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Graduate Aptitude Test in Engineering

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1

Numerical

The activity of a freshly prepared radioactive sample is 10^{10} disintegrations per second, whose mean life is 10^{9} s. The mass of an atom of this radioisotope is 10^{$$-$$25} kg. The mass (in mg) of the radioactive sample is _________.

Your Input ________

Correct Answer is **1**

Activity $$A = \lambda N$$, where $$\lambda$$ is decay constant and N is number of particles present. Therefore,

$$N = {A \over \lambda } = A\tau $$

where $$\tau$$ = 1 / $$\lambda$$ is the mean life of the sample. The mass of the sample is

$$M = mN = mA\tau $$

where m is mass of an atom. Therefore, the mass of the radioactive sample is

M = 10^{$$-$$25} $$\times$$ 10^{10} $$\times$$ 10^{9} = 10^{$$-$$6} kg = 1 mg

2

Numerical

An $$\alpha$$-particle and a proton are accelerated from the rest by a potential difference of 100 V. After this, their de Broglie wavelengths are $$\lambda$$_{$$\alpha$$} and $$\lambda$$_{p}, respectively. The ratio $${{{\lambda _p}} \over {{\lambda _\alpha }}}$$, to the nearest integer, is _____________.

Your Input ________

Correct Answer is **3**

The de Broglie wavelength of a particle with momentum p is given by

$$\lambda$$ = h/p.

The momentum and kinetic energy of a particle of mass m are related by

$$p = \sqrt {2mK} $$.

The kinetic energy of a charge q, accelerated through potential V, is given by K = qV. Thus,

$$\lambda = h/\sqrt {2mK} = h/\sqrt {2mqV} $$,

which gives

$${{{\lambda _p}} \over {{\lambda _\alpha }}} = \sqrt {{{2{m_\alpha }{q_\alpha }V} \over {2{m_p}{q_p}V}}} = \sqrt {{{2\,.\,4u\,.\,2e\,.\,100} \over {2\,.\,1u\,.\,1e\,.\,100}}} $$

$$ = \sqrt 8 = 2.8 \approx 3$$

On those following papers in Numerical

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2022 Paper 1 Online (1)

JEE Advanced 2021 Paper 2 Online (1)

JEE Advanced 2019 Paper 2 Offline (1)

JEE Advanced 2018 Paper 2 Offline (1)

JEE Advanced 2013 Paper 1 Offline (1)

IIT-JEE 2011 Paper 2 Offline (1)

IIT-JEE 2011 Paper 1 Offline (1)

IIT-JEE 2010 Paper 1 Offline (1)

Units & Measurements

Motion

Laws of Motion

Work Power & Energy

Simple Harmonic Motion

Impulse & Momentum

Rotational Motion

Gravitation

Properties of Matter

Heat and Thermodynamics

Waves

Wave Optics

Geometrical Optics

Electrostatics

Current Electricity

Magnetism

Electromagnetic Induction

Alternating Current

Dual Nature of Radiation

Atoms and Nuclei