List of top Questions asked in AP EAPCET

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
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 \( \lim_{x \to 0} \frac{f(x) - f(0)}{x} \)
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:
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 a straight line \( L \) perpendicular to the line \( 3x - 4y = 6 \) forms a triangle of area 6 square units with coordinate axes, then the minimum perpendicular distance from the point \( (1,1) \) to the line \( L \) is:
Let \([ \cdot ]\) denote the greatest integer function.
Assertion (A): \(\lim_{x \to \infty} \frac{[x]}{x} = 1\)
Reason (R): \(f(x) = x - 1\), \(g(x) = [x]\), \(h(x) = x\) and \(\lim_{x \to \infty} \frac{f(x)}{x} = \lim_{x \to \infty} \frac{h(x)}{x} = 1\):
The bulk modulus \( B \) and compressibility \( k \) are related by:
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:
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 \(P(1, -2)\)
Which of the following statements are correct? i. \( [\text{Mn(CN)}_6]^{3-},\ [\text{MnCl}_6]^{3-} \) both are paramagnetic
ii. Both \( [\text{NiCl}_4]^{2-},\ [\text{Ni(CO)}_4] \) are tetrahedral and diamagnetic
iii. \( [\text{Co(NH}_3)_6]^{3+} \) is inner orbital complex, but \( [\text{Ni(NH}_3)_6]^{2+} \) is outer orbital complex
Deficiency of which vitamin causes convulsions?
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:
Which one of the following is a homogeneous differential equation?
At any instant \( t \), the vertical distance \( Y \) and horizontal distance \( X \) of a projectile are given by \[ 2Y = 6t - g t^2 \quad \text{and} \quad X = 4t, \] The initial velocity of the projectile is:
Physically, the self-inductance plays the role of:
The radio horizon of the transmission of an antenna placed on the 20\(^\text{th}\) floor in a shopping mall, where the height of each floor is 2 m is
Given below are two statements
Statement I: The changes in pH with temperature are so small that we often ignore it
Statement II: When the hydrogen ion concentration changes by a factor of 100, the pH changes by one unit
In the light of above statements, identify the correct answer from the options given below
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:
The degree of the polynomial \( \left( x + \sqrt{x^4 - 1} \right)^9 + \left( x - \sqrt{x^4 - 1} \right)^9 \) is:
The set \( \{ x \in \mathbb{R} : 16(2^x)>16^{x-1} \} \) is:
If a set \( A \) has \( n \) elements, then the number of functions defined from \( A \) to \( A \) that are not one-one is:
If \( 1 + \sqrt{1 + a} = (1 + \sqrt{1 - a}) \cot \alpha \) and \( 0<a<1 \), then \( \sin 4\alpha = \)
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 \( a + b = \):
The substitution \( x = vy \) converts which one of the following differential equations to an equation solvable by the variable separable method?
The relation between the mean life time \( \tau \) and the half life time \( T_{1/2} \) of a radioactive substance is: