TS EAMCET 2023 (Online) 12th May Evening Shift

If the equation whose roots are $P$ times the roots of the equation $x^4-2 a x^3+4 b x^2+8 a x+16=0$ is a reciprocal equation, then $|P|=$

If $\alpha$ and $\beta$ are the roots of the equation $x^2+2 x+2=0$, then $\alpha^{15}+\beta^{15}=$

Assertion (A) The variance of the first $n$ odd natural numbers is $\frac{n^2-1}{3}$.

Reason (R) The sum of the first $n$ odd natural numbers is $n^2$ and the sum of the squares of the first $n$ odd natural numbers is $\frac{n\left(4 n^2-...

A line $L$ has intercepts $a$ and $b$ on the coordinate axes. When the coordinate axes are rotated through an angle $\alpha$ and keeping the origin fixed, the same line $L$ has intercepts $p$ and $q$ on the new axes. Then,

If $\theta$ is the acute angle between the lines joining the origin to the points of intersection of the curve $x^2+x y+y^2+x+3 y+1=0$ and the straight line $x+y+2=0$, then $\cos \theta=$

Two lines $L_1$ and $L_2$ passing through the point $P(1,2)$ cut the line $x+y=4$ at a distance of $\frac{\sqrt{6}}{3}$ units from $P$. Then, the angles made by $L_1, L_2$ with positive $X$-axis are

The equation of the straight line passing through the point $(3,2)$ and inclined at an angle of $60^{\circ}$ with the line $\sqrt{3} x+y=1$ is

An equilateral triangle is constructed between the lines $\sqrt{3} x+y-6=0$ and $\sqrt{3} x+y+9=0$ with base on one line and vertex on the other. The area (in sq units) of the triangle, so formed is

A pair of straight lines drawn though the origin forms. an isosceles triangle right angled at the origin with the line $2 x+3 y=6$. The area (in sq units) of the triangle, so formed is

Consider the following statements:
Assertion (A) : The direction ratios of a line $L_1$ are 2,5, 7 and the direction ratios of another line $L_2$ are $\frac{4}{\sqrt{19}}$, $\frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}$. Then, the lines $L_1,...

If $A=(1,-1,2), B=(3,4,-2), C=(0,3,2)$ and $D=(3$, $5,6)$, then the angle between the lines $\mathbf{A B}$ and $\mathbf{C D}$ is

A line $L$ is parallel to both the planes $2 x+3 y+z=1$ and $x+3 y+2 z=2$. If line $L$ makes an angle $\alpha$ with the positive direction of $X$-axis, then $\cos \alpha=$

If $M$ is the foot of the perpendicular drawn from $P($ -1,2,-1 ) to the plane passing through the point $A(3,-2,1)$ and perpendicular to the vector $4 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$, then the length of $P M$ is

\(\text { If } \frac{2 \sin \theta}{1+\cos \theta+\sin \theta}=y, \text { then } \frac{1-\cos \theta+\sin \theta}{1+\sin \theta}=\)

If $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{4 \pi}{7}=\frac{\sin \frac{8 \pi}{7}}{8 \sin \frac{\pi}{7}}$, then $\sin \frac{\pi}{14} \sin \frac{3 \pi}{14} \sin \frac{5 \pi}{14} \sin \frac{7 \pi}{14} \sin \frac{9 \pi}{14} \sin \fra...

If $f(\theta)=\cos ^3 \theta+\cos ^3\left(\frac{2 \pi}{3}+\theta\right)+\cos ^3\left(\theta-\frac{2 \pi}{3}\right)$, then $f\left(\frac{\pi}{5}\right)=$

Let $\mathbf{a}$ and $\mathbf{b}$ be non-collinear vectors. If the vectors $(\lambda-1) \mathbf{a}+2 \mathbf{b}$ and $3 \mathbf{a}+\lambda \mathbf{b}$ are collinear, then the set of all possible values of $\lambda$ is

$\mathbf{b}$ and $\mathbf{c}$ are non-collinear vectors and $(\mathbf{c} \cdot \mathbf{c}) \mathbf{a}=\mathbf{c}$. If $(\mathbf{a} \cdot \mathbf{c}) \mathbf{b}-(\mathbf{a} \cdot \mathbf{b}) \mathbf{c}+(\mathbf{a} \cdot \mathbf{b}) \mathbf{b...

If two vectors $\mathbf{a}$ and $\mathbf{b}$ which are perpendicular to each other are such that $|\mathbf{a}|=8$ and $|\mathbf{b}|=3$, then $|\mathbf{a}-2 b|=$

Vectors $\mathbf{p}=a \hat{\mathbf{i}}+b \hat{\mathbf{j}}+c \hat{\mathbf{k}}, \mathbf{q}=d \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{r}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ forming a $\triangle ...

