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Which of the following is not a statement in logic?

I. Earth is a planet. II. Plants are living objects. III. √-3 is a rational number. IV. x2 - 5x + 6 < 0, where x ϵ - R 1) I 2) III... View Article

The contrapositive of ‘If two triangles are identical, then these are similar’ is

1) If two triangles are not similar, then these are not identical 2) If two triangles are not, then these are not similar 3) If two... View Article

The statement ~ (p → q) is equivalent to

1) p ⋀ (~ q) 2) ~ p ⋀ q 3) p ⋀ q 4) ~ p ⋀ ~ q 5) p ⋁ q Solution: (1) p ⋀ (~ q) The logical equivalency ~ (p → q) ≡ p ⋀ (~ q)... View Article

If (p ⋀ ~ r) → (~ p ⋁ q) is false, then the truth values of p, q, and r are respectively

1) T, F and F 2) F, F and T 3) F, T and T 4) T, F and T Solution: p q r ~ p ~ r p ⋀ ~ r... View Article

The negation of the statement ‘He is rich and happy’ is given by

1) he is not rich and not happy 2) he is not rich or not happy 3) he is rich and happy 4) he is not rich and happy Solution: (2) he... View Article

For the circuit shown below, the boolean polynomial is

1) (~ p ⋁ q) ⋁ (p ⋁ ~ q) 2) (~ p ⋀ q) ⋀ (p ⋀ q) 3) (~ p ⋀ ~ q) ⋀ (q ⋀ p) 4) (~ p ⋀ q) ⋁ (p ⋀ ~ q) Solution: (4) (~ p ⋀ q) ⋁ (p... View Article

If p: 4 is an even prime number, q: 6 is a divisor of 12 and r: the HCF of 4 and 6 is 2, then which one of the following is correct?

1) (p ⋀ q) 2) (p ⋁ q) ⋀ ~ r 3) ~ (q ⋀ r) ⋁ p 4) ~ p ⋁ (q ⋀ r) 5) p ↔ (q ⋀ r) Solution: (4) ~ p ⋁ (q ⋀ r) p: 4 is an even prime... View Article

The dimensions of Planck’s constant are

1) [M2 L2 T -2 ] 2) [M L T -2 ] 3) [M L2 T -2 ] 4) [M L2 T -1 ] Answer: 4) [M L2 T -1 ] Energy of photon is given as... View Article

If force is proportional to square of velocity, then the dimensions of proportionality constant are

1) [ML -1 T ] 2) [ML -1 T0 ] 3) [ MLT0] 4) [ M0 LT -1 ] Answer: 2) [ML -1 T0 ] Solution: force is proportional to... View Article

The dimensions of kinetic energy are

1) [M2 L2 T] 2) [ML2 T] 3) [ML2 T-2 ] 4) [ML2 T -1 ] Answer: 3) [ML2 T-2 ] Solution: The formula for the kinetic energy is... View Article

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and current I, would be

1) [ML2 T -3I -1 ] 2) [ML2 T -2] 3) [ML2 T -1I -1 ] 4) [ML2 T -3I -2] Answer: 4) [ML2 T -3I -2] Solution: R = V/i = W/qi... View Article

Dimensional formula for force is

Dimensional formula for force is 1) [ML2 T -2 ] 2) [MLT -2 ] 3) [ML -1 T -2 ] 4) [ML2 T -3 ] Answer: 2) [MLT -2 ] Solution:... View Article

The energy (E), angular momentum (L) and universal gravitational constant (G) are chosen as fundamental quantities.

The energy (E), angular momentum (L) and universal gravitational constant (G) are chosen as fundamental quantities. The dimensions of universal... View Article

The dimensions of gravitational constant G and the moment of inertia are, respectively

1) [ML3 T-2 ], [ML2 T0 ] 2) [M-1L3 T-2 ], [ML2 T0 ] 3) [M-1L3 T-2 ], [M-1 L2 T ] 4) [ML3 T-2 ], [M-1L2 T ] Answer: 2)... View Article

If F denotes force and t time, then in equation F = at^-1 + bt² , the dimensions of a and b, respectively are

1) [LT-4 ] and [LT-1 ] 2) [LT-1 ] and [LT-4 ] 3) [MLT-4 ] and [MLT-1 ] 4) [MLT-1 ] and [MLT-4 ] 5) [MLT-3 ] and [MLT-2 ] Answer: 4)... View Article

If C be the capacitance and V be the electric potential, then the dimensional formula of CV² is

1) [ML-3 TA] 2) [M0 LT-2A0] 3) [ML1 T-2 A-1 ] 4) [ML2 T-2 A0 ] Answer: 4) [ML2 T-2 A0 ] Solution: Energy, E=CV2... View Article

The dimensional formula of physical quantity is [M^a L^b T^c ]. Then, that physical quantity is

1) spring constant, if a =1, b = 1, and c = –2 2) surface tension, if a =1, b =1, and c = –2 3) force, if a =1, b =1,c = 2 4) angular... View Article

If the force is given by F = at + bt² with t as time. The dimensions of a and b are

1) [MLT-4], [MLT-4] 2) [MLT-3], [MLT-4] 3) [ML2 T-3], [ML2T-2] 4) [ML2 T-3], [ML3 T-4] Answer: 2) [MLT-3], [MLT-4] Solution: Each term in... View Article

To find the distance d over which a signal can be seen clearly in foggy conditions

To find the distance d over which a signal can be seen clearly in foggy conditions, a railway engineer uses dimensional analysis and assumes that... View Article

Density of liquid in CGS system is 0.625 g–cm-3 . What is its magnitude in SI system?

1) 0.625 2) 0.0625 3) 0.00625 4) 625 Answer: 4) 625 In CGS units d = 0.625 gcm−3 In SI units d = 0.625×10−3kg10−6m3... View Article

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