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In an experiment, the percentage errors that occurred in the measurement of physical quantities $A$, $B$, $C$, and $D$ are $1\%$, $2\%$, $3\%$, and $4\%$ respectively. Then, the maximum percentage of error in the measurement of $X$, where $X = \frac{A^2 B^{1/2}}{C^{1/3} D^3}$, will be:
Which of the following quantities has the same dimensions as that of energy?
Enzymes that utilize ATP in phosphate transfer require an alkaline earth metal (M) as the cofactor. M is:
The value of electron gain enthalpy of $Na^+$, if $IE_1$ of Na = 5.1 eV, is:
The unit of self inductance of a coil is
Volt/metre is the unit of
The velocity of a particle depends upon time as $v = a + bt + ct^2$; if the velocity is in m/sec, the unit of $a$ will be:
Which of the following is a basic amino acid?
A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$. After some time, the velocity of the ball attains a constant value known as terminal velocity $v_T$. The terminal velocity depends on the mass of the ball $m$, $\eta$, $r$, and acceleration due to gravity $g$. Which of the following relations is dimensionally correct?
Time intervals measured by a clock give the following readings: $1.25 \text{ s}, 1.24 \text{ s}, 1.27 \text{ s}, 1.21 \text{ s}, 1.28 \text{ s}$. What is the percentage relative error of the observations?
Dimensions of stress are:
The number of particles crossing a unit area perpendicular to the $x$-axis in unit time is given by $n = -D\frac{n_2 - n_1}{x_2 - x_1}$, where $n_1$ and $n_2$ are the number of particles per unit volume for the value of $x$ equal to $x_1$ and $x_2$ respectively. The dimensions of $D$, known as the diffusion constant, will be:
In which of the following systems of units is the Weber the unit of magnetic flux?
The unit of specific resistance is:
Two similar thin equi-convex lenses, of focal length $f$ each, are kept coaxially in contact with each other such that the focal length of the combination is $F_1$. When the space between the two lenses is filled with glycerine (which has the same refractive index ($\mu = 1.5$) as that of glass) then the equivalent focal length is $F_2$. The ratio $F_1 : F_2$ will be :
Inductance $L$ can be dimensionally represented as:
Dimensions of coefficient of viscosity are
The dimensions of Planck's constant and angular momentum are respectively:
Hertz is the unit of
The compound among the following that is used in cosmetic surgery is: