If the angular velocity of coil in an AC generator is doubled while keeping other parameters constant, the maximum induced emf

Monochromatic lights of wavelengths \( 620 \text{ nm} \) and \( 626 \text{ nm} \), respectively are used to study diffraction at a single slit of aperture \( 0.7 \text{ mm} \). The distance between the slit and the screen is \( 1.8 \text{ m} \). The separation between the positions of the first maxima of the diffraction pattern obtained in the two cases is :

Read the following statements and identify the correct statements.
(A) In a semiconductor doped with trivalent impurity, the holes are the majority carriers and electrons are minority carriers.
(B) In pure semiconductors, the number of free electrons is equal to the number of holes.
(C) In a semiconductor doped with pentavalent impurity, electrons become the majority carriers and holes the minority carriers.
(D) Important electronic devices can be developed using intrinsic semiconductors.
Choose the correct answer from the options given below:

A charged particle enters a uniform magnetic field at an angle of \(45 ^\circ\) with the field. The path along which the particle moves in the field will be

A cube is placed at the origin as shown in the figure. The electric field in the region is given as \( \vec{E} = (200 x^2 \hat{i}) \frac{\text{N}}{\text{C}} \). The flux coming out of the cube is:

The wavelength of the de-Broglie wave associated with an electron accelerated through 150 V is:

A potential difference of 6 V is applied across a conductor of length 12 cm. If the mobility of electrons is \( 5.6 \times 10^{-6} \text{ m}^2/\text{V}\cdot\text{s} \), their drift velocity will be:

The function \(f(x)=\sin x(1+\cos x) ; x \in\left[0, \frac{3 \pi}{2}\right]\) will have:

The interval in which the function \(f(x)=10-6 x-2 x^2\) is decreasing is :

Select the brain capacity of Homo erectus from the following:

Read the passage carefully and answer the questions based on the passage:
Species diversity on earth is not uniformly distributed. It is generally highest in the tropics and decreases towards the poles. Earth's fossil history reveals the incidences of mass extinctions in the past. Earth's rich biodiversity is vital for the very survival of mankind. It is believed that communities with high diversity tend to be less variable and more productive. The reasons of conserving biodiversity are narrowly utilitarian, broadly utilitarian and ethical. Biodiversity conservation may be in-situ as well as ex-situ.
How many episodes of mass extinction of species have occurred since the origin and diversification of life on earth?

Arrange the following in the increasing order of their energy gap between their conduction and valence bands:
(A) Si
(B) C (diamond)
(C) Ge
(D) Sn
choose the correct answer from the options given below:

The value of the determinant \(\left|\begin{array}{cc}a \cos \theta & a \sin \theta \\ -a \sin \theta & a \cos \theta\end{array}\right|\) is: