List of top Questions asked in AP EAPCET

The capacitance of an isolated sphere of radius \( r_1 \) is increased by 5 times when enclosed by an earthed concentric sphere of radius \( r_2 \). The ratio \( \frac{r_1}{r_2} \) is:
Identify the incorrect set from the following:
If \( \vec{i} - 2\vec{j} + 3\vec{k}, 2\vec{i} + 3\vec{j} - \vec{k}, -3\vec{i} - \vec{j} - 2\vec{k} \) are the position vectors of three points A, B, C respectively, then A, B, C:
The equation of the tangent to the curve \[ y = x^3 - 2x + 7 \] at the point \( (1,6) \) is:
Which of the allotropic forms of carbon is aromatic in nature?
A → P is a zero-order reaction. At 298 K, the rate constant of the reaction is \( 1 \times 10^{-3} \) mol L\(^{-1}\) s\(^{-1}\). Initial concentration of 'A' is 0.1 mol L\(^{-1}\). What is the concentration of 'A' after 10 sec?
If all the letters of the word ‘SENSELESSNESS’ are arranged in all possible ways and an arrangement among them is chosen at random, then, the probability that all the E’s come together in that arrangement is:
The differential equation formed by eliminating arbitrary constants \( A \) and \( B \) from the equation \[ y = A \cos 3x + B \sin 3x \] is:
A particle is projected from the surface of the Earth with a velocity equal to twice the escape velocity. When the particle is far from the Earth, its speed will be:
If \( a \) is in the 3rd quadrant, \( \beta \) is in the 2nd quadrant such that \( \tan \alpha = \frac{1}{7}, \sin \beta = \frac{1}{\sqrt{10}} \), then \[ \sin(2\alpha + \beta) = \]
If \( A, B, C \) are the angles of a triangle, then \[ \sin 2A - \sin 2B + \sin 2C = \]
Evaluate the integral $$ \int_{0}^{\frac{\pi}{4}} \frac{x^2}{(x \sin x + \cos x)^2} dx. $$
If \( x \) is real and \( \alpha, \beta \) are maximum and minimum values of \( \frac{x^2 - x + 1}{x^2 + x + 1} \) respectively, then \( \alpha + \beta = \):

X, Y are oxoacids of phosphorous
X, Y are oxoacids of phosphorous. The number of P – OH bonds in X, Y respectively is:

What are \( X \) and \( Y \) respectively in the following reaction sequence?
When a parallel plate capacitor is charged up to 95 V, its capacitance is \( C \). If a dielectric slab of thickness 2 mm is inserted between plates and the plate separation is increased by 1.6 mm such that the potential difference remains constant, find the dielectric constant of the material:
A block of metal 4 kg is in rest on a frictionless surface. It was targeted by a jet releasing water of 2 kg/s at a speed of 10 ms\(^{-1}\). The acceleration of the block is:
Cobalt (III) chloride forms a green-colored complex ‘X’ with NH\(_3\). Number of moles of AgCl formed when excess AgNO\(_3\) solution is added to 100 mL of 1M solution of ‘X’ is:
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:
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:
In the expansion of \(\frac{2x+1}{(1+x)(1-2x)}\), the sum of the coefficients of the first 5 odd powers of \(x\) is:
The velocity of a particle is given by the equation \( v(x) = 3x^2 - 4x \), where \( x \) is the distance covered by the particle. The expression for its acceleration is:
If \( 1 \cdot 3 \cdot 5 + 3 \cdot 5 \cdot 7 + 5 \cdot 7 \cdot 9 + \dots \) (n terms) = \( n(n + 1)f(n) - 3n \), then \( f(1) = \):

If \(n\) is an integer and \(Z = \cos \theta + i \sin \theta\), \(\theta \neq (2n + 1)\) \(\frac{\pi}{2}\), then: \(\frac{1 + Z^{2n}}{1 - Z^{2n}}\) = ?

Assertion (A): If \( A = 10^\circ, B = 16^\circ, C = 19^\circ \), then: \[ \tan(2A) \tan(2B) + \tan(2B) \tan(2C) + \tan(2C) \tan(2A) = 1. \] Reason (R): If \( A + B + C = 180^\circ \), then: \[ \cot\left(\frac{A}{2}\right) + \cot\left(\frac{B}{2}\right) + \cot\left(\frac{C}{2}\right) = \cot\left(\frac{A}{2}\right) \cot\left(\frac{B}{2}\right) \cot\left(\frac{C}{2}\right). \]