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TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
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PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A body moving with uniform acceleration, travels a distance of 25 m in the fourth second and 37 m in the sixth second. The distance covered by body in the next two seconds is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The number of -OH groups present in the structures of bithionol, terpineol and chloroxylenol is respectively
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Which of the following statement regarding nature of physical laws is not correct?
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The internal and external diameters of hollow cylinder measured with vernier callipers are $(5.73 \pm 0.01) \mathrm{cm}$ and $(6.01 \pm 0.01) \mathrm{cm}$ respectively. Then, the thickness of the cylinder wall is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A body is projected from the ground at an angle of $\tan ^{-1}(\sqrt{7})$ with the horizontal. At half of the maximum height, the speed of the body is $n$ times the speed of projection. The value of $n$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A ball of mass 1.2 kg moving with a velocity of $12 \mathrm{~ms}^{-1}$ makes one-dimensional collision with anothe stationary ball of mass 1.2 kg . If the coefficient of restitution is $\frac{1}{\sqrt{2}}$, then the ratio of the total kinetic energy of the balls after collision and the initial kinetic energy is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A solid sphere and a disc of same mass $M$ and radius $R$ - are kept such that their curved surfaces are in contact and their centres lie along the same horizontal line. The moment of inertia of the two body system about an axis passing through their point of contact and perpendicular to the plane of the disc is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
An alphabet $T$ made of two similar thin uniform metal plates of each length $L$ and width $a$ is placed on a horizontal surface as shown in the figure. If the alphabet is vertically inverted, the shift in the position of its centre of mass from the horizontal surface is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
An aircraft executes a horizontal loop of radius 9 km at a constant speed of $540 \mathrm{kmh}^{-1}$. The wings of the aircraft are banked at an angle of (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Two stars of masses $M$ and $2 M$ that are at a distance $d$ apart, are revolving one around another. The angular velocity of the system of two stars is ( $G$-Universal gravitational constant)
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A body thrown vertically upwards from the ground reaches a maximum height $h$. The ratio of the kinetic and potential energies of the body at a height $40 \%$ of $h$ from the ground is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A wooden cube of side 10 cm floats at the interface between water and oil with its lower surface 3 cm below the interface. If the density of oil is $0.9 \mathrm{~g} \mathrm{~cm}^{-3}$, the mass of the wooden cube is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A big liquid drop splits into $n$ similar small drops under isothermal conditions, then in the process
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If a body dropped freely from a height of 20 m reaches the surface of a planet with a velocity of $31.4 \mathrm{~ms}^{-1}$. then the length of a simple pendulum that ticks seconds on the planet is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The displacement equations of sound waves produced by two sources are given by $y_1=5 \sin 400 \pi t$ and $y_2=8 \sin 408 \pi t$, where $t$ is time in seconds. If the waves are produced simultaneously, the number of beats produced per minute is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The difference between the fundamental frequencies of an open pipe and a closed pipe of same length is 100 Hz . The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A block of mass 2 kg is tied to one end of a 2 m long metal wire of $1.0 \mathrm{~mm}^2$ area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is 2 mm , the Young's modulus of the metal is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The thickness of a uniform rectangular metal plate is 5 mm and the area of each surface is $5 \mathrm{~cm}^5$. In steady state, the temperature difference between the two surfaces of the plate is $14^{\circ} \mathrm{C}$. If the heat flowing through the plate in one second from one surface to the other surface is 42 J , then the thermal conductivity of the metal is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A thin plano-convex lens of focal length 73.5 cm has a circular aperture of diameter 8.4 cm . If the refractive index of the material of the lens is $\frac{5}{3}$, then the thickness of the lens is nearly
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
37 g of ice at $0^{\circ} \mathrm{C}$ temperature is mixed with 74 g of water at $70^{\circ} \mathrm{C}$ temperature. The resultant temperature is (specific heat capacity of water $=1 \mathrm{cal} {\mathrm{g}^{-1o}} \mathrm{C}^{-1}$ and latent heat of fusion of ice $=80 \mathrm{cal} \mathrm{g}^{-1}$ )
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A vessel contains hydrogen and nitrogen gases in the ratio $2: 3$ by mass. If the temperature of the mixture of the gases is $30^{\circ} \mathrm{C}$, then the ratio of the average kinetic energies per molecule of hydrogen and nitrogen gases is (Molecular mass of hydrogen $=2$ and molecular mass of nitrogen $=28$ )
