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The value of ∫_-π/2^π/2 log [(2 – sin θ) / (2 + sin θ)] dθ is

1) 0 2) 1 3) 2 4) None of these Solution: (1) 0... View Article

∫_-π/2^π/2 [dx / (1 + cos x)] =

1) 0 2) 1 3) 2 4) 3 Solution: (3) 2... View Article

∫₀¹ [dx / (x + √1 – x²)] =

1) π/3 2) π/2 3) 1/2 4) π/4 Solution: (4) π/4... View Article

The value of ∫₀¹ log [x] dx is

1) 0 2) 1 3) log 1 4) None of these Solution: (4) None of these... View Article

In an experiment, the initial number of radioactive nuclei is 3000.

In an experiment, the initial number of radioactive nuclei is 3000. It is found that 1000 ± 40 nuclei decayed in the first 1.0 s.... View Article

The physical quantity which is not a unit of energy is

1) volt-coulomb 2) MeV-s 3) henry (ampere)2 4) farad- (volt)2 Answer: 2) MeV-s Solution: MeV-s is not a unit of energy, while others are... View Article

Which one of the following is not a fundamental SI unit?

1) ampere 2) candela 3) newton 4) kelvin Answer: 3) newton Solution: F = ma = kg ms-2 SI unit for force is Newton Newton is a derived unit... View Article

The relation between [latex]left [ E right ][/latex] and [latex]left [ B right ][/latex] is

1) 2) 3) 4) Answer: 3) Solution:... View Article

A wire of length l = 6 ±0.06 cm and radius r = 0.5 ± 0.005 cm and mass m = 0.3 ± 0.03 gm. Maximum percentage error in density is

1) 4 2) 2 3) 1 4) 6.8 Answer: 1) 4 Solution:... View Article

The length of a simple pendulum is about 100 cm known to an accuracy of 1 mm.

The length of a simple pendulum is about 100 cm known to an accuracy of 1 mm. Its period of oscillation is 2s determined by measuring the time... View Article

The percentage errors in the measurement of length and time period of a simple pendulum are 1% and 2% respectively. Then, the maximum error in the measurement of the acceleration due to gravity is

1) 8% 2) 3% 3) 4% 4) 6% 5) 5% Answer: 5% Solution: Maximum percentage error in g = 1 x 100 + 2 x 2 x 100 = 5 x 100 = 5%... View Article

A vernier callipers has 1 mm marks on the main scale.

A vernier callipers has 1 mm marks on the main scale. It has 20 equal divisions on the vernier scale which match with 16 main scale divisions.... View Article

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it.

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage... View Article

A cube has a side of length 1.2 x 10^-2 m. Calculate its volume

1) 1.7 x 10-6 m3 2) 1.73 x 10-6 m3 3) 1.70 x 10-6 m3 4) 1.728 x 10-6 m3 Solution Length of the cube, L = 1.2 x 10-2 m Volume... View Article

If the variance of the following frequency distribution

If the variance of the following frequency distribution : Class 10-20 20-30 30-40 Frequency 2 x 2... View Article

Let PQ be a diameter of the circle x²+y²= 9.

Let PQ be a diameter of the circle x2+y2 = 9. If α and β are the lengths of the perpendiculars from P and Q on the straight line, x+y... View Article

If [latex]\vec{a}= 2\hat{i}+\hat{j}+2\hat{k}[/latex] , then the value of [latex]\left | \hat{i} \times (\vec{a}\times \hat{i})\right |^{2}+\left | \hat{j} \times (\vec{a}\times \hat{j})\right |^{2}+\left | \hat{k} \times (\vec{a}\times \hat{k})\right |^{2}[/latex] is equal to

Solution: = = 1+4 = 5 Similarly = 4+4 = 8 = 4+1 = 5 ⇒ 5+8+5 = 18 Answer: 18... View Article

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