TS EAMCET 2020 (Online) 11th September Evening Shift

If $S_1$ and $S_2$ are the variances of the first $2 k$ and $k(k>1)$ natural numbers respectively, then ( $S_1 / S_2$ ) lies in the interval

The standard deviations of two sets of observations $X=\left\{x_i\right\}$ and $Y=\left\{y_i\right\}(i=1,2, \ldots, 100)$ are respectively 5 and 6 . If $\bar{x}, \bar{y}$ are their means and $\sum_{i=1}^{100}\left(x_i-\bar{x}\right)\left(y_...

When the coordinate axes are rotated through an angle $\theta$ in anti clockwise direction, if the transformed equation of $x^2+y^2+2 x y+2 x+6 y+1=0$ is $(2+\sqrt{3}) X^2+2 X Y+(2-\sqrt{3}) Y^2+a X+b Y+2=0$, then $3 a-b=$

If $\left|\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right|=0$, then the lines $a_i x+b_i y+c_i=0$
( $i=1,2,3$ ) represent

If the sides of a triangle $A B C$ are $2 x^2-y^2=0$, $x+y-1=0$ and the sides of another triangle $P Q R$ are $2 x^2-5 x y+2 y^2=0,7 x-2 y-12=0$, then the distance between the centroid of $\triangle A B C$ and the orthocentre of $\triangle ...

If the lines $3 x+y-4=0, x-a y-10=0, b x+2 y+9=0$ form three successive sides of a rectangle in that order and the fourth side passes through $(1,2)$, then the area of that rectangle (in sq. units) is

For integer $k$, if the area of the triangle formed by the pair of lines $S=3 x^2-2 k x y+y^2=0$ with the line $L=2 x-y-6=0$ is 36 sq. units, then for the angle $\theta$ between the lines $S=0, \sin \theta=$

The points $A(2,1), B(3,-2)$ and $C(a, b)$ are vertices of the rectangle $A B C D$. If the point $P(3,4)$ lies on $C D$ produced, then $5 a+10 b=$

If $A(4,7,8), B(2,3,4)$ and $C(2,5,7)$ are the vertices of $\triangle A B C$, then the length of the internal bisector of the angle $A$ is

For scalars $\lambda, \mu$ if the vector equation of a plane is $\mathbf{r}=(2+3 \lambda-\mu) \hat{\mathbf{i}}+(1-2 \lambda+3 \mu) \hat{\mathbf{j}}+(-2+2 \lambda+\mu) \hat{\mathbf{k}}$, then its Cartesian equation is

If $A(4,3,2), B(5,4,6), C(-1,-1,5)$ are the vertices of a triangle, then the coordinates of the point in which the bisector of the angle $A$ meet the side $B C$ is

Assertion (A) The direction ratios of line $L_1$ are 2, 5, 7 and those of line $L_2$ are $\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}$. The lines $L_1, L_2$ are parallel.
$\boldsymbol{\operatorname { R e a s o n }}(R)$ T...

If $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-7}{2}$ lies in the plane $a x+b y+z=7$, then $a+b=$

The position vectors of the points $A$ and $B$ are respectively $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}$ and $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$. If the points $P$ and $Q$ are respectively the orthogonal projections of $A$ a...

\(\text { Match the items of List-I with those of List-II }\)


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The period of $\cos (3 x+5)+7$ is

If $\cos \left(\frac{\alpha-\beta}{2}\right)=2 \cos \left(\frac{\alpha+\beta}{2}\right)$, then $\tan \frac{\alpha}{2} \tan \frac{\beta}{2}=$

$\mathbf{x}, \mathbf{y}, \mathbf{z}$ are three vectors each of magnitude $\sqrt{2}$ and each making an angle $60^{\circ}$ with one another. If $\mathbf{a}=\mathbf{x} \times(\mathbf{y} \times \mathbf{z}), \mathbf{b}=\mathbf{y} \times(\mathbf...

Let $\mathbf{a}=2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=-\hat{\mathbf{j}}+\hat{\mathbf{k}}$. If $\mathbf{c}$ is a vector such that $\mathbf{a} \cdot \mathbf{c}=|\mathbf{c}|,|\mathbf{c}-\mathbf{a}|=2 \sqrt{2}$ and ...

The equation of the plane in normal form passing through the point $A(\bar{a})$, parallel to a vector $\bar{b}$ and containing a vector $\bar{c}$ is

For an $R$ - $L-C$ circuit, driven with voltage of amplitude $V_m$ and frequency $\omega_0=\frac{1}{\sqrt{L C}}$, the current exhibits resonance. The quality factor $Q$ is

The binding energy (BE) per nucleon for an element is 7.14 MeV . If the BE of element is 28.6 MeV , then the number of nucleons in the element is

Find potential difference points $A & F$ and $F & B$.