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
When an object of height 12 cm is placed at a distance from a convex lens, an image of height 18 cm is formed on a screen. Without changing the positions of the object and the screen. If the lens is moved towards the screen, another clear image is formed on the screen. The height of this image is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The ratio of the specific heat capacities of a gas is 1.5 . When the gas undergoes adiabatic process, its volume is doubled and pressure becomes $p_1$. When the gas undergoes isothermal process, its volume is doubled and pressure becomes $p_2$. If $p_1=p_2$, the ratio of the initial pressures of the gas when it undergoes adiabatic and isothermal processes is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A $10 \mu \mathrm{~F}$ capacitor is charged by a 100 V battery. It is disconnected from the battery and is connected to another uncharged capacitor of capacitance $30 \mu \mathrm{~F}$. During this process, the electrostatic energy lost by the first capacitor is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The relation between the current $i$ (in ampere) in a conductor and the time $t$ (in second) is $i=12 t+9 t^2$. The charge passing through the conductor between the times $t=2 \mathrm{~s}$ and $t=10 \mathrm{~s}$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
In Young's double slit experiment, intensity of light at a point on the screen, where the path difference becomes $\lambda$ is $I$. The intensity at a point on the screen, where the path difference becomes $\frac{\lambda}{3}$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A conductor of length 1.5 m and area of cross-section $3 \times 10^{-5} \mathrm{~m}^2$ has electrical resistance of $15 \Omega$.
The current density in the conductor for an electric field of $21 \mathrm{Vm}^{-1}$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Two point charges $-10 \mu \mathrm{C}$ and $-5 \mu \mathrm{C}$ are situated on $X$-axis at $x=0$ and $x=\sqrt{2} \mathrm{~m}$. The point along the $X$-axis, where the electric field becomes zero is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A straight wire of length 20 cm carrying a current of $\frac{3 .}{\pi^2} \mathrm{~A}$ is bent in the form of a circle. The magnetic field at the centre of the circle is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A circular coil of area $200 \mathrm{~cm}^2$ and 50 turns is rotating about its vertical diameter with an angular speed of $\theta$ $40 \mathrm{rads}^{-1}$ in a uniform horizontal magnetic field of magnitude $2 \times 10^{-2} \mathrm{~T}$. The maximum emf induced in the coil is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
An inductor and a resistor are connected in series to an AC source of 10 V . If the potential difference across the inductor is 6 V , then the potential difference across the resistor is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The operation of a nuclear reactor is said to be critical when the value of neutron multiplication factor $K i s$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A long straight rod of diameter 4 mm carries a steady current $i$. The current is uniformly distributed across its cross-section. The ratio of the magnetic fields at distances 1 mm and 4 mm from the axis of the rod is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A circular coil carrying a current of 2.5 A is free to rotate about an axis in its plane perpendicular to an external field. When the coil is made to oscillate, the time period of oscillation is $T$. If the current through the coil is 10 A , the time period of oscillation is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If the peak value of the magnetic field of an electromagnetic wave is $30 \times 10^{-9} \mathrm{~T}$, then the peak value of the electric field is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The process of the loss of strength of a signal while propagating through a medium is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The ratio of the centripetal accelerations of the electron in two successive orbits of hydrogen is $81: 16$. Due to ${ }^3$ transition between these two states, the angular momentum of the electron changes by ( $h=$ Planck's constant)
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Normally a capacitor is connected across the output terminals of a rectifier to
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The voltage gain of a transistor in common emitter configuration is 160 . The resistances in base and collector sides of the circuit are $1 \mathrm{k} \Omega$ and $4 \mathrm{k} \Omega$ respectively. If the change in base current is $100 \mu \mathrm{~A}$, then the change in output current is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
An $\alpha$-particle of energy $E$ is liberated during the decay of a nucleus of mass number 236. The total energy released in this process is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The de-Broglie wavelength of a proton is twice the de-Broglie wavelength of an alpha particle. The ratio of the kinetic energies of the proton and the alpha particle is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The standard enthalpy of combustion of C (graphite). $\mathrm{H}_2(g)$ and $\mathrm{CH}_3 \mathrm{OH}(l)$ respectively are $-393,-286$ and $-726 \mathrm{~kJ} \mathrm{~mol}^{-1}$. What is the standard enthalpy of formation of methanol?
