If the equation of this circle is \( x^2 + y^2 + 2gx + 2fy + c = 0 \), then a possible value of \( g \) is
The approximate value of \( \sqrt[3]{730} \) obtained by the application of derivatives is:

Identify the wrong pair:

If A and B are arbitrary constants, then the differential equation having \[ y = Ae^{-x} + B \cos x \] as its general solution is:
If \( (1,1), (-2,2), (2,-2) \) are 3 points on a circle \( S \), then the perpendicular distance from the center of the circle \( S \) to the line \( 3x - 4y + 1 = 0 \) is:
If \(P\left( \frac{\pi}{4} \right)\), \(Q\left( \frac{\pi}{3} \right)\) are two points on the circle \(x^2 + y^2 - 2x - 2y - 1 = 0\), then the slope of the tangent to this circle which is parallel to the chord \(PQ\) is:
The combined equation of a possible pair of adjacent sides of a square with area 16 square units whose centre is the point of intersection of the lines \[ x + 2y - 3 = 0 \quad \text{and} \quad 2x - y - 1 = 0 \] is: \
If half of the space between the plates of a parallel plate capacitor is filled with a medium of dielectric constant 4, the capacitance is \( C_1 \). If one-third of the space between the plates of the capacitor is filled with the medium of dielectric constant 4, the capacitance is \( C_2 \). If in both cases, the dielectric is placed parallel to the plates of the capacitor, then \( C_1 : C_2 \) is:
A paramagnetic substance in the form of a cube of side 3 cm has a magnetic moment of \(243 \times 10^{-6}\) Am\(^2\), when a magnetic field of intensity \(150 \times 10^{3}\) Am\(^{-1}\) is applied. The susceptibility of the substance is:
A current carrying wire is first bent in the form of a circular loop and then bent in the form of a square loop. The ratio of the magnetic fields induced at the centres of the loops in the two cases is:
The common solution set of the inequalities \[ x^2 - 4x \leq 12 \quad \text{and} \quad x^2 - 2x \geq 15 \] taken together is:
S' is the focus of the ellipse \( \frac{x^2}{25} + \frac{y^2}{b^2} = 1, (b<5) \) lying on the negative X-axis and \( P(\theta) \) is a point on this ellipse. If the distance between the foci of this ellipse is 8 and \( S'P = 7 \), then \( \theta \) is:

A zener diode of zener voltage 30 V is connected in a circuit as shown in the figure. The maximum current through the Zener diode is:
 

A man of mass 80 kg goes to the market on a scooter of mass 100 kg with certain speed. On applying brakes, the stopping distance is \( S_1 \). The man returns home on the same scooter, with the same speed, with a 60 kg bag of rice. If \( S_2 \) is the new stopping distance when the brakes are applied with the same force, then:
The uncertainty in the determination of the position of a small ball of mass 10 g is \(10^{-33}\) m. With what \% of accuracy can its speed be measured, if it has a speed of 52.5 m s\(^{-1}\)?
A voltmeter of resistance \(400 \, \Omega\) is used to measure the emf of a cell with an internal resistance of \(4 \, \Omega\). The error in the measurement of emf of the cell is:
If \( Q \) and \( R \) are the images of the point \( P(2,3) \) with respect to the lines \( x - y + 2 = 0 \) and \( 2x + y - 2 = 0 \) respectively, then \( Q \) and \( R \) lie on