TG EAPCET 2024 (Online) 10th May Evening Shift

Assertion (A) : $1+\frac{2 \cdot 1}{3 \cdot 2}+\frac{2 \cdot 5}{3 \cdot 6} \frac{1}{4}+\frac{2 \cdot 5 \cdot 8}{3 \cdot 6 \cdot 9} \frac{1}{8}+\ldots \infty=\sqrt[3]{4}$
Reason (R) : |x| < 1,(1-x) $=1+n x+\frac{n(n+1)}{1 \cdot 2} x^2$$+\fra...

The variance of the first 10 natural numbers which are multiples of 3 is

The combined equation of a possible pair of adjacent sides of a square with area 16 square units whose centre is the point of intresection of the lines $x+2 y-3=0$ and $2 x-y-1=0$ is

If the line $2 x+b y+5=0$ forms an equilateral to triangle with $a x^{2}-96 b x y+k y^{2}=0$, then $a+3 k=$

By shifting the origin to the point $(h, 5)$ by the translation of coordinate axes, if the equation $y=x^{3}-9 x^{2}+c x-d$ transforms to $Y=X^{3}$, then $\left(d-\frac{c}{h}\right)=$

The equation of the straight line whose slope is $\frac{-2}{3}$ and which divides the line segment joining $(1,2),(-3,5)$ in the ratio $4: 3$ externally is

$7 x+y-24=0$ and $x+7 y-24=0$ represent the equal sides of an isosceles triangle. If the third side passes through $(-1,1)$ then, a possible equation for the third side is

$\mathbf{n}$ is a unit vector normal to the plane $\pi$ containing the vectors $\hat{\mathbf{i}}+3 \hat{\mathbf{k}}$ and $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$. If this plane $\pi$ passes through the point $(-3,7,1)$ and $p$...

If the harmonic conjugate of $P(2,3,4)$ with respect to the line segment joining the points $A(3,-2,2)$ and $B(6,-17,-4)$ is $Q(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma=$

The foot of the perpendicular drawn from $A(1,2,2)$ oril the the plane $x+2 y+2 z-5=0$ is $B(\alpha, \beta, \gamma)$. If $\pi(x, y, z)$ $=x+2 y+2 z+5=0$ is a plane, then $-\pi(A): \pi(B)=$

If $L$ is the line of intersection of two planes $x+2 y+2 z=15$ and $x-y+z=4$ and the direction ratio of the line $L$ are $(a, b, c)$, then $\frac{\left(a^{2}+b^{2}+c^{2}\right)}{b^{2}}=$

Suppose, $\theta_{1}$ and $\theta_{2}$ are such that $\left(\theta_{1}-\theta_{2}\right)$ lies in 3rd or 4th quadrant. If $\sin \theta_{1}+\sin \theta_{2}=-\frac{21}{65}$ and $\cos \theta_{1}+\cos \theta_{2}=-\frac{27}{65}$, then $\cos \lef...

If $A$ is the solution set of the equation $\cos ^{2} x=\cos ^{2} \frac{\pi}{6}$ and $B$ is the solution set of the equation $\cos ^{2} x=\log _{16} P$ where, $P+\frac{16}{P}=10$, then, $B-A=$

If $\sin h x=\frac{12}{5}$, then $\sin h 3 x+\cos h 3 x=$

If $0 < \theta < \frac{\pi}{4}$ and $8 \cos \theta+15 \sin \theta=15$, then $15 \cos \theta-8 \sin \theta=$

$\sin 20^{\circ}\left(4+\sec 20^{\circ}\right)=$

If $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=3(\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}})$ and $\mathbf{c}$ is a vector such that $\mathbf{a} \times \mathbf{c}=\mathbf{b}$ and $\mathbf{a} . \mathb...

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three vectors each having $\sqrt{2}$ magnitude such that $(\mathbf{a}, \mathbf{b})=(\mathbf{b}, \mathbf{c})=(\mathbf{c}, \mathbf{a})=\frac{\pi}{3}$. If $\mathbf{x}=\mathbf{a} \times(\mathbf{b} \times...

$\mathbf{a}$ is a vector perpendicular to the plane containing non zero vectors $\mathbf{b}$ and $\mathbf{c}$. If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are such that$|\mathbf{a}+\mathbf{b}+\mathbf{c}|=\sqrt{|\mathbf{a}|^{2}+|\mathbf{b}|^{2}+...

If $\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{c}=-\hat{\mathbf{k}}$ are position vectors of two points and $\mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}, \mathbf{d}=\hat{\mathbf{i}}+...

An inductor of inductive reactance $R$, a capacitor of capacitive reactance $2 R$ and a resistor of resistance $R$ are connected in series to an AC source. The power factor of the series $L-C-R$ circuit is

The ground state energy of hydrogen atom is -13.6 cv . The potential energy of the electron in the first excited state of hydrogen is

$\mathrm{A}_{92} \mathrm{U}^{238}$ nucleus decays to a ${ }_{82} \mathrm{~Pb}^{214}$ nucleus. The number of $\alpha$ and $\beta^{-}$particles emitted are

After the decay of a single $\beta$-particle, the parent and daughter nuclei are

A capacitor of capacitance $(4.0 \pm 0.2) \mu \mathrm{F}$ is charged to a potential of $(10.0 \pm 0 \mathrm{l}) \mathrm{V}$. The charge on the capacitor is

Two capacitors of capacitances $1 \mu \mathrm{~F}$ and $2 \mu \mathrm{~F}$ can separately withstand potentials of 6 kV and 4 kV respectively. The total potential, they together can withstand when they are connected in series is

A circular plate of radius $r$ is removed from a uniform circular plate $P$ of radius $4 r$ to form a hole. If the distance between the centre of the hole formed and the centre of the plate $P$ is $2 r$, then the distance of mass of the rem...

