A proton is moving in a circular path of radius R in a uniform magnetic field B. It carries a kinetic energy of 2 MeV. What should be the energy of an \(\alpha\)-particle to move in a circle of same radius in the same field ?

If electron, deutron, \(\alpha\)-particle and proton have same kinetic energy, which one has the largest deBroglie wavelength.

The de-Broglie wavelength associated with a ball of mass \( m = 150 \, g \) traveling at \( v = 30.0 \, m/s \) would be

Two coherent monochromatic light beams of intensities I and 16 I, respectively, superimpose over each other. The resultant intensity in the constructive interference is

The resistance of a potentiometer wire of length 4 m is \( 10 \ \Omega \).
A resistance box and a 2 V accumulator are connected in series with it.
What resistance should be introduced in the box to have a potential drop of \( 1 \ \mu\text{V/mm} \) along the potentiometer wire?

By using Einstein photoelectric equation, if we consider kinetic energy of photo electrons on y-axis and frequency of incident radiation on x-axis. The slope of the graph will represent (the symbols have their usual meanings)

An LCR series circuit with L = 100 mH, C = 100 \( \mu \)F, R = 10 \( \Omega \) is connected to an AC source of emf 220 V. The resonant frequency of the circuit will be nearly

The area (in sq.units) of region bounded by \(y^2=9 x, x=2, x=4\) and the \(x\)-axis in the first quadrant is

Read the following passage carefully and answer the given questions.
Theory of Evolution
The evolution of life is a gradual process through which simple organisms are transformed into complex life forms over billions of years. It involves genetic changes, adaptation to the environment, and the emergence of diversity in species. Fossil records provide evidence of extinct life forms and transitional stages. Evolution is influenced by factors such as mutation, genetic recombination, and environmental pressure, shaping the biodiversity we see today. Charles Darwin and Alfred Russel Wallace were pioneering naturalists who developed the theory of evolution by natural selection.
The study of fossils in different sedimentary layers indicates ______.

With reference to transition metals which of the following statements are correct?
A. Electronic configuration is represented by ( \(n -2\) ) d1-10 ns1-2
B. They exhibit catalytic property
C. Some of them form interstitial compounds
D. In \(Ni ( CO ) 4\) and \(Fe ( CO ) 5\), the oxidation state of Ni and Fe are +4 and + 5 respectively.
Choose the correct answer from the options given below:

In class XII, suppose \(5 \% \) of boys and \(0.25\%\) of girls are physically fit for a game.
A fit student is selected at random from this class having same number of boys and girls.
If the probability that the selected student is a girl is \(\frac{m}{n}\), \(\operatorname{gcd}(m, n)=1\), then \(m+n\) is equal to

The stationary point of \(f(x)=\sin ^4 x+\cos ^4 x, x \in\left(0, \frac{\pi}{2}\right)\) is given by:

The IUPAC name of the following compound is: