Unit and measurements Questions
If y = sin x & x = 3t then dy/dt will be;
The graph for the equation y = 4 is;
If in a right-angled triangle, sin A = 3/5, then find tan A.
Value of tan(15°) = .....
Find dimensional formula of surface tension ‘S’. Use S = F/l, where F is force and l is the length.
The roots of equation 2x^2 + 5x - 12 = 0 are;
A physical quantity P is given by the relation P = P_0e^{-αt^2}. If t denotes the time, the dimensional formula of constant α is;
The value of ∫ (x−1)(x−2)dx is; (c = integration constant)
Given below are two statements: Statement-I: Screw gauge with a pitch of 0.5 mm is more accurate than 1 mm for same number of circular scale divisions. Statement-II: Higher pitch can make an instrument more accurate. In the light of the above stateme
A screw gauge of pitch 0.5 mm is used to measure the diameter of uniform wire of length 6.8 cm, the main scale reading is 1.5 mm and circular scale reading is 7. The calculated curved surface area of wire to appropriate significant figures is: [Screw
A student performs an experiment to measure the thickness of a slab with a vernier caliper whose 50 divisions of the vernier scale are equal to 49 divisions of the main scale. He noted that zero of the vernier scale is between 7.00 cm and 7.05 cm mar
In a vernier callipers, one main scale division is x cm and n division of the vernier scale coincide with (n − 1) division of the main scale. The least count (in cm) of the callipers is:
The period of oscillation of a simple pendulum in the experiment is recorded as 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s respectively. The average absolute error is:
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R: Assertion A: If the percentage error in the measurement of radius of the sphere is 0.3%, then the permissible percentage error in its surface area i
If the length of rod A is 3.25 ± 0.01 cm and that of B is 4.19 ± 0.01 cm then the rod B is longer than rod A by:
The period of oscillation of a simple pendulum is given by T = 2\pi\sqrt{\frac{l}{g}} where l is 100 cm and is known to have 1 mm accuracy. The time for 100 oscillations of the pendulum is found to be 200 s is measured by a stop watch of least count
In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, respectively. The relative error in the measurement of density is:
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage error in the measurement of X, where X = \frac{A^2B^{1/2}}{C^{1/3}D^3} will be:
If L = 2.331 cm, B = 2.1 cm, then L + B = ?
The number of significant figures is 5.69 × 10^-15 kg is:
If units of length, mass and pressure are chosen as fundamental units, the dimension of time would be:
The position x of a particle at time "t" is given by x = (v_0/a)(1 - e^{-at}) Where v_0 and a are:
Suppose refractive index \mu is given as \mu = A + B/\lambda^2 Where A and B are constants and \lambda is the wavelength, then dimensions of B are same as that of:
A force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density?
The force is given in terms of time t and displacement x by the equation F = A\cos Bx + C\sin Dt. The dimensional formula of AD/B is:
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R: Assertion A: Dimensional constants are the quantities whose magnitudes are constant. Reason R: Dimensional constants are always unitless. In the lig
Dimensions of T/\mu, where T is tension and \mu is mass per unit length, are:
The wavelength associated with a moving particle depends upon p^th power of its mass, q^th power of its velocity v and r^th power of Planck’s constant h. Then, the correct set of values of p, q and r is:
If momentum (P), area (A) and time (T) are taken to be fundamental quantities, then the dimensional formula for energy is:
The density of a material in SI unit is 128 kg m^-3. In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material nearly is:
Given below are two statements: Statement-I: In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement-II: The vernier constant is given by one main scale division multiplied by the number of vernier
\int(\cos(x/2)-\sin(x/2))^2dx = c = constant of integration
A force is given as F = (\alpha^2/\beta)\cos(v/\beta) where v is velocity and α and β are constants. The dimensional formula of α^4β^-2 is:
The value of gravitational constant G in SI units is . What is the value of G in CGS system of units?
Find the sum of geometric progression: 1 + 1/2 + 1/4 + 1/8 + ........ upto .
For 10(at+3), if t is time, then the dimension of a is
Number of significant figures in expression 4.327 g / 2.51 cm³
The dimensions of 1/2 ε₀E² (ε₀ is permittivity of free space, E is electric field) are
Match the following and choose appropriate option
The dimensional formula of a physical quantity whose unit is pascal per second, is
A quantity z is given as . If percentage error in a, b, c and d are 2%, 3%, 2% and 1% respectively, then maximum percentage error in z will be
The smallest division on the main scale of a Vernier calipers is 0.1 cm. Ten divisions of the Vernier scale correspond to nine divisions of the main scale. The figure below on the left shows the reading of this calipers with no gap between its two ja
If force = , then the dimensional formulae of α and β are respectively
In a new system of units, unit of mass is 5 kg, unit of length is 2 m and unit of time is 10 sec. Valueof 5 N in new system of unit is;
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R: Assertion A: Dimensional constants are the quantities whose magnitudes are constant. Reason R: Dimensional constants are always unitless. In the lig
The wavelength associated with a moving particle depends upon pth power of its mass, qth power of its velocity v and rth power of Planck’s constant h. Then, the correct set of values of p, q and r is:
If momentum (P), area (A) and time (T) are taken to be fundamental quantities, then the dimensional formula for energy is:
In a vernier calliper, when both jaws touch each other, zero of the vernier scale shift towards left and its 4th division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero
The density of a material in SI unit is 128 kg m-3 . In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material nearly is:
A packet contains silver powder having mass (20.23 ± 0.01) g. Some additional powder of mass (5.75 ± 0.01) g is added to the packet, the total mass of the powder now is;