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The normality of 20 volume solution of hydrogen peroxide is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
At 400 K , an ideal gas is enclosed in a $0.5 \mathrm{~m}^3$ vessel at pressure of 203 kPa . What is the change in temperature required (in K ), if it occupies a volume of $0.2 \mathrm{~m}^3$ under a pressure of 304 kPa ? (Nearest interger)
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The uncertainty in determination of position of a small ball of mass 10 g is $10^{-33} \mathrm{~m}$. With what $\%$ of accuracy its speed can be measured, if it has a speed of 52.5 $\mathrm{ms}^{-1} ?\left(h=6.6 \times 10^{-34} \mathrm{Js}\right)$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The wavenumber of first spectral line of Lyman series of $\mathrm{He}^{+}$ion is $x \mathrm{~m}^{-1}$. What is the wave number ( $\mathrm{in}^{-1}$ ) of second spectral line of Balmer series of $\mathrm{Li}^{2+}$ ion?
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
At $300 \mathrm{~K}, 0.06 \mathrm{~kg}$ of an organic solute is dissolved in 1 kg water. The vapour pressure of solution at 300 K is 3.768 kPa . If vapour pressure of water at that temperature is 3.78 kPa , what is the molar mass of the organic solute (in $\mathrm{g} \mathrm{mol}^{-1}$ )? Assume the solution is dilute
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
In which of the following ionic pairs, second ion is smaller in size than the first ion?
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The molar conductivity of 0.02 M solution of an electrolyte is $124 \times 10^{-4} \mathrm{~S} \mathrm{~m}^2 \mathrm{~mol}^{-1}$.
What is the resistance of same solution (in ohms), kept in a cell of cell constant $129 \mathrm{~m}^{-1}$ ?
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
An element with molar mass $2.7 \times 10^{-2} \mathrm{~kg} \mathrm{~mol}^{-1}$ forms a cubic unit cell with edge length of 405 pm . If its density is $2.7 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$, the number of atoms present in one unit cell of it is
(Given; $N_A=6.023 \times 10^{23} \mathrm{~mol}^{-1}$ )
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Match the following.
| List.l (Substance) | List II (Equivalent weight) |
| A $\mathrm{Na}_2 \mathrm{CO}_3$ | I. $\frac{M}{5}$ |
| B $\mathrm{KMnO}_4 / \mathrm{H}^{+}$ | II. $\frac{M}{3}$ |
| C $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7 / \mathrm{H}^{+}$ | III. $\frac{M}{2}$ |
| D $\mathrm{KMnO}_4 / \mathrm{H}_2 \mathrm{O}$ | IV. $\frac{M}{6}$ |
( $M=$ Formula weight)
The correct answer is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
10 mL of 0.5 M NaCl is required to coagulate 1 L of $\mathrm{Sb}_2 \mathrm{~S}_3 \mathrm{sol}$ in 2 hours time. The flocculating value of NaCl (in millimoles) is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The decomposition of benzene diazonium chloride is a first order reaction. The time taken for its decomposition to $\frac{1}{4}$ and $\frac{1}{10}$ of its initial concentration are $t_{\frac{1}{4}}$ and $t_{\frac{1}{4}}^{10}$ respectively. The value of $\frac{t_{\frac{1}{4}}^4}{t_1} \times 100$ is (Give: $\log 2=0.3$ )
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Match the following.
The correct answer is
| List I (Molecule) | List II (Shape) |
| A $\mathrm{SF}_4$ | I. T-shaped |
| B $\mathrm{CIF}_3$ | II. Square planar |
| C $\mathrm{BrF}_5$ | III. See-saw |
| D $\mathrm{XeF}_4$ | IV. Square pyramidal |
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Identify the set of molecules which are not in the correct order of their dipole moments
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Observe the following species.
(i) $\mathrm{NH}_3$
(ii) $\mathrm{AlCl}_3$
(iii) $\mathrm{SnCl}_4$
(iv) $\mathrm{CO}_2$
(v) $\mathrm{Ag}^{+}$
(vi) $ \mathrm{HSO}_{4}^{-} $
How many of the above species act as Lewis acids?
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Observe the following reactions (not balanced)
$$ \begin{aligned} & \mathrm{BF}_3+\mathrm{LiAlH}_4 \xrightarrow{\left(\mathrm{C}_2 \mathrm{H}_5\right)_2 \mathrm{O}} X+\mathrm{LiF}+\mathrm{AlF}_3{ }^{-} \\ & X+\mathrm{NaH} \longrightarrow Y \end{aligned} $$
The incorrect statement about $Y$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Choose the correct statement from the following.
I. In vapour phase $\mathrm{BeCl}_2$ exists as chlorobridge dimer.
II. $\mathrm{BeSO}_4$ is readily soluble in water.
III. BeO is completely basic in nature.
IV. $\mathrm{BeCO}_3$ being unstable, is kept in the atmosphere of $\mathrm{CO}_2$.
V. $\mathrm{BeCO}_3$ is less soluble among all the carbonates of group 2 elements.
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Consider the following reactions.
$$ \begin{array}{r} \mathrm{Cs}+\mathrm{O}_2 \text { (excess) } \rightarrow X \\ \mathrm{Na}+\mathrm{O}_2 \rightarrow Y \end{array} $$
Identify the correct Statement about $X$ and $Y$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
An organic compound containing phosphorous on oxidation with $\mathrm{Na}_2 \mathrm{O}_2$ gives a compound ' $X$ '. This ' $X$ ' when boiled with $\mathrm{HNO}_3$ followed by treatment with a reagent gives yellow precipitate $Y . X$ and $Y$ respectively are
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Xenon (VI) fluoride on complete hydrolysis gives an oxide of xenon ' $O$ '. The total number of $\sigma$ and $\pi$-bonds $\sin$ ' $O$ ' is i"
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Among the hydrides $\mathrm{NH}_3, \mathrm{PH}_3$ and $\mathrm{BiH}_3$, the hydride with highest boiling point is $X$ and the hydride with lowest boiling point is $Y$. What are $X$ and $Y$ respectively?
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Identify the complex ion with electronic configuration $t_{2 g}^3 e_g^2$.
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The set of elements which obey the general electronic configuration $(n-1) d^{1-10} n s^2$ is?
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Kaolinite is a silicate mineral of metal ' $X$ ' and calamine is a carbonate mineral of metal ' $Y^{\prime}, X$ and $Y$ respectively are
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The major product ' $Y^{\prime}$ in the given sequence of reactions is
$$ \mathrm{C}_3 \mathrm{H}_7 \mathrm{OH} \xrightarrow[443 \mathrm{~K}]{\text { Conc. } \mathrm{H}_2 \mathrm{SO}_4} X \xrightarrow[\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CO}\right)_2 \mathrm{O}_2]{\mathrm{HBr}} Y $$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Acrolein $(X)$ is one of the chemicals formed when $\mathrm{O}_3$ and $\mathrm{NO}_2$ react with unburnt hydrocarbons present in the polluted air. The structure of ' $X$ ' is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The correct IUPAC name of the structure given below is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
In which of the following ions the spin only magnetic moment is lowest?
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Arrange the following in the increasing order of pKa values
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Compound ' $A$ ' on heating with sodalime gives propane. Identify the compound ' $A$ '.
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Identify the products $R$ and $S$ in the reaction sequence given
$\left(\mathrm{CH}_3\right)_3 \mathrm{COH} \xrightarrow{\mathrm{Na}} P \xrightarrow{\mathrm{CH}_3 \mathrm{Br}} Q \xrightarrow[\Delta]{\mathrm{HI}} R+S$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$$ \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH} \xrightarrow[443 \mathrm{~K}]{\text { Conc. } \mathrm{H}_2 \mathrm{SO}_4} X \xrightarrow[\text { (ii) } \mathrm{Zn} / \mathrm{H}_2 \mathrm{O}\,(2 Moless)]{\text { (i) } \mathrm{O}_3} Y \xrightarrow[\text { (i) } \mathrm{H}^{+}]{\text {(i) Conc. } \mathrm{NaOH}} \mathrm{Z} $$
$Z$ is a mixture of alcohol and acid. Reaction of conversion of $Y$ to $Z$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\mathrm{NH}_2 \mathrm{CONH}_2+2 \mathrm{H}_2 \mathrm{O} \rightarrow[\mathrm{X}] \rightleftharpoons 2 \mathrm{NH}_3+\mathrm{H}_2 \mathrm{O}+[\mathrm{Y}]$
The hybridisation of carbon in $X$ and $Y$ respectively are
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Conversion of $X$ to $Y$ in the above reaction is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
In the given reaction sequence sequence, $Z$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
What is ' $C$ ' in the following reaction sequence?
