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TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
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PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The maximum horizontal range of a ball projected from the ground is 32 m . If the ball is thrown with the same speed horizontally from the top of a tower of . height 25 m , the maximum horizontal distance covered by the ball is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
At 300 K , the vapour pressure of toluene and benzene are 3.63 kPa and 9.7 kPa respectively. What is the composition of vapour in equilibrium with the solution containing 0.4 mole fraction of toluene?
(Assume the solution is ideal)
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The correct formula of borax is $\mathrm{Na}_{2}\left[\mathrm{~B}_{4} \mathrm{O}_{5}(\mathrm{OH})_{x}\right] \cdot y \mathrm{H}_{2} \mathrm{O}$. The sum of $x$ and $y$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The position $x$ (in metre) of a particle moving along a straight line is given by $x=t^{3}-12 t+3$, where $t$ is time (in second). The acceleration of the particle when its velocity becomes $15 \mathrm{~ms}^{-1}$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A block of mass 5 kg is kept on a smooth horizontal surface. A horizontal stream of water coming out of a pipe of area of cross-section $5 \mathrm{~cm}^{2}$ hits the block with a velocity of $5 \mathrm{~ms}^{-1}$ and rebounds back with the same velocity. The initial acceleration of the block is (density of water is $1 \mathrm{~g} / \mathrm{cc}$ )
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A body of mass $m$ and radius $r$ rolling horizontally $m$ an inclined plane to a vertical
a velocity $v$ rolls up an height $\frac{v^{2}}{g}$. The body is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A ball $A$ of mass 1.2 kg moving with a velocity of $8.4 \mathrm{~ms}^{-1}$ makes one-dimensional elastic collision with a ball $B$ of mass 3.6 kg at rest. The percentage of kinetic energy transferred by ball $A$ to ball $B$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The range of gravitational forces is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A constant force of $(8 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}) \mathrm{N}$ acting on a body of mass 2 kg displaces the body from $(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}) \mathrm{m}$ to $(4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}) \mathrm{m}$. The work done in the process is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A meter scale is balanced on a knife edge at its centre. When two coins, each of mass 9 g are kept one above the other at the 10 cm mark, the scale is found to be balanced at 35 cm . The mass of the meter scale is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If the excess pressures inside two soap bubbles are in the ratio $2: 3$, then the ratio of the volumes of the somp bubbles is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A simple pendulum is made of a metal wire of length $L$, area of cross-section $A$, material of Young's modulus $Y$ and a bob of mass $m$. This pendulum is hung in abus moving with a uniform speed $v$ on a horizontal circular road of radius $R$. The elongation in the wire is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The velocities of air above and below the surfaces of a flying aeroplane wing are $50 \mathrm{~ms}^{-1}$ and $40 \mathrm{~ms}^{-1}$, respectively. If the area of the wing is $10 \mathrm{~m}^{2}$ and the mass of the aeroplane is 500 kg , then as time passes of (density of air $=13 \mathrm{~kg} \mathrm{~m}^{-3}$ )
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
In a simple pendulum experiment for the determination of acceleration due to gravity, the error in the measurement of the length of the pendulum is $1 \%$ and the error in the measurement of the time period is $2 \%$. The error in the estimation of acceleration due to gravity is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
An object of mass $m$ at a distance of $20 R$ from the centre of a planet of mass $M$ and radius $R$ has an initity velocity $u$. The velocity with which the object hits the surface of the planet is
( $G$-Universal gravitational constant)
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A massless spring of length $l$ and spring constant $k$ oscillates with a time period $T$ when loaded with a mass $m$. The spring is now cut into three equal parts and are connected in parallel. The frequency of oscillation of the combination when it is loaded with ${ }_{3}$ mass 4 m is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
