The flow rate of water from a tap of diameter \(1.25 \mathrm{~cm}\) is 3 litres per min. If coefficient of viscosity of water is \(10^{-3} \mathrm{~Pa}-\mathrm{s}\). the nature of flow is

The plates of a parallel plate capacitor are charged upto \(100 \mathrm{~V}\). A \(2 \mathrm{~mm}\) thick insulator sheet is inserted between the plates. Then to maintain the same potential difference, the distance between the plates is increased by \(1.6 \mathrm{~mm}\). The dielectric constant of the insulator is

A thin magnetic iron rod of length \(30 \mathrm{~cm}\) is suspended in a uniform magnetic field. Its time period of oscillation is \(4 \mathrm{~s}\). It is broken into three equal parts. The time period in seconds of oscillation of one part when suspended in the same magnetic field is

A particle is placed at rest inside a hollow hemisphere of radius \(R\). The coefficient of friction between the particle and the hemisphere is \(\mu=\frac{1}{\sqrt{3}}\). The maximum height upto which the particle can remain stationary is

The acceleration at the end of $2 \mathrm{s}$, of a particle whose motion is represented by the equation $S=4{\mathrm{t}}^3-8{\mathrm{t}}^2+5\mathrm{t}+4$ is ______

Velocity and acceleration vectors of charged particle moving perpendicular to the direction of a magnetic field at a given instant of time are \(\overrightarrow{\mathbf{v}}=2 \hat{\mathbf{i}}+c \hat{\mathbf{j}}\) and \(\overrightarrow{\mathbf{a}}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}\) respectively. Then the value of \(c\) is

Two open organ pipes of lengths \(50 \mathrm{~cm}\) and \(51 \mathrm{~cm}\) are totally immersed in a medium. They are found to give 40 beats in \(10 \mathrm{~s}\) when each is sounding at its fundamental note. The speed of sound in this medium is

From the following, identify the reactions which are responsible for depletion of ozone layer.
\(\begin{aligned}
& \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{NO}_2(g) \rightarrow \mathrm{ClONO}_2(g) \\
& \mathrm{CF}_2 \mathrm{Cl}_2(g) \xrightarrow{\text { uv }} \mathrm{Cl}(g)+\dot{\mathrm{CF}}_2 \mathrm{Cl}(g) \\
& \dot{\mathrm{Cl}}(g)+\mathrm{CH}_4(g) \rightarrow \mathrm{HCl}(g)+\dot{\mathrm{C}} \mathrm{H}_3(g) \\
& \dot{\mathrm{C}} \mathrm{l}(\mathrm{g})+\mathrm{O}_3(g) \rightarrow \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{O}_2(g) \\
& \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{O}(g) \rightarrow \dot{\mathrm{C}} \mathrm{l}(g)+\mathrm{O}_2(g)
\end{aligned}\)

Which of the following is divisible by $x^2-y^2, \forall x\ne y?$

If $\int \frac{1-(\cot x{)}^{2021}}{\tan x+(\cot x{)}^{2022}}dx=\frac{1}{A}\log \left|(\sin x{)}^{2023}+(\cos x{)}^{2023}\right|+c$, then $A=$______

If the circles \(x^2+y^2+k x+4 y+2=0\) and \(2\left(x^2+y^2\right)-4 x-3 y+k=0\) cut orthogonally, then \(k=\)

The half-life period of a radioactive element A is 62 years. It decays into another stable element B. An archeologist found a sample in which A and B are in 1:15 ratio. The age of the sample is

Which of the following types of isomerism is exhibited by
\[
\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{NO}_2\right)\right]\left(\mathrm{NO}_3\right)_2
\]
i. Optical ii. Linkage iii. Ionization
iv. Coordination