Consider the following three statements : P : 5 is a prime number Q : 7 is a factor of 192 R : L.C.M. of 5 and 7 is 35 Then the truth value of which one of the following statements is true ?

Consider the statement : "P(n) : n2 – n + 41 is prime". Then which one of the following is true ?

The logical statement [ $$\sim$$ ( $$\sim$$ p $$\vee$$ q) $$\vee$$ (p $$\wedge$$ r)] $$\wedge$$ ($$\sim$$ q $$\wedge$$ r) is equivalent to :

If the Boolean expression (p $$\oplus$$ q) $$\wedge$$ (~ p $$\odot$$ q) is equivalent to p $$\wedge$$ q, where $$\oplus ,\odot \in \left\{\wedge ,\vee \right\}$$, then the ordered pair $$\left(\oplus ,\odot \right)$$ is :

Which of the following combinations has the dimension of electrical resistance ($$\in$$0 is the permittivity of vacuum and $$\mu$$0 is the permeability of vacuum)?

In the formula X = 5YZ2 , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?

The area of a square is 5.29 cm2. The area of 7 such squares taking into account the significant figures is :-

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 error in the measurement of density is :

If surface tension (S), Moment of inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for linear momentum would be :-

The force of interaction between two atoms is given by F = $$\alpha$$$$\beta$$exp \left( { - {{{x^2}} \over {\alpha kt}}} \right); where x is the distance, k is the Boltzmann constant and T is temperature and $$\alpha$$ and $$\beta$$ are two constants. The dimension of $$\beta$$ is :

In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to :-

In SI units, the dimensions of \sqrt {{{{ \in _0}} \over {{\mu _0}}}} is :

The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 $$\mu$$m diameter of a wire is :

If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young,s modulus will be:

The diameter and height of a cylinder are measured by a meter scale to be 12.6 $$\pm$$ 0.1 cm and 34.2 $$\pm$$ 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures ?

The density of a material in SI units 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 is -

The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are 5.5 mm and 48 respectively, the thickness of this sheet is :

Expression for time in terms of G(universal gravitional constant), h (Planck constant) and c (speed of light) is proportional to :

A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is :

Let $$\ell$$, r, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of {\ell \over {rCV}} in SI units will be :