In an ideal step up transformer, if the input voltage and input power are $V_1$ and $R_1$ respectively and the output voltage and output power are $V_2$ and $P_2$ respectively, then

The ratio of the energies of the electron in the hydrogen atom in the first and second excited states is

Nuclear fission and fusion can be explained on the basis of

If $F_1$ and $F_2$ are the relative strengths of the gravitational and weak nuclear forces respectively, then $F_2 / F_1$ is nearly

In the following nuclear reaction $X$ is
\({ }_{13} \mathrm{Al}^{27}+{ }_2 \mathrm{He}^4 \longrightarrow{ }_0 n^1+X\)

If a capacitor of capacitance $100 \mu \mathrm{~F}$ is charged at a steady rate of $100 \mu \mathrm{C} \mathrm{s}^{-1}$, then the time taken to produce a potential difference of 100 V between the capacitor plates is

The need for modulation is

A potentiometer balances at 44 cm when a cell of internal resistance $1 \Omega$ is in the secondary circuit. To obtains the balancing point at 40 cm , the resistance to be connected parallel to cell is

Two wires made of the same material have lengths in the ratio $2: 3$ and radii in the ratio $8: 9$. If the same potential difference is applied across the ends of the wires, the ratio of the electric currents flowing through them is

The additional energy that should be given to an electron to reduce its de-Broglie wavelength from 1 nm to 0.5 nm is

Two wires $A$ and $B$ of same length, same radius and same Young's modulus are heated to same range of temperatures. If the coefficient of linear expansion of $A$ is $\frac{3}{2}$ times that of $B$, then the ratio of the thermal stresses pr...

A boy is playing with the empty rim of a cycle wheel of radius 40 cm by rolling it along a horizontal road towards north with angular speed of $20 \mathrm{rad} \mathrm{s}^{-1}$. Considering the effect of magnetic field of earth, the e.m.f i...

If the vertical component of earth's magnetic field is $0.5 \times 10^{-4} \mathrm{~T}$ at a point. When an aeroplane of wing span 4 m is moving horizontally at this place at $360 \mathrm{kmh}^{-1}$, then the motional emf forced across the ...

The correct statement among the following is

The electric field and electric potential at a point due to a point charge are $500 \mathrm{NC}^{-1}$ and 30 V respectively, then the magnitude of the charge is

Three identical vessels are filled with three liquids ${ }_{A, B}$ and $C$ with equal masses but having densities $\rho_{A, \rho_B}$ and $\rho_C$ respectively. If $\rho_A>\rho_B>\rho_C$ then the pressure at the bottom of the vessels will be

If the work done in blowing a soap bubble of radius $R$ is $W$, then the work done in blowing the soap bubble of radius $2 R$ is

The ratio of the radii of two planets is $r$ and the ratio of accelerations due to gravity on the planets is $x$. Then the ratio of the escape velocities from the planets is

Two rod of same area of cross-section have lengths $L$ and $2 L$ and coefficients of linear expansions $2 \alpha$ and $a$ respectively. If they are welded to form a composite rod of length $3 L$ then the coefficient of linear expansion of t...

For a given mass of a gas at constant temperature, the volume and the pressure are $V$ and $p$ respectively. Then the slope of the graph drawn between $\log _e V$ on $X$-axis and $\log _e p$ on $Y$-axis is

An ideal gas at $127^{\circ} \mathrm{C}$ is compressed suddenly to $8 / 27 \mathrm{}$of its initial volume. If $\gamma=5 / 3$ for an ideal gas, then rise in its temperature is

An insulating cylinder contains 4 moles of an ideal diatomic gas. When a heat $Q$ is supplied to it, 2 moles of the gas molecules dissociate. If the temperature of the gas remains constant, then the value of $Q$ is ( $R=$ universal gas cons...

A body of mass 6 kg is moving with a uniform velocity $4 \mathrm{~ms}^{-1}$. Its velocity changes to $6 \mathrm{~ms}^{-1}$ when a force of 12 N acts on it. Then its displacement is

A person initially at rest, starts walking towards east without slipping or skidding. What is the type of friction acting on the person from the ground and in which direction the frictional force acts?

The magnetic susceptibility of ferromagnetic materials is

A person walks in such a way that he covers equal distance in each step. The person takes 2 steps forwards towards east, then takes a right turn and
walks 4 steps towards south, then takes a right turn and walks 6 steps towards west and the...

The ratio of the displacements of a freely falling body during first, second and third seconds of its motion is

A circular coil of area $2 \mathrm{~cm}^2$ has 1000 turns. If the current through the coil is 1 A , then its magnetic moment is

The magnetic field at a perpendicular distance of one metre from a wire carrying current of 1 A is

The angles of incidence and emergence of a light ray passing through a prism of angle $A$ are $i$ and $e$ respectively. The total deviation produced by the prism is