When the object and the screen are 90 cm apart, it is observed that a clear image is formed on the screen when a convex lens is placed at two positions separated by 30 cm between the object and the screen. The focal length of the lens is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A pendulum clock loses 10.8 s a day when the temperature is $38^{\circ} \mathrm{C}$ and gains 108 s a day when the temperature is $18^{\circ} \mathrm{C}$. The coefficient of linear expansion of the metal of the pendulum clock is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
For a gas in a thermodynamic process, the relation between internal energy $U$, the pressure $p$ and the volume $V$ is $U=3+15 p V$. The ratio of the specific heat capacities of the gas at constant volume and constant pressure is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Two closed pipes when sounded simultaneously in their fundamental modes produce 6 beats per second. If the length of the shorter pipe is 150 cm , then the length of the longer pipe is
(Speed of sound in air $=336 \mathrm{~ms}^{-1}$ )
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A liquid cools from a temperature of 368 K to 358 K in 22 min . In the same room, the same liquid takes 12.5 min to cool from 358 K to 353 K . The room temperature is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The tension applied to a metal wire of one metre length produces an elastic strain of $1 \%$. The density of the metal is $8000 \mathrm{kgm}^{-3}$ and Young's modulus of the metal is $2 \times 10^{11} \mathrm{Nm}^{-2}$. The fundamental frequency of the transverse waves in the metal wire is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The electric flux due to an electric field $\mathbf{E}=(8 \hat{\mathbf{i}}+13 \hat{\mathbf{j}}) \mathrm{NC}^{-1}$ through an area $3 \mathrm{~m}^{2}$ lying in the $X Z$-plane is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
An object placed at a distance of 24 cm from a concave mirror forms an image at a distance of 12 cm from the mirror. If the object is moved with a speed of $12 \mathrm{~ms}^{-1}$, then the speed of the image is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
When a monochromatic light is incident on a surface separating two media, both the reflected and refracted lights have the same
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A voltmeter of resistance $400 \Omega$ is used to measure the emf of a cell with an internal resistance of $4 \Omega$. The error in the measurement of emf of the cell is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
When two wires are connected in the two gaps of a meter bridge, the balancing length is 50 cm . When the wire in the right gap is stretched to double its lengt ${ }^{-}$ and again connected in the same gap, then the new balancing length from the left. end of the bridge wiu :
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
At a pressure $p$ and temperature $127^{\circ} \mathrm{C}$, a vessel contains 21 g of a gas. A small hole is made into the vessel, so that the gas in it leaks out. At a pressure of $\frac{2 p}{3}$ and a temperature of $t^{\circ} \mathrm{C}$, the mass of the gas leaked out is 5 g . Then, $t=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The energy stored in a coil of inductance 80 mH carrying a current of 2.5 A is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The magnetising field which produces a magnetic flux of $22 \times 10^{-6} \mathrm{~Wb}$ in a metal bar of area of cross-section $2 \times 10^{-5} \mathrm{~m}^{2}$ is (susceptibility of the metal $=699$ )
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A straight wire carrying a current of $2 \sqrt{2} \mathrm{~A}$ is making an angle of $45^{\circ}$ with the direction of uniform magnetic field of 3 T . The force per unit length of the wire due to the magnetic field is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A magnetic field is applied in $y$-direction on an $\alpha$-particle travelling along $x$-direction. The motion of the $\alpha$-particle will be
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A capacitor of capacitance $C$ is charged to a potential $V$ and disconnected from the battery. Now, if the space between the plates is completely filled with a substance of dielectric constant $K$, the final charge and the final potential on the capacitor are respectively.
