List of top Questions asked in AP EAPCET

If the line passing through the points \( (5,1,a) \) and \( (3,b,1) \) crosses the YZ plane at the point \( \left( 0, \frac{17}{2}, \frac{-13}{2} \right) \), then \( a + b = \):
If \( f(x) = \begin{vmatrix} 1 & 6 + x & 36 + x^2 \\ 0 & x - 3 & 3x^2 - 27 \\ 0 & 2x - 4 & 8x^2 - 32 \end{vmatrix} \), then \( \lim\limits_{x \to 1} \frac{f(x)}{f(-x)} \) is:
If \( \alpha \in \mathbb{R} \setminus \{-1\} \) and \[ f(x) = |x| + \alpha |x|(|x| - 1), \] then the number of points at which \( f(x) \) is not differentiable is:
If p and q are the x and y intercepts respectively of the line passing through the points \( (a \cos \alpha, b \sin \alpha) \) and \( (a \cos \beta, b \sin \beta) \), then:
Physically, the self-inductance plays the role of:
If \( \frac{6x^3 + 7x^2 - 14x + 11}{6x^3 + x^2 - 10x + 3} = \frac{a}{x + p} + \frac{b}{qx + 3} + \frac{c}{3x + p} \), then \( a + b \) is:
Among the following the correct statements are:
I. Carbon black is obtained by burning hydrocarbons in a limited supply of air
II. Carbon black is obtained by burning hydrocarbons in absence of air
III. Coke is obtained by burning coal at high temperatures in a limited supply of air
IV. Coke is obtained by burning coal at high temperatures in absence of air
The greatest term in the expansion of $ (1+x)^{15} $, when $ x = \frac{1}{2} $ is
If a circle \(S\) passing through the points \(A(1, 2)\) and \(B(2, 1)\) has its centre \(C\) located in the third quadrant at a distance of \(\frac{7}{\sqrt{2}}\) units from \(AB\), then the point \(P(1, -2)\)
The substitution \( x = vy \) converts which one of the following differential equations to an equation solvable by the variable separable method?
The probability that a non-leap year contains 53 Sundays is
The set \( \{ x \in \mathbb{R} : 16(2^x)>16^{x-1} \} \) is:
If $\log y$ is an integrating factor of $\frac{dx}{dy}+P(y)x=Q(y)$, then $P(y)=$
If \( f(x) = \begin{cases} x \left( 1 + \frac{1}{2} \sin(\log x^2) \right), & x \neq 0 \\ 0, & x = 0 \end{cases} \), then \( \lim_{x \to 0} \frac{f(x) - f(0)}{x} \)
Let \( A(2, 3) \), \( B(3, -1) \), and \( C(-3, 2) \) be three points. If the centre of the circle passing through A, B, and C is \( (h, k) \), then \( 2k - 4 = \):
The lengths of the intercepts made by a circle \(S\) on the \(X\) and \(Y\)-axes are \(\frac{2\sqrt{13}}{3}\) and \(\frac{2\sqrt{17}}{3}\) respectively. Then the equation of the circle is:
A disc starts rotating from rest with constant acceleration and attains angular velocity of 20 rad/s in 5 seconds. The total angular displacement during this interval is
If \( A(3, -1, 1), B(0, 2, 3), C(4, 8, 11) \) are three points, then the coordinates of the foot of the perpendicular drawn from the point A to the line joining the points B and C is:
Given that $\frac{d}{dx} \int_{0}^{\phi(x)} f(t) dt = f(\phi(x)) \phi'(x)$. For all $x \in (0, \frac{\pi}{2})$, if $\int_{1}^{\cos x} t^2 f(t) dt = \cos 2x$, then $f\left(\frac{1}{\sqrt{2}}\right) =$
Reaction of phenol with which of the following reagents form picric acid?
What are X and Y respectively in the following reaction? $$ CH_3CH_2CHO + 2Cu^{2+} + 5OH^- \rightarrow X + Y + 3H_2O $$
Observe the following half cell reactions and choose the correct options
(I) 2H2O(l) → O2(g)+4H+ +4e− E0 = 1.23V
(II) H+(aq) + e− → 1/2 H2(g) E0 = 0.00V
(III) 2SO4^2− (aq) → S2O8^2− (aq)+2e− E0 = −1.96V
(a) In dilute H2SO4 solution, H+ ions are reduced at cathode.
(b) In concentrated H2SO4 solution, water is oxidized at anode.
(c) In dilute H2SO4 solution, water is oxidized at anode.
(d) In dilute H2SO4 solution, SO4^2− ions are oxidized at anode.
\( \int_{-4\pi}^{4\pi} \tan^9 x \sin^6 x \cos^3 x \, dx = \)
In a photoelectric graph of stopping potential vs frequency, straight line makes angle \( \theta \) with Y-axis. Then \( \tan \theta = \):
In which of the following, orbitals are correctly arranged in the increasing order of their energies?