List of top Questions asked in AP EAPCET

If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors and \(\vec{a} \perp \vec{b}\), and \((\vec{a} - \vec{c}) \cdot (\vec{b} + \vec{c}) = 0\), and \(\vec{c} = l\vec{a} + m\vec{b} + n(\vec{a} \times \vec{b})\), then \(n^2 =\)
The uncertainty in the position of electron ($\Delta x$) is approximately 100 pm. The uncertainty in momentum (in kg m s$^{-1}$) of an electron is [h = 6.626 $\times 10^{-34}$ Js]
\( \int \frac{1 + x + \sqrt{x + x^2}}{\sqrt{x + \sqrt{1 + x}}} dx = \)
If \( a \pm bi \) and \( b \pm ai \) are roots of \( x^4 - 10x^3 + 50x^2 - 130x + 169 = 0 \), then find the value of \( \frac{a}{b} + \frac{b}{a} \).
If the intercept of a line \(L\) made between the straight lines \(5x - y - 4 = 0\) and \(3x + 4y - 4 = 0\) is bisected at the point (1, 5), then the equation of \(L\) is
If \(\theta\) is the acute angle between the asymptotes of a hyperbola \(7x^2 - 9y^2 = 63\), then \(\cos \theta =\)
If the points A, B, C, D with position vectors \(\vec{i} + \vec{j} - \vec{k}, -\vec{i} + 2\vec{k}, \vec{i} - 2\vec{j} + \vec{k}, 2\vec{i} + \vec{j} + \vec{k}\) form a tetrahedron, then angle between faces ABC and ABD is
A circle touches the line \(2x + y - 10 = 0\) at (3, 4) and passes through the point (1, -2). Then a point that lies on the circle is
A straight wire of resistance $18~\Omega$ is bent in the form of an equilateral triangle. The effective resistance between any two vertices of the triangle is
The oxides of nitrogen obtained by the reaction of nitric acid with
If \(x\) is a real number, then the number of solutions of \(\tan^{-1}\left(\sqrt{x(x+1)}\right) + \sin^{-1}\left(\sqrt{x^2 + x + 1}\right) = \dfrac{\pi}{2}\) is
If (a, b) is the common point of the circles \(x^2 + y^2 - 4x + 4y - 1 = 0\) and \(x^2 + y^2 + 2x - 4y + 1 = 0\), then \(a^2 + b^2 =\)
Activation energy for the hydrolysis of sucrose by acid is X kJ mol$^{-1}$ and by sucrase is Y kJ mol$^{-1}$. X and Y respectively are
The radii of inner and outer spheres of a spherical capacitor are $8~\text{cm$ and $9~\text{cm}$ respectively. The outer sphere is earthed and the inner sphere is charged. If the space is filled with a dielectric constant $K = 5$, the capacitance is}
The structure of the nitrogen-containing heterocyclic base shown below represents:
A plane EM wave of frequency $25~\text{MHz}$ propagates in vacuum. If electric field is $6.3~\text{V/m}$, then magnitude of magnetic field is
If the four points (6,2,4), (1,3,5), (1,-2,3), and (6,k,2) are coplanar, then \(k =\)
If \(A + B + C = \dfrac{\pi}{4}\), then \(\sin 4A + \sin 4B + \sin 4C =\)
A liquid drop of diameter $D$ splits into $3375$ small identical drops. If $S$ is the surface tension of the liquid, then the change in the surface energy in the process is
The tangents drawn to the hyperbola \(5x^2 - 9y^2 = 90\) through a variable point \(P\) make angles \(\alpha\) and \(\beta\) with its transverse axis. If \(\alpha\) and \(\beta\) are complementary angles, then the locus of \(P\) is
The area of the region (in sq. units) enclosed between the curves \( y = |x| \), \( y = [x] \) and the ordinates \( x = -1, x = 0, x = 1 \) is
If \(O(0,0,0), A(1,2,1), B(2,1,3)\), and \(C(-1,1,2)\) are the vertices of a tetrahedron, then the acute angle between its face \(OAB\) and edge \(BC\) is
If the half-life of a radioactive element is $12.5$ hours, then the time taken to disintegrate $256~g$ of the substance into $1~g$ is (in hours)
If the maximum and minimum temperatures at a place on a day are measured as $44^\circ C \pm 0.5^\circ C$ and $22^\circ C \pm 0.5^\circ C$ respectively, then the temperature difference is
Consider the following.
Statement-I: Gold sol is prepared by Bredig’s arc method.
Statement-II: Bredig’s arc method involves only dispersion but not condensation.