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
For the displacement current through the plates of a parallel plate capacitor of capacitance $30 \mu \mathrm{~F}$ to be $150 \mu \mathrm{~A}$, the potential difference across the plates of the capacitor has to vary at the rate of
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Half-life periods of two nuclei $A$ and $B$ are $T$ and $2 T$ respectively. Initially $A$ and $B$ have same number of nuclei. After a time of $4 T$, the ratio of the remaining number of nuclei of $A$ and $B$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The work functions of two photosensitive metal surfaces $A$ and $B$ are in the ratio $2: 3$. If $x$ and $y$ are the slopes of the graphs drawn between the stopping potential and frequency of incident light for the surfaces $A$ and $B$ respectively, then $x: y=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If the ratio of the radii of nuclei ${ }_{52} X^{A}$ and ${ }_{13} \mathrm{AI}^{27}$ is $5: 3$, then the number of neutrons in the nucleus $X$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
To get output 1 for the following logic circuit, the correct choice of the inputs is 
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A capacitor and a resistor are connected in series to an AC source. If the ratio of the capacitive reactance of the capacitor and the resistance of the resistor is $4: 3$, then the power factor of the circuit is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
In hydrogen atom, the frequency of the photon emitted when an electron jumps from second orbit to first orbit is $f$. The frequency of the photon emitted when an electron jumps from third excited state to first excited state is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The maximum distance between the transmitting and receiving antennas is $D$. If the heights of both transmitting and receiving antennas are doubled, then the maximum distance between the two antennas is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $n, l$ represent the principal and azimuthal quantum numbers respectively, the formula used to know the number of radial nodes possible for a given orbital is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
At what temperature will the RMS velocity of sulphur dioxide molecules at 400 K be the same as the most probable velocity of oxygen molecules?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
At $300 \mathrm{~K}, 3.0$ moles of an ideal gas at 3.0 atm pressure is compressed isothermally to one half of its volume by an external pressure of 6.0 atm . The work done (in kJ ) is (Given, $\left.R=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)(1 \mathrm{~L} \mathrm{~atm}=1013 \mathrm{~J})$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Match the devices given in List-I with their uses given in List-II.
| List-I | List -II |
| a Transistor | e Filter circuit |
| b Diode | f Voltage regulator |
| c Zener diode | g Rectifier |
| d Capacitor | h Amplifier |
The correct answer is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If the radius of first orbit of hydrogen like ion is $1.763 \times 10^{-2} \mathrm{~nm}$, the energy associated with that orbit (in J ) is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
0.592 g of copper is deposited in 60 minutes by passing
0.5 A current through a solution of copper (II) sulphate. The electro chemical equivalent of copper (II) (in $\mathrm{gC}^{-1}$ ) is
( $F=96500 \mathrm{C} \mathrm{mol}^{-1}$ )
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
For the gaseous reaction, $\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow 2 \mathrm{NO}_{2}+\frac{1}{2} \mathrm{O}_{2}$
the rate can be expressed as
$ \begin{array}{l} -\frac{d\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right]}{d t}=K_{1}\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right] \\\\ +\frac{d\left[\mathrm{NO}_{2}\right]}{d t}=K_{2}\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right] \\\\ +\frac{d\left[\mathrm{O}_{2}\right]}{d t}=K_{3}\left[\mathrm{~N}_{2} \mathrm{O}_{5}\right] \end{array} $
The correct relation between $K_{1}, K_{2}$ and $K_{3}$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
At $T(K)$ the equilibrium constants for the following two reactions are given below
$ 2 A(g) \rightleftharpoons B(g)+C(g) ; K_{1}=16 $
$ 2 B(g)+C(g) \rightleftharpoons 2 D(g) ; K_{2}=25 $
What is the value of equilibrium constant $(K)$ for the reaction given below at $T(K)$ ?
$ A(g)+\frac{1}{2} B(g) \rightleftharpoons D(g) $
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If first ionisation enthalpy $\left(\Delta_{i} H\right)$ values of $\mathrm{Na}, \mathrm{Mg}$ and Si are respectively 496,737 and $786 \mathrm{~kJ} \mathrm{~mol}^{-1}$, the first ionisation enthalpy value of $\mathrm{Al}\left(\mathrm{in} \mathrm{kJ} \mathrm{mol}^{-1}\right.$ ) will be
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
According to molecular orbital theory, which of the following statements is not correct?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
In bcc lattice containing $X$ and $Y$ type of atoms, $X$ type of atoms are present at the corners and $Y$ type of atoms are present at the centers. In its unit cell, if three atoms are missing in the corners, the formula of the compound is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Among the oxides $\mathrm{SiO}_{2}, \mathrm{SO}_{2}, \mathrm{Al}_{2} \mathrm{O}_{3}$ and $\mathrm{P}_{2} \mathrm{O}_{3}$, the correct order of acidic strength is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The melting point of $o$-hydroxybenzaldehyde $(A)$ is lower than that of $p$-hydroxybenzaldehyde $(B)$. This is because
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Identify the pair of hydrides which have polymeric structure
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The bond angles $\mathrm{H}-\mathrm{O}-\mathrm{N}$ and $\mathrm{O}-\mathrm{N}-\mathrm{O}$ in the planar structure of nitric acid molecule are respectively
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Which among the following oxoacids of phosphorous will have $\mathrm{P}-\mathrm{O}-\mathrm{P}$ bonds?