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
One of the values of $(-64 i)^{5 / 6}$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Which of the following vitamin is also called pyridoxine?
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Identify the structure of the polymer 'P' formed in the given reaction
Caprolactam $\xrightarrow[\mathrm{H}_2 \mathrm{O}]{533-543 \mathrm{~K}} P$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $z=x+i y$ and if the point $P$ represents $z$ in the argand plane, then the locus of $z$ satisfying the equation $|z-1|+|z+i|=2$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $x$ and $y$ are two positive real numbers such that $x+i y=\frac{13 \sqrt{-5+12 i}}{(2-3 i)(3+2 i)}$, then $13 y-26 x=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\mathbf{Assertion (A)}$ Silicones are used for water proofing of fabrics.
$\mathbf{Reason (R)}$ The repeating unit in silicones is
The correct answer is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $\alpha, \beta$ are the roots of the equation $x+\frac{4}{x}=2 \sqrt{3}$, then $\frac{2}{\sqrt{3}}\left|\alpha^{2024}-\beta^{2024}\right|=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3+3 x^2-10 x-24=0$. If $\alpha>\beta>\gamma$ and $\alpha^3+3 \beta^2-10 \gamma-24=11 k$, then $k=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If all the possible 3-digit numbers are formed using the digits $1,3,5,7$ and 9 without repeating any digit, then the number of such 3 -digit numbers which are divisible by 3 is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Among the following four statements, the statement which is not true, for all $n \in N$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\alpha, \beta$ and $\gamma$ are the roots of the equation $8 x^3-42 x^2+63 x-27=0$. If $\beta<\gamma<\alpha$ and $\beta, \gamma$ and $\alpha$ are in geometric progression, then the extreme value of the expression $\gamma x^2+4 \beta x+\alpha$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\alpha, \beta$ are the real roots of the equation $12 x^{\frac{1}{3}}-25 x^{\frac{1}{6}}+12=0$. If $\alpha>\beta$, then $6 \sqrt{\frac{\alpha}{\beta}}=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If the probability distribution of a random variable $X$ is as follow, then the variance of $X$ is
| $X=x$ | 2 | 3 | 5 | 9 |
| $P(X=x)$ | $k$ | $2 k$ | $3 k^2$ | $k$ |
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
All the letters of word 'COLLEGE' are arranged in all possible ways and all the seven letter words (with or without meaning) thus formed are arranged in the dictionary order. Then, the rank of the word 'COLLEGE' is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If two cards are drawn at random simultaneously from a well shuffled pack of 52 playing cards, then the probability of getting a cards having a composite number and a card having a number which is a multiple of 3 is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
Bag $P$ contains 3 white, 2 red, 5 blue balls and bag $Q$ contains 2 white, 3 red, 5 blue balls. A ball is chosen at random from $P$ and is placed in $Q$. If a ball is chosen from bag $Q$ at random, then the probability that it is a red ball is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A question paper has 3 parts $A, B$ and $C$. Part $A$ contains 7 questions, part $B$ contains 5 questions and Part Ccontains 3 questions. If a candidate is allowed to answer not more than 4 questions from part $A$; not more than 3 questions from part $B$ and not more than 2 questions from part $C$, then the number of ways in which a candidate can answer exactly 7 questions is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If two dice are thrown, then the probability of getting co-prime numbers on the dice is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$P$ and $Q$ are the points of trisection of the segment $A B$. If $2 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $4 \hat{\mathbf{i}}+\hat{\mathbf{j}}-6 \hat{\mathbf{k}}$ are the position vectors of $A$ and $B$ respectively, then the position vector of the point which divides $P Q$ in the ratio $2: 3$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $p$ and $q$ are the real numbers such that the 7 th term in the expansion of $\left(\frac{5}{p^3}-\frac{3 q}{7}\right)^8$ is 700 , then $49 p^2=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The position vector of the point of intersection of the line joining the points $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and the line joining the points $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-6 \hat{\mathbf{k}}, 3 \hat{\mathbf{i}}-\hat{\mathbf{j}}-7 \hat{\mathbf{k}}$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $T_4$ represents the 4 th term in the expansion of $\left(5 x+\frac{7}{x}\right)^{\frac{-3}{2}}$ and $x \notin\left[-\sqrt{\frac{7}{5}}, \sqrt{\frac{7}{5}}\right]$, then $\left(x^7 \sqrt{5 x}\right) T_4=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $\mathbf{a}=4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\mathbf{b}=6 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ are two vectors, then the magnitude of the component of $\mathbf{b}$ parallel to $\mathbf{a}$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A plane $\pi_1$ passing through the point $3 \hat{\mathbf{i}}-7 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ is perpendicular to the vector $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and another plane $\pi_2$ passing through the point $2 \hat{\mathbf{i}}+7 \hat{\mathbf{k}}-8 \hat{\mathbf{k}}$ is perpendicular to the vector $3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$. If $p_1$ and $p_2$ are the perpendicular distances from the origin to the planes $\pi_1$ and $\pi_2$ respectively, then $p_1-p_2=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$A(2,3, k), B(-1, k,-1)$ and $C(4,-3,2)$ are the vertices of $\triangle A B C$. If $A B=A C$ and $k>0$, then $\triangle A B C$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $a \neq b \neq c, \Delta_1=\left[\begin{array}{lll}1 & a^2 & b c \\ 1 & b^2 & c a \\ 1 & c^2 & a b\end{array}\right]$, $\Delta_2=\left[\begin{array}{ccc}1 & 1 & 1 \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3\end{array}\right]$ and $\frac{\Delta_1}{\Delta_2}=\frac{6}{11}$, then $11(a+b+c)=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $M_1$ is the mean deviation from the mean of the discrete data $44,5,27,20,8,54,9,14,35$ and $M_2$ is the mean deviation from the median of the same data, then $M_1-M_2=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $a, b$ and $c$ are the intercepts made on $X, Y, Z$-axes respectively by the plane passing through the points $(1,0,-2),(3,-1,2)$ and $(0,-3,4)$, then $3 a+4 b+7 c=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The mean of a binomial variate $X \sim B(n, p)$ is 1 . If $n>2$ and $P(X=2)=\frac{27}{128}$, then the variance of the distribution is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The system of equations $x+3 y+7=0$, $3 x+10 y-3 z+18=0$ and $3 y-9 z+2=0$ has
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $\sin h^{-1}(-\sqrt{3})+\cos ^{-1}(2)=K$, then $\cosh K=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If the real valued function $f(x)=\sin ^{-1}\left(x^2-1\right)-3 \log _3\left(3^x-2\right)$ is not defined for all $x \in(-\infty, a) \cup(b, \infty)$, then $3^a+b^2=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $\tan A+\tan B+\cot A+\cot B=\tan A \tan B-\cot A \cot B$ and $0^{\circ} < A+B<270^{\circ}$, then $A+B=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The equation that is satisfied by the general solution of the equation $4-3 \cos ^2 \theta=5 \sin \theta \cos \theta$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\tan A=\frac{-60}{11}$ and $A$ does not lie in the 4th quadrant. $\sec B=\frac{41}{9}$ and $B$ does not lie in the 1st quadrant. If $\operatorname{cosec} A+\cot B=K$, then $24 K=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $\sin ^{-1}(4 x)-\cos ^{-1}(3 x)=\frac{\pi}{6}$, then $x=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $\log y=y^{\log x}$, then $\frac{d y}{d x}=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $\cos ^2 84^{\circ}+\sin ^2 126^{\circ}-\sin 84^{\circ} \cos 126^{\circ}=K$ and $\cot A+\tan A=2 K$, then the possible values of $\tan A$ are
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The approximate value of $\sec 59^{\circ}$ obtained by taking $1^{\circ}$ $=0.0174$ and $\sqrt{3}=1.732$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
