A physical quantity z depends on four observables a, b, c and d, as z = {{{a^2}{b^{{2 \over 3}}}} \over {\sqrt c {d^3}}}. The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is :

The quantities x = {1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}, y = {E \over B} and z = {l \over {CR}} are defined where C-capacitance, R-Resistance, l-length, E-Electric field, B-magnetic field and $${\epsilon }_0$$, $${\mu }_0$$, - free space permittivity and permeability respectively. Then :

A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5mm is noticed on the pitch scale. The nature of zero error involved and the least count of the screw gauge, are respectively :

A quantity f is given by f = \sqrt {{{h{c^5}} \over G}} where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm, 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as :

If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is

Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as

The dimension of {{{B^2}} \over {2{\mu _0}}}, where B is magnetic field and $${\mu }_0$$ is the magnetic permeability of vacuum, is :

The dimension of stopping potential V0 in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :

If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is :

The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and 4th VSD coincides with a main scale division. The length of the cylinder is : (VSD is vernier scale division)

If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be

For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i) A1 = 24.36, B1 = 0.0724, C1 = 256.2 (ii) A2 = 24.44, B2 = 16.082, C2 = 240.2 (iii) A3 = 25.2, B3 = 19.2812, C3 = 236.183 (iv) A4 = 25, B4 = 236.191, C4 = 19.5

If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye-piece, should be close to :

A double convex lens has power P and same radii of curvature R of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power 1.5 P is :

A point like object is placed at a distance of 1 m in front of a convex lens of focal length 0.5 m. A plane mirror is placed at a distance of 2 m behind the lens. The position and nature of the final image formed by the system is :

For a concave lens of focal length f, the relation between object and image distances u and v, respectively, from its pole can best be represented by (u = v is the reference line) :

A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object? (Figure drawn as schematic and not to scale)

A thin lens made of glass (refractive index = 1.5) of focal length f = 16 cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is f1 , then the ratio {{{f_1}} \over f} is closest to the integer :

The magnifying power of a telescope with tube 60 cm is 5. What is the focal length of its eye piece ?