I. $\mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{5}$
II. $\mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{6}$
III. $\mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7}$
IV. $\left(\mathrm{HPO}_{3}\right)_{3}$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The hydroxide of which of the following metal reacts with both acid and alkali?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Match the following
| List I (Alloy) | List II (Use) |
| A Li-Pb | I. In aircraft construction |
| B Be-Cu | II. To make bearings for motor engines |
| C Mg-Al | III. To make tetraethyl lead |
| D Na-Pb | IV. To make high strength springs |
The correct answer is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Observe the following $f$-block elements
$\mathrm{Eu}(Z=63) ; \mathrm{Pu}(Z=94) ; \mathrm{Cf}(Z=98)$;
$\operatorname{Sm}(Z=62) ; \mathrm{Gd}(Z=64) ; \mathrm{Cm}(Z=96)$
How many of the above have half-filled $f$-orbitals in their ground state?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Copper matte is mixture of
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Match the following
| List I (Industrial process) | List II (Catalyst used) |
| A Ostwald's process | I $\mathrm{CuCl}_2$ |
| B Haber's process | II Zeolites |
| C Deacon's process | III Pt gauge |
| D Cracking of hydrocarbons | IV Fe |
The correct answer is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Eutrophication can lead to
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Which one of the following complex ions has geometrical isomers?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The organic halide, which does not undergo hydrolysis by $\mathrm{S}_{\mathrm{N}} 1$ mechanism is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
In which of the following options, the IUPAC name is not correctly matched with the structure of the compound?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Consider the following reaction sequence
$ \text { 2-methylpropane } \xrightarrow{\mathrm{KMnO}_{4}} X \xrightarrow[358 \mathrm{~K}]{20 \% \mathrm{H}_3 \mathrm{PO}_4} Y \xrightarrow[\text { (ii) } \mathrm{Zn} / \mathrm{H}_{2} \mathrm{O}]{\text { (i) } \mathrm{O}_{3}} A+B \text {. } $
What are $A$ and $B$ ?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
What is the % carbon in the product ' $Z$ ' formed in the reaction?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Consider the following carbocations.
Arrange the above carbocations in the order of decreasing stability
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
What are $Y$ and $Z$ respectively in the given reaction sequence?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
What is the value of ' $n$ ' in ' $Z$ ' of the following sequence?
Lauryl alcohol $\xrightarrow{\mathrm{H}_{2} \mathrm{SO}_{4}}$
( $X$ )
Lauryl hydrogen sulphate $\xrightarrow{\mathrm{NaOH}(a q)}$
( $Y$ )
$ \mathrm{CH}_{3}-\left(\mathrm{CH}_{2}\right)_{n}-\mathrm{CH}_{2} \mathrm{OSO}_{3} \mathrm{Na} $
(Z)
Sodium lauryl sulphate
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
What is $C$ in the given sequence of reactions?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Match the following
The correct answer is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
What is ' $Z$ ' in the given sequence of reactions?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Identify the end product $(Z)$ in the sequence of the following reactions.
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Formic acid on heating with concentrated $\mathrm{H}_{2} \mathrm{SO}_{4}$ at 373 K gives $X$, a colourless substance and $Y$, a good reducing agent. The number of $\sigma$ and $\pi$ bonds in $X, Y$ are respectively
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\alpha, \beta$ are the roots of the equation $x^{2}+2 x+4=0$. If the point representing $\alpha$ in the argand diagram lies in the 2nd quadrant and $\alpha^{2024}-\beta^{2024}=i k,(i=\sqrt{-1})$, then $k=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $f(x)$ is a quadratic function such that $f(x) f\left(\frac{1}{x}\right)=f(x)+f\left(\frac{1}{x}\right)$, then $\sqrt{f\left(\frac{2}{3}\right)+f\left(\frac{3}{2}\right)}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Which one of the following is not an example of condensation polymer?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $\alpha$ is a root of the equation $x^{2}-x+1=0$, then $\left(\alpha+\frac{1}{\alpha}\right)^{3}+\left(\alpha^{2}+\frac{1}{\alpha^{2}}\right)^{3}+\left(\alpha^{3}+\frac{1}{\alpha^{3}}\right)^{3}+\left(\alpha^{4}+\frac{1}{\alpha^{4}}\right)^{3}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
What is the IUPAC name of the product $Y$ in the given reaction sequence?