A circular freeway entrance and exit are commonly banked to control a moving car at $14 \mathrm{~m} / \mathrm{s}$. To design similar ramp for $28 \mathrm{~m} / \mathrm{s}$ one should

A cyclist leans with the horizontal at angle $30^{\circ}$, while negotiating round a circular road of radius $20 \sqrt{3} \mathrm{~m}$. The speed of the cycle should be

The electromagnetic waves of frequency 6 GHz are used in

Four $4 \Omega$ resistors are connected together along the edges of a square. A 12 V battery with internal resistance of $2 \Omega$ is connected across a pair of the diagonally opposite corners of the square. The power dissipated in the cir...

In a photoelectric effect experiment if the frequency of light is doubled, the stopping potential will

A monochromatic light of wavelength $\lambda$ ejects photoelectrons from a metal surface with work function ( $\phi) 2.4 \mathrm{eV}$. These photoelectrons are made to collide with hydrogen atoms in ground state. The maximum value of $\lamb...

Young's modulus is proportionality constant that relates the force per unit area applied perpendicularly at the surface of an object to

The typical wavelength of X-ray is

The electric flux from a cube of edge $l$ is $\phi$ in an enclosed charge. If the edge of the cube is made $\frac{2}{3} l$ and the charge enclosed in the cube is doubled, then the electric flux value will be

If the dielectric constant of a substance $K=\frac{4}{3}$, then the electric susceptibility $\chi$ in terms of vacuum permittivity $\varepsilon_0$ is

The change in surface energy when a big spherical drop fo radius $R$ is split into $n$ spherical droplets of radius $r$ is ( $T=$ surface tension)

The long range force experienced by a neutral particle with a finite mass

If the radius of the earth shrinks by $1 \%$, its mass remaining the same, then the acceleration due to gravity on the earth surface would

Different material of two identical long bars $A$ and $B$ are coated with wax and have their one end immersed in a hot oil bath. When the steady state is reached, the lengths for which wax melt are $l_A$ and $l_B$. If $k_A$ and $k_B$ are th...

A gas is at constant pressure $4 \times 10^5 \mathrm{~N} / \mathrm{m}^2$. When a heat energy of 2000 J is supplied to the gas, its volume changes by $3 \times 10^{-3} \mathrm{~m}^3$. What is the increase in its internal energy?

Certain amount of heat supplied to an ideal gas under isothermal condition will result in

A sheet of steel at $20^{\circ} \mathrm{C}$ has size as shown in figure below. If the co-efficient of linear expansion for steel is $10^{-5}{ }^{\circ} \mathrm{C}^{-1}$, then what is the change in the area at $60^{\circ} \mathrm{C}$ ?

A solenoid has a core of a material with relative permeability $\frac{800}{\pi}$. The windings of the solenoid are insulated from the core and carry current of 2 A . If the number of turns is 1000 per metre, find the magnetic field $B$.

A particle of mass $m=1 \mathrm{~kg}$ moves in the $x y$-plane. The force on it at time $t$ is $F(t)=[2 \sin (\alpha t) \hat{\mathbf{i}}+3 \cos (\alpha t) \hat{\mathbf{j}}] \mathrm{N}$, where $\alpha=1 \mathrm{~s}^{-1}$. At time $t=0$, the ...

A particle aimed at a target, projected with an angle $15^{\circ}$ with the horizontal is short of the target by 10 m . If projected with an angle of $45^{\circ}$ is away from the target by 10 m , then the angle of projection to hit the tar...

Consider that a truck is moving initially with $54 \mathrm{~km} / \mathrm{h}$. It has stopped by the driver after looking at an obstacle with a deceleration of $10 \mathrm{~m} / \mathrm{s}^2$. The distance travelled by truck before coming t...

A ball is thrown vertically upwards with an initial velcoity $u$ reaches maximum height in 5 s . The ratio of distance travelled by the ball in the 2nd and 7th second is (assume, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A straight wire of mass 0.2 kg and length 1.5 m carries a current 2A is shown in the figure. It is suspended in mid-air by a uniform magnetic field $B$ pointing to the plane of paper. The magnitude of magnetic field is (ignore, earth's magn...

The ratio of the magnetic field inside a solenoid at an axial point well inside and at an axial end point is

An infinite long wire lying along the $Y$-axis, is carrying a current $I$ as shown in the figure. The magnetic flux through a circular loop of radius $R$ in the $x y$-plane is [assume, $\mu_0=$ magnetic in free space permeability]

A prism is made of a glass having refractive index $\sqrt{2}$. If the angle of minimum deviation is equal to angle of the prism, then the angle of prism is

A thin glass prism of angle $9^{\circ}$ with refractive index 1.4 is combined with another glass prism of refractive index 1.6 as shown in the figure. The combination of the prism provides dispersion without deviation. Determine the angle $...