In triangle $A B C$, if $a=4, b=3$ and $c=2$, then $2(a-b \cos C)(a-c \sec B)=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
In $\triangle A B C$, if $A=45^{\circ}, C=75^{\circ}$ and $R=\sqrt{2}$, than $r=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $A(1,2,-3), B(2,3,-1)$ and $C(3,1,1)$ are the vertices of $\triangle A B C$, then $\left|\frac{-\cos A}{\cos B}\right|=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $A$ and $B$ are arbitrary constants, then the differential equation having $y=A e^{-x}+B \cos x$ as its general solution is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The general solution of the differential equation $\frac{d y}{d x}+\frac{\sin (2 x+y)}{\cos x}+2=0$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $y=a \cos 3 x+b e^{-x}$, then $y^{\prime \prime}(3 \sin 3 x-\cos 3 x)=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If the function
$$
f(x)= \begin{cases}\frac{\tan a(x-1)}{x-1}, & \text { if } 04\end{cases}
$$
domain, then $6 a+9 b^4=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The area of the region enclosed by the curves $y^2=4(x+1)$ and $y^2=5(x-4)$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $\lim \limits_{x \rightarrow 4} \frac{2 x^2+(3+2 a) x+3 a}{x^3-2 x^2-23 x+60}=\frac{11}{9}$, then $\lim \limits_{x \rightarrow a} \frac{x^2+9 x+20}{x^2-x-20}=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $f$ is a real valued function from $A$ onto $B$ defined by $f(x)=\frac{1}{\sqrt{|x-|x||}}$, then $A \cap B=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If the function $f(x)=x^3+a x^2+b x+40$ satisfies the conditions of Rolle's theorem on the interval $[-5,4]$ and $-5,4$ are two roots of the equation $f(x)=0$, then one of the values of $c$ as stated in that theorem is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $x$ and $y$ are two positive integers such that $x+y=24$ and $x^3 y^5$ is maximum, then $x^2+y^2=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
A point $P$ is moving on the curve $x^3 y^4=2^7$. The $x$-coordinate of $P$ is decreasing at the rate of 8 units per second. When the point $P$ is at $(2,2)$, the $y$-coordinate of $P$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The equation of the normal drawn to the curve $y^3=4 x^5$ at the point $(4,16)$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If the expression $7+6 x-3 x^2$ attains its extreme value $\beta$ at $x=\alpha$, then the sum of the squares of the roots of the equation $x^2+\alpha x-\beta=0$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $(h, k)$ is the internal centre of similitude of the circles $x^2+y^2+2 x-6 y+1=0$ and $x^2+y^2-4 x+2 y+4=0$, then $4 h=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\int \sqrt{4 \cos ^2 x-5 \sin ^2 x} \cos x d x=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\int\left(\frac{\left(\sin ^4 x+2 \cos ^2 x-1\right) \cos x}{(1+\sin x)^6}\right) d x=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\int\left(\frac{4 \tan ^4 x+3 \tan ^2 x-1}{\tan ^2 x+4}\right) d x=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If the tangents $x+y+k=0$ and $x+a y+b=0$ drawn to the circle $S=x^2+y^2+2 x-2 y+1=0$ are perpendicular to each other and $k, b$ are both greater than 1 , then $b-k=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$(1, k)$ is a point on the circle passing through the points $(-1,1),(0,-1)$ and $(1,0)$. If $k \neq 0$, then $k=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If the focal chord of the parabola $x^2=12 y$, drawn through the point $(3,0)$ intersects the parabola at the points $P$ and $Q$ then the sum of the reciprocals of the abscissae of the points $P$ and $Q$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $(p, q)$ is the centre of the circle which cuts the three circles $x^2+y^2-2 x-4 y+4=0, x^2+y^2+2 x-4 y+1=0$ and $x^2+y^2-4 x-2 y-11=0$ orthogonally, then $p+q=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$x^2+y^2+2 x-6 y-6=0$ and $x^2+y^2-6 x-2 y+k=0$ are two intersecting circles and $k$ is not an integer. If $\theta$ is the angle between the two circles and $\cos \theta=\frac{-5}{24}$, then $k=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If