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $z=\frac{(2-i)(1+i)^{3}}{(1-i)^{2}}$, then $\arg (z)=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Number of ways in which the number 831600 can be split into two factors which are relatively prime is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $\alpha, \beta, \gamma$ are the roots of the equation $4 x^{3}-3 x^{2}+2 x-1=0$, then $\alpha^{3}+\beta^{3}+\gamma^{3}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\alpha, \beta$ are the real roots of the equation $x^{2}+a x+b=0$. If $\alpha+\beta=\frac{1}{2}$ and $\alpha^{3}+\beta^{3}=\frac{37}{8}$, then $a-\frac{1}{b}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The equation $16 x^{4}+16 x^{3}-4 x-1=0$ has a multiple root. If $\alpha, \beta, \gamma, \delta$ are the roots of this equation, then $\frac{1}{\alpha^{4}}+\frac{1}{\beta^{4}}+\frac{1}{\gamma^{4}}+\frac{1}{\delta^{4}}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The sum of all the 4-digit numbers formed by taking all the digits from $0,3,6,9$ without repetition is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $1 \cdot 3 \cdot 5+3 \cdot 5 \cdot 7+5 \cdot 7 \cdot 9 \ldots$ to $n$ terms $=n(n+1) f(n)$, then $f(2)=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If two dice are rolled, then the probability of getting a multiple of 3 as the sum of the numbers appeared on the top faces of the dice, if it is known that their sum is an odd number, is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If a random variable $X$ has the following probability distribution, then its variance is
| X = x | 1 | 3 | 5 | 2 |
| P(X = x) | $3 K^2$ | K | $K^2$ | 2K |
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The numbers $2,3,5,7,11,13$ are written on six distinct paper chits. If 3 of them are chosen at random, then the probability that the sum of the numbers on the obtained chits is divisible by 3 , is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If 4 letters are selected at random from the letters of the word PROBABILITY, then the probability of getting a combination of letters in which atleast one letter is repeated is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The number of ways in which 6 distinct things can be distributed into 2 boxes so that no box is empty is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The solution set of the inequation $\sqrt{x^{2}+x-2} > (1-x)$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The set of all real values of $x$ for which the expansion of $\left(125 x^{2}-\frac{27}{x}\right)^{\frac{-2}{3}}$ is valid, is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The coefficient of $x y^{2} z^{3}$ in the expansion of $(x-2 y+3 z)^{6}$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ are the position vectores of two points $A$ and $B$ respectively and $C$ divides $A B$ in the ratio $3: 2$ : If $3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ is the position of vector of a point $D$, then the unit vector in the direction of $C D$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $A(-2,4, a), B(1, b, 3), C(c, 0,4)$ and $D(-5,6,1)$ are collinear points, then $a+b+c=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A unit vector $\hat{\mathbf{e}}=a \hat{\mathbf{i}}+b \hat{\mathbf{j}}+c \hat{\mathbf{k}}$ is coplanar with the vectors $\hat{\mathbf{i}}-3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$, and $3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-5 \hat{\mathbf{k}}$. If $\hat{\mathbf{e}}$ is perpendicular to the vector $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$, then $2 a^{2}+3 b^{2}+4 c^{2}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$z=x+i y$ and the point $P$ represents $z$ in the argand plane. If the amplitude of $\left(\frac{2 z-i}{z+2 i}\right)$ is $\frac{\pi}{4}$, then the equation of the locus of $P$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A plane $\pi$ passing through the points $2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}, 3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}$ is parallel to the vector $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$. If a line joining the points $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}$ and $\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ intersects the plane $\pi$ at the point $a \hat{\mathbf{i}}+b \hat{\mathbf{j}}+c \hat{\mathbf{k}}$, then $a+b+2 c=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $x=k$ satisfies the equation $\left|\begin{array}{ccc}x-2 & 3 x-3 & 5 x-5 \\\\ x-4 & 3 x-9 & 5 x-25 \\\\ x-8 & 3 x-27 & 5 x-125\end{array}\right|=0$, then $x=k$ also satisfies the equation