A ball $P$ of mass 0.5 kg moving with a velocity of $10 \mathrm{~ms}^{-1}$ collides with another ball $Q$ of mass 1 kg at rest. If the coefficient of restitution is 0.4 , the ratio of the velocities of the balls $P$ and $Q$ after the collis...

For an amplitude modulated wave, the maximum and minimum amplitudes are found to be 10 V and 2 V respectively. Then, the modulation index is

The resistance of a wire is $2.5 \Omega$ at a temperature 373 K . If the temperature coeffficient of resistance of the material of the wire is $3.6 \times 10^{-3} \mathrm{~K}^{-1}$, its resistance at a temperatrue 273 K is nearly.

When two identical resistors are connected in series to an ideal cell, the current through each resistor is 2 A . If the resistors are connected in parallel to the cell, the current through each resistor is

Wave picture of light has failed to explain

The efficiency of a bulb of power 60 W is $16 \%$. The peak value of the electric field produced by the electromagnetic radiation from the bulb at a distance of 2 m from the bulb is $\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \ma...

The work function of a photosensitive metal surface is 1.1 eV . Two light beams of energies 1.5 eV and 2 eV incident on the metal surface. The ratio of the maximum velocities of the emitted photoelectrons is

A wire of cross-sectional area $10^{-6} \mathrm{~m}^{2}$ is elongated by $0.1 \%$ when the tension in it is 1000 N . The Young's modulus of the material of the wire is (assume radius of the wire is constant)

The mutual inductance of two coils is 8 mH . The current in one coil changes according to the equation $I=12 \sin 100 t$, where $I$ is in ampere and $t$ is time in second. The maximum value of emf induced in the second coil is

A proton and an $\alpha$-particle are both accelerated from rest in a uniform electric field. The ratio of work done by the electric field on the proton and the $\alpha$-particle in a given time is

Three identical vessels are filled up to the same height with three different liquids $A, B$ and $C$ of densities $\rho_{A} \rho_{B}$ and $\rho_{C}$, respectively. If $\rho_{A} > \rho_{B} > \rho_{C}$, then the pressure at the bottom of the ...

The ratio of the radii of a planet and the earth is $1: 2$, the ratio of their mean densities is $4: 1$. If the acceleration due to gravity on the surface of the earth is $9.8 \mathrm{~ms}^{-2}$, then the acceleration due to gravity on the ...

Steam of mass 60 g at a temperature $100^{\circ} \mathrm{C}$ is mixed with water of mass 360 g at a temperature $40^{\circ} \mathrm{C}$. The ratio of the masses of steam and water in equilibrium is (Latent heat of steam is $540 \mathrm{cal}...

When $Q_{1}$ amount of heat supplied to a monoatomic gas, the work done by the gas is $W$. When $Q_{2}$ amount of heat is supplied to a diatomic gas, the work done by the gas is $2 W$. Then, $Q_{1}: Q_{2}$.

The temperature at which the rms speed of oxygen molecules is $75 \%$ or rms speed of nitrogen molecules at a temperature of $287^{\circ} \mathrm{C}$

The temperature difference between the ends of two cylindrical rods $A$ and $B$ of the same material is $2: 3$. In steady state the ratio of the rates of flow of heat through the rods $A$ and $B$ is $5: 9$. If the radii of the rods $A$ and ...

A block is kept on a rough horizontal surface. The acceleration of the block increases from $6 \mathrm{~ms}^{-2}$ to $11 \mathrm{~ms}^{-2}$ when the horizontal force acting on it increases from 20 N to 30 N . The coefficient of kinetic fric...

A short bar magnet placed in a uniform magnetic field making an angle with the field experiences a torque.If the angle made by the magnet with field is changed from $30^{\circ}$ to $45^{\circ}$, the torque on the magnet

From a height of $h$ above the ground, a ball is projected up at an angle $30^{\circ}$ with the horizontal. If the ball strikes the ground with a speed of 1.25 times its initial speed of $40 \mathrm{~ms}^{-1}$, the value of $h$ is (accelera...

A body is thrown vertically upwards with a velocity of $35 \mathrm{~ms}^{-1}$ from the ground. The ratio of the speeds of the body at times 3 s and 4 s of its motion is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

Two long straight parallel wires $A$ and $B$ separated by 5 m carry currents 2 A and 6 A respectively in the same direction. The resultant magnetic field due to the two wires at a point of 2 m distance from the wire $A$ in between the two w...

An electron falling freely under the influence of gravity enters a uniform magnetic field directed towards south. The electron is initially deflected towards

The refractive index of the material of a small angled prism is 1.6. If the angle of minimum deviation is $4.2^{\circ}$, the angle of the prism is