List of top Questions asked in AP EAPCET

\(f(x)\) is a quadratic polynomial satisfying the condition \( f(x) + f\left(\frac{1}{x}\right) = f(x)f\left(\frac{1}{x}\right) \). If \(f(-1)=0\), then the range of \(f\) is
The general solution of the differential equation \( \frac{dy}{dx} = \frac{x+y}{x-y} \) is
The differential equation of the family of circles passing through the origin and having centre on X-axis is
If \( x^6 = (\sqrt{3}-i)^5 \), then the product of all of its roots is
Which method is used to purify liquids having very high boiling points and liquids which decompose at or below their boiling point?
In the given reaction sequence conversion of Y to Z is
reaction sequence conversion of Y to Z is
The preferred reagent for the preparation of pure alkyl chloride from alcohol is
What are X and Y respectively in the following set of reactions? X and Y respectively in the following set of reactions
Consider the reaction sequence Dimethyl ketone \( \xrightarrow{\text{(i)CH}_3\text{MgCl (ii)H}_2\text{O}} \) X \( \xrightarrow{\text{(i)Na (ii)CH}_3\text{Br}} \) Y How many sp\(^3\) carbons are present in Y?
The height of ceiling in an auditorium is 30 m. A ball is thrown with a speed of \( 30 \, \text{m s}^{-1} \) from the entrance such that it just moves very near to the ceiling without touching it and then it reaches the ground at the end of the auditorium. Then the length of auditorium is [Acceleration due to gravity \( = 10 \, \text{m s}^{-2} \)]
The de Broglie wavelength of an electron in the third Bohr orbit of H-atom is
Each nuclear fission of \( {}^{235}\text{U} \) releases 200 MeV of energy. If a reactor generates 1 MW power, then the rate of fission in the reactor is
The set of all real values of \(x\) for which \(f(x) = \sqrt{\frac{|x|-2}{|x|-3}}\) is a well defined function is
\( \int_{0}^{\pi/4} \frac{\cos^2 x}{\cos^2 x + 4\sin^2 x} dx = \)
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 four letters are chosen from the letters of the word ASSIGNMENT and are arranged in all possible ways to form 4 letter words (with or without meaning), then total number of such words that can be formed is
Let 'a' be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation \( x^3 - ax^2 + ax - 1 = 0 \) is identical with this cubic equation, then 'a' =
1.95 g of non-volatile and non-electrolyte solute dissolved in 100 g of benzene lowered the freezing point of it by 0.64 K. The molar mass of the solute (in g mol\(^{-1}\)) (\(K_f(\text{C}_6\text{H}_6) = 5.12 \, \text{K kg mol}^{-1}\)) is
Match the following:
List-I (Hormones)List-II (Functions)
A) GlucocorticoidsI) Control the carbohydrate metabolism
B) MineralocorticoidsIII) Control the level of excretion of water and salt by the kidneys
C) ProgesteroneII) Prepares the uterus for implantation of fertilised egg
D) EstradiolIV) In the control of menstrual cycle
At 298 K, 0.714 moles of liquid A is dissolved in 5.555 moles of liquid B. The vapour pressure of the resultant solution is 475 torr. The vapour pressure of pure liquid A at the same temperature is 280.7 torr. What is the vapour pressure of pure liquid B in torr?
If \( \vec{a} = 2\vec{i} - \vec{j} + 6\vec{k} \); \( \vec{b} = \vec{i} - \vec{j} + \vec{k} \) and \( \vec{c} = 3\vec{j} - \vec{k} \), then \( \vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a} = \)
If the threshold wavelength of light for photoelectric emission to take place from a metal surface is \( 6250 \, \text{\AA} \), then the work function of the metal is (Planck's constant \( = 6.6 \times 10^{-34} \, \text{Js} \))
The equation which represents Freundlich adsorption isotherm is (x = amount of gas, m = mass of solid)
Two satellites A and B are revolving around the earth in orbits of heights \(1.25R_E\) and \(19.25R_E\) from the surface of earth respectively, where \(R_E\) is the radius of the earth. The ratio of the orbital speeds of the satellites A and B is
If two sides of a triangle are represented by \( 3x^2 - 5xy + 2y^2 = 0 \) and its orthocentre is (2,1), then the equation of the third side is