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$A(1,-2,1)$ and $B(2,-1,2)$ are the end points of a line segment. If $D(\alpha, \beta, \gamma)$ is the foot of the perpendicular drawn from $C(1,2,3)$ to $A B$, then $\alpha^{2}+\beta^{2}+\gamma^{2}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $A$ is a non-singular matrix, then $\operatorname{adj}\left(A^{-1}\right)=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If the homogeneous system of linear equations $x-2 y+3 z=0,2 x+4 y-5 z=0,3 x+\lambda y+\mu z=0$ has non-trivial solution, then $8 \mu+11 \lambda=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The foot of the perpendicular drawn from the point $(-2,-1,3)$ to a plane $\pi$ is $(1,0,-2)$. If $a, b, c$ are the intercepts made by the plane $\pi$ on $X, Y, Z$-axis respectively, then $3 a+b+5 c=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $(\sin \theta-\operatorname{cosec} \theta)^{2}+(\cos \theta+\sec \theta)^{2}=5$ and $\theta$ lies in the third quadrant, then $(\sin \theta+\cos \theta)^{3}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $\sin ^{-1} x-\cos ^{-1} 2 x=\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)-\cos ^{-1}\left(\frac{\sqrt{3}}{2}\right)$, then $\tan ^{-1} x+\tan ^{-1}\left(\frac{x}{x+1}\right)=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $\theta$ is an acute angle and $2 \sin ^{2} \theta=\cos ^{4} \frac{\pi}{8}+\sin ^{4} \frac{3 \pi}{8}+\cos ^{4} \frac{5 \pi}{8}+\sin ^{4} \frac{7 \pi}{8}$, then $\theta=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $0 < B < A < \frac{\pi}{4}, \cos ^{2} B-\sin ^{2} A=\frac{\sqrt{3}+1}{4 \sqrt{2}}$ and $2 \cos A \cos B=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}$, then $\cos ^{2} \frac{4 B}{3}-\sin ^{2} \frac{4 A}{5}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The variance of the data: $1,2,3,5,8,13,17$ is approximately
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\operatorname{sech}^{-1}\left(\frac{3}{5}\right)-\tanh ^{-1}\left(\frac{3}{5}\right)=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
In a $\triangle A B C$, if $a=5, b=3, c=7$, then $\sqrt{\frac{\sin (A-B)}{\sin (A+B)}}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A function $f: R \rightarrow R$ is such that $y f(x+y)+\cos m x y=1+y f(x)$. If $m=2$, then $f^{\prime}(x)=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $2 \tan ^{2} \theta-4 \sec \theta+3=0$, then $2 \sec \theta=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
In a $\triangle A B C$, if $r_{1}=6, r_{2}=9, r_{3}=18$, then $\cos A=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $y=\tan ^{-1}\left[\frac{\sin ^{3}(2 x)-3 x^{2} \sin (2 x)}{3 x \sin ^{2}(2 x)-x^{3}}\right]$, then $\frac{d y}{d x}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $y=\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\sqrt{\sin (\log 2 x)+\ldots \infty,}}}$ then $\frac{d y}{d x}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If the real valued function $f(x)=\int \frac{\left(4^{x}-1\right)^{4} \cot (x \log 4)}{\sin (x \log 4) \log \left(1+x^{2} \log 4\right)}, \quad$ if $x \neq 0$ is continuous at $x=0$, then $e^{k}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
Derivative of $(\sin x)^{x}$ with respect to $x^{(\sin x)}$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\int_{-\pi / 15}^{\pi / 5} \frac{\cos 5 x}{1+e^{5 x}} d x=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The area of the region (in sq units) enclosed by the curves $y=8 x^{3}-1, y=0, x=-1$ and $x=1$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If the equation of the curve which passes through the point $(1,1)$ satisfies the differential equation $\frac{d y}{d x}=\frac{2 x-5 y+3}{5 x+2 y-3}$, then the equation of that curve is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\lim\limits_{x \rightarrow \frac{3}{2}} \frac{\left(4 x^{2}-6 x\right)\left(4 x^{2}+6 x+9\right)}{\sqrt[3]{2 x}-\sqrt[3]{3}}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
