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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 \(\begin{array}{l}\begin{array}{l} \text { Given } \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \log... View Article

∫_-π/2^π/2 [dx / (1 + cos x)] =

1) 0 2) 1 3) 2 4) 3 Solution: (3) 2 \(\begin{array}{l}I =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{d x}{1+\cos x}\\=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{d x}{2 \cos ^{2}... View Article

∫₀¹ [dx / (x + √1 – x²)] =

1) π/3 2) π/2 3) 1/2 4) π/4 Solution: (4) π/4 \(\begin{array}{l}\begin{array}{l} I=\int_{0}^{1} \frac{d x}{x+\sqrt{1-x^{2}}}\\ I=\int_{0}^{\frac{\pi}{2}} \frac{\cos \phi d \phi}{\sin... 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 \(\begin{array}{l}I=\int_{0}^{1} \ln [x] d... 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... 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,... 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... View Article

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

1)\(\begin{array}{l}\left [ E \right ]= \left [ B \right ]\left [ L\right ]\left [ T\right ]\end{array} \) 2)\(\begin{array}{l}\left [ E... 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: \(\begin{array}{l}\rho =\frac{m}{l\pi r^{2}}\end{array} \) \(\begin{array}{l}\frac{\Delta \rho }{\rho }=\frac{\Delta... 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... 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: \(\begin{array}{l}Time period(T)= 2\pi \sqrt{\frac{l}{g}}\end{array} \) \(\begin{array}{l}or \frac{\Delta... 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... 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... 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... 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 is 50, then... 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... 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: \(\begin{array}{l}\left | \hat{i} \times (\vec{a}\times \hat{i})\right |^{2} = \left | \vec{a} -(a.\hat{i})\hat{i}\right |^{2}\end{array} \) = \(\begin{array}{l}\left | \hat{j}+2\hat{k} \right... View Article

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