the normal drawn at the point $P(9,9)$ on the parabola $y^2=9 x$ meets the parabola again at $Q(a, b)$, then $2 a+b=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The slope of a common tangent to the circles $x^2+y^2-4 x-8 y+16=0$ and $x^2+y^2-6 x-16 y+64=0$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The slope of the tangent drawn from the point $(1,1)$ to the hyperbola $2 x^2-y^2=4$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$(0, k)$ is the point to which the origin is to be shifted by the translation of the axes so as to remove the first degree terms from the equation $a x^2-2 x y+b y^2-2 x+4 y+1=0$ and $\frac{1}{2} \tan ^{-1}(2)$ is the angle through which the coordinate axes are to be rotated about the origin to remove the $x y$-term from the given equation, then $a+b=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\beta$ is the angle made by the perpendicular drawn from origin to the line $L \equiv x+y-2=0$ with the positive $X$-axis in the anticlockwise direction. If $a$ is the $X$-intercept of the line $L=0$ and $p$ is the perpendicular distance from the origin to the line $L=0$, then $a \tan \beta+p^2=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $Q$ and $R$ are the images of the point $P(2,3)$ with respect to the lines $x-y+2=0$ and $2 x+y-2=0$ respectively, then $Q$ and $R$ lie on
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The line $2 x+y-3=0$ divides the line segment joining the points $A(1,2)$ and $B(-2,1)$ in the ratio $a: b$ at the point $C$. If the point $C$ divides the line segment joining the points $P\left(\frac{b}{3 a},-3\right)$ and $Q\left(-3,-\frac{b}{3 a}\right)$ in the ratio $p: q$, then $\frac{p}{q}+\frac{q}{p}=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If the distance from a variable point $P$ to the point $(4,3)$ is equal to the perpendicular distance from $P$ to the line $x+2 y-1=0$, then the equation of the locus of the point $P$ is
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $(2,-1)$ is the point of intersection of the pair of lines $2 x^2+a x y+3 y^2+b x+c y-3=0$, then $3 a+2 b+c=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$S$ is the focus of the ellips $\frac{x^2}{25}+\frac{y^2}{b^2}=1,(b<5)$ lying on the negative $X$-axis and $P(\theta)$ is a point on this ellipes. If the distance between the foci of this ellipse is 8 and $S^{\prime} P=7$, then $\theta=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
The length of the latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ is $\frac{8}{3}$. If the distance from the centre of the ellipse to its focus is $\sqrt{5}$, then $\sqrt{a^2+6 a b+b^2}=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $\frac{2 x^3+1}{2 x^2-x-6}=a x+b+\frac{A}{P x-2}+\frac{B}{2 x+q}$, then 51 apB $=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\mathbf{c}=2 \hat{\mathbf{k}}-\hat{\mathbf{i}}$ are three vectors and $\mathbf{d}$ is a unit vector perpendicular to $\mathbf{c}$. If $\mathbf{a}, \mathbf{b}$ and $\mathbf{d}$ are coplanar vectors, then $|\mathbf{d} \cdot \mathbf{b}|=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $A=\left[\begin{array}{lll}x & y & y \\ y & x & y \\ y & y & x\end{array}\right]$ is a matrix such that $5 A^{-1}=\left[\begin{array}{ccc}-3 & 2 & 2 \\ 2 & -3 & 2 \\ 2 & 2 & -3\end{array}\right]$, then $A^2-4 A=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $A=\left[\begin{array}{lll}9 & 3 & 0 \\ 1 & 5 & 8 \\ 7 & 6 & 2\end{array}\right]$ and $A A^T-A^2=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]$, then $\sum\limits_{\substack{1 \leq i \leq 3 \\ 1 \leq j \leq 3}} a_{i j}=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $y=\cos ^{-1}\left(\frac{6 x-2 x^2-4}{2 x^2-6 x+5}\right)$, then $\frac{d y}{d x}=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
If $y=\log \left[\tan \sqrt{\frac{2^x-1}{2^x+1}}\right], x>0$, then $\left(\frac{d y}{d x}\right)_{x=1}=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\int_0^\pi\left(\sin ^3 x+\cos ^2 x\right)^2 d x=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\int_{\frac{-\pi}{8}}^{\frac{\pi}{8}} \frac{\sin ^4(4 x)}{1+e^{4 x}} d x=$
PYP
TG EAPCET 2024 ONLINE 10TH MAY MORNING SHIFT
$\int(\log x)^3 d x=$
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