For a given function $y=f(x), \delta y$ denote the actual error in $y$ corresponding to actual error $\delta x$ in $x$ and $d y$ denotes the approximately value of $\delta y$. If $y=f(x)=2 x^{2}-3 x+4$ and $\delta x=0.02$, then the value of $\delta y-d y$ when $x=5$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The length of the normal drawn at $t=\frac{\pi}{4}$ on the curve $x=2(\cos 2 t+t \sin 2 t), y=4(\sin 2 t+t \cos 2 t)$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The general solution of the differential equation $\left(6 x^{2}-2 x y-18 x+3 y\right) d x-\left(x^{2}-3 x\right) d y=0$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If Water is poured into a cylindrical tank of radius 3.5 ft at the rate of $1 \mathrm{cu} \mathrm{ft} / \mathrm{min}$, then the rate at which the level of the water in the tank increases (in $\mathrm{ft} / \mathrm{min}$ ) is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$y=2 x^{3}-8 x^{2}+10 x-4$ is a function defined on [1,2]. If the tangent drawn at a point $(a, b)$ on the graph of this function is parallel to X-axis $a \in(1,2)$, then $a=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $m$ and $M$ are respectively the absolute minimum and absolute maximum values of a function $f(x)=2 x^{3}+9 x^{2}+12 x+1$ defined on $[-3,0]$, then $m+M=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$P$ and $Q$ are the points of trisection of the line segment joining the points $(3,-7)$ and $(-5,3)$. If $P Q$ subtends right angle at a variable point $R$, then the locus of $R$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$f(x)=a x^{2}+b x+c$ is an even function and
$g(x)=p x^{3}+q x^{2}+r x$ is an odd function.
If $h(x)=f(x)+g(x)$ and $h(-2)=0$, then $8 p+4 q+2 r=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\int \frac{\sec x}{3(\sec x+\tan x)+2} d x=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $\int e^{x}\left(x^{3}+x^{2}-x+4\right) d x=e^{x} f(x)+c$, then $f(1)=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\int \frac{d x}{(x+1) \sqrt{x^{2}+4}}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\int \frac{d x}{4+3 \cot x} d x=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A circle passes through the points $(2,0)$ and $(1,2)$. If the power of the point $(0,2)$ with respect to this circle is 4 , then the radius of the circle is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The line $x+y+1=0$ intersects the circle $x^{2}+y^{2}-4 x+2 y-4=0$ at the points $A$ and $B$. If $M(a, b)$ is the mid-point of $A B$, then $a-b=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A circle $S$ passes through the points of intersection of the circles $x^{2}+y^{2}-2 x-3=0$ and $x^{2}+y^{2}-2 y=0$. If $x+y+1=0$ is a tangent to the circle $S$, then equation of $S$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$x-2 y-6=0$ is a normal to the circle $x^{2}+y^{2}+2 g x+2 f y-8=0$. If the line $y=2$ touches this circle, then the radius of the circle can be
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
A circle passing through the points $(1,1)$ and $(2,0)$ touches the line $3 x-y-1=0$. If the equation of this circle is $x^{2}+y^{2}+2 g x+2 f y+c=0$, then a possible value of $g$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $A(1,2), B(2,1)$ are two vertices of an acute angled triangle and $S(0,0)$ is its circumcenter, then the angle subtended by $A B$ at the third vertex is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$(1,1)$ is the vertex and $x+y+1=0$ is the directrix of a parabola. If $(a, b)$ is its focus and $(c, d)$ is the point of intersection of the directrix and the axis of the parabola, then $a+b+c+d=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The area of the parallelogram formed by the lines $L_{1} \equiv \lambda x+4 y+2=0, L_{2} \equiv 3 x+4 y-3=0$, $L_{3} \equiv 2 x+\mu y+6=0, L_{4} \equiv 2 x+y+3=0$, where $L_{1}$ is parallel to $L_{2}$ and $L_{3}$ is parallel to $L_{4}$ is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$(a, b)$ is the point to which the origin has to be shifted by translation of axes so as to remove the first-degree terms from the equation $2 x^{2}-3 x y+4 y^{2}+5 y-6=0$. If the angle by which the axes are to be rotated in positive direction about the origin to remove the $x y$-term from the equation $a x^{2}+23 a b x y+b y^{2}=0$ is $\theta$, then $\tan 2 \theta=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The axis of a parabola is parallel to $Y$-axis. If this parabola passes through the points $(1,0),(0,2),(-1,-1)$ and its equation is $a x^{2}+b x+c y+d=0$, then $\frac{a d}{b c}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If the common chord of the circles $x^{2}+y^{2}-2 x+2 y+1=0$ and $x^{2}+y^{2}-2 x-2 y-2=0$ is the diameter of a circle $S$, then the center of the circles is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$P(\theta)$ is a point on the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{9}=1, S$ is its $\mathrm{fOO}_{4 /}$ lying on the positive $X$-axis and $Q=(0,1)$. If $S Q=\sqrt{26}$ and $S P=6$, then $\theta=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If the normal drawn at the point $(2,-1)$ to the ellipse $x^{2}+4 y^{i}=8$ meets the ellipse again at $(a, b)$, then $17 a=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\mathrm{C}+$ Conc. $\mathrm{H}_{2} \mathrm{SO}_{4} \xrightarrow{\Delta} X+Y+\mathrm{H}_{2} \mathrm{O}$
$X$ and $Y$ in the above reaction are
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$A(1,-2), B(-2,3), C(-1,-3)$ are the vertices of a $\triangle A B C . L_{1}$ is the perpendicular drawn from $A$ to $B C$ and $L_{2}$ is the perpendicular bisector of $A B$. If $(l, m)$ is the point of intersection of $L_{1}$ and $L_{2}$, then $26 m-3=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If the angle between the pair of lines given by the equation $a x^{2}+4 x y+2 y^{2}=0$ is $45^{\circ}$, then the possible values of $a$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If the focus of an ellipse is $(-1,-1)$, equation of its directrix corresponding to this focus is $x+y+1=0$ and its eccentricity is $\frac{1}{\sqrt{2}}$, then the length of its major axis is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
The mean and variance of a binomial variate $X$ are $\frac{16}{5}$ and $\frac{48}{25}$ respectively. IfP $(X > 1)=1-K\left(\frac{3}{5}\right)^{7}$, then $5 K=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
0.43 g of a metal of valence 2 was dissolved in 50 mL of $0.5 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$ solution. The unreacted acid required 14.2 mL of 1 M NaOH solution for neutralisation. The atomic weight of the metal is
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}, \hat{\mathbf{b}}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{c}}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ are three vectors. If $\hat{\mathbf{d}}$ is a normal to the plane of $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ and d. $\hat{\mathbf{c}}=2$, then $|\hat{\mathbf{d}}|=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\hat{\mathbf{r}} .(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}})=5$ and $\hat{\mathbf{r}} .(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})=3$ are two planes. A plane $\pi$ passing through the line of intersection of these two planes, passes through the point $(0,1,2)$. If the equation of $\pi$ is $\hat{\mathbf{r}} .(a \hat{\mathbf{i}}+b \hat{\mathbf{j}}+c \hat{\mathbf{k}})=m$, then $\frac{b c}{a^{2}}=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$A=\left[\begin{array}{ll}1 & 2 \\\\ 2 & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}x & y \\\\ 1 & 2\end{array}\right]$ are two matrices such that $(A+B)(A-B)=A^{2}-B^{2}$ If $C=\left[\begin{array}{ll}x & 2 \\\\ 1 & y\end{array}\right]$, then trace $(C)=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
If $\frac{x^{2}}{2 x^{4}+7 x^{2}+6}=\frac{A x+B}{x^{2}+a}+\frac{C x+D}{a x^{2}+3}$, then $A+B+C-2 D=$
PYP
TG EAPCET 2024 ONLINE 11TH MAY MORNING SHIFT
$\int_{\frac{\pi}{5}}^{\frac{3 \pi}{10}} \frac{d x}{\sec ^{2} x+\left(\tan ^{2024} x-1\right)\left(\sec ^{2} x-1\right)}=$
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