List of top Questions asked in AP EAPCET

Radius of gyration of a thin uniform rod of length \( L \) about an axis passing through its centre and perpendicular to its length is:
The adsorption of a gas on a solid surface follows Freundlich adsorption isotherm. At \( T \)(K), the gas pressure is \( 2 \) atm. What is the value of \( \frac{x}{m} \)? (\( n = 2 \) and \( k \) = constant)
A unit vector that is perpendicular to the vector \( 2\vec{i} - \vec{j} + 2\vec{k} \) and coplanar with the vectors \( \vec{i} + \vec{j} - \vec{k} \) and \( 2\vec{i} - 2\vec{j} - \vec{k} \) is
At \( T \)(K), the vapour pressure of pure benzene and toluene are \( 75 \) and \( 22 \) mm Hg respectively. 23.4 g of benzene and 64.4 g of toluene are mixed to form an ideal solution. If the vapours are in equilibrium with the liquid mixture, the mole fraction of toluene in vapour phase is:
The sum of all integers between 1 and 100 (both inclusive) which are divisible by 5 or 13 is
The ratio of the magnitudes of the electric field and \( 10^8 \) times the magnetic field of a plane electromagnetic wave is:
The general solution of the differential equation \( \sec(x - y + 1) dy = dx \) is:
If a proton and an alpha particle are accelerated through the same potential difference, then the ratio of their de Broglie wavelengths is:
Which one of the following acts as an autocatalyst during titration of \( KMnO_4 \) and oxalic acid in presence of dilute \( H_2SO_4 \)?
If the sum of two roots of the equation \( x^4 + 2x^3 - 7x^2 - 8x + 12 = 0 \) is zero, then the sum of the squares of the other two roots is
The number of solutions of the equation $\sec x \cos 5x + 1 = 0$ in the interval $[0, 2\pi]$ is
If \( \frac{1}{2} \leq \frac{x^2+x+a}{x^2-x+a} \leq 2 \ \forall x \in \mathbb{R} \), then \( a = \)
For any two non-zero complex numbers \(z_1\) and \(z_2\), if \(|z_1 + z_2|^2 = |z_1|^2 + |z_2|^2\), then
If the lengths of the tangent, subtangent, normal, and subnormal for the curve \( y = x^2 + x - 1 \) at the point \( (1,1) \) are \( a, b, c, \) and \( d \) respectively, then their increasing order is:
If the coefficients of $x^{10}$ and $x^{11}$ in the expansion of $(1 + \alpha x + \beta x^2)(1+x)^{11}$ are 396 and 144 respectively, then $\alpha^2 + \beta^2 =$
At \(25 ^\circ\text{C}\), \(K_a\) of formic acid is \(1.8 \times 10^{-4}\). What is the \(K_b\) of \( \text{HCOO}^- \)?
If \( x \ne (2n+1)\frac{\pi}{4} \), then the general solution of \( \cos x + \cos 3x = \sin x + \sin 3x \) is
Let \( A_1 \) be the area of the given ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \). Let \( A_2 \) be the area of the region bounded by the curve which is the locus of mid point of the line segment joining the focus of the ellipse and a point P on the given ellipse, then \( A_1 : A_2 = \)
If the equation of the tangent of the hyperbola \( 5x^2 - 9y^2 - 20x - 18y - 34 = 0 \) which makes an angle \( 45^\circ \) with the positive X-axis in positive direction is \( x+by+c=0 \) then \( b^2+c^2 = \)
If the vector \( \vec{v} = \vec{i} - 7\vec{j} + 2\vec{k} \) is along the internal bisector of the angle between the vectors \( \vec{a} \) and \( \vec{b} = -2\vec{i} - \vec{j} + 2\vec{k} \) and the unit vector along \( \vec{a} \) is \( \hat{a} = x\vec{i} + y\vec{j} + z\vec{k} \) then \( x = \)
If A(1,0), B(0,-2), C(2,-1) are three fixed points, then the equation of the locus of a point P such that area of \( \triangle \text{PAB} \) is equal to area of \( \triangle \text{PAC} \) is
Consider the following A) 0.0025 B) 500.0 C) 2.0034 Number of significant figures in A, B and C respectively, are
As shown in the figure, if the values of the electric potential at three points A, B and C in a uniform electric field (\( \vec{E} \)) are \(V_A\), \(V_B\), and \(V_C\) respectively, then
electric potential at three points A, B and C
If the circles \( x^2+y^2-2\lambda x - 2y - 7 = 0 \) and \( 3(x^2+y^2) - 8x + 29y = 0 \) are orthogonal, then \( \lambda = \)
If \( \frac{ax+5}{(x^2+b)(x+3)} = \frac{x+21}{12(x^2+b)} + \frac{c}{12(x+3)} \), then \( b^2 = \)