A proton accelerated through a potential difference of V volts has a de-Broglie wavelength \( \lambda \) associated with it. In order to get the same wavelength with an \( \alpha \)-particle, the required accelerating potential is

A small telescope has an objective lens of focal length 100 cm and an eye-piece of focal length 5 cm. The magnifying power of the telescope when the final image is formed at the least distance of distinct vision will be

A 0.5 m long solenoid has 500 turns and has a flux density of \( 2.52 \times 10^{-3} \text{ T} \) at its centre.
The current flowing in the solenoid would be (given, \( \mu_0 = 4\pi \times 10^{-7} \text{ Hm}^{-1} \))

Carbon, silicon and germanium have four valence electrons each. Their valence and conduction bands are separated by energy gap \( E_g \). If we represent \( (E_g)_C, (E_g)_{Si} \) and \( (E_g)_{Ge} \) as their respective energy gaps, then which of the following is true

Find the true statement:

The wavelength of light coming from a sodium source is 589 nm. Its wavelength in crown glass having refractive index 1.52 is

An electron is moving at a velocity of 100 m/s along the X-axis in the presence of an electric field of 30 V/m directed along the Y-axis and a magnetic field of 300 G directed along the Z axis. The magnitude and direction of force acting on the electron is (Given: the charge on the electron is "e")

Which of the following device is used to culture large volumes of living cells to get products on large scale?

Read the passage carefully and answer the questions based on the passage:
Alcohols are versatile compounds as they can act as both nucleophile and electrophile. They undergo reactions based on cleavage of O-H and C-O bonds. The cleavage of O-H bond reflects the acidic character of alcohols. However they are weaker acids than water, phenol and carboxylic acids. Alkoxide ion formed by loss of proton from the OH group of alcohols reacts with water to form the corresponding conjugate acid - base pair. They act as Bronsted base due to presence of unshared electron pairs on oxygen.Both alcohols and phenol react with carboxylic acids, acid chlorides and anhydrides to form esters. The introduction of acetyl group in alcohols or phenol is known as acetylation. Alcohols react with hydrogen halides to form alkyl halides which form the basis of Lucas test. They also undergo acid catalyzed dehydration to form alkenes. Alcohols can be easily oxidized with variety of oxidizing agents. The nature of the product depends on the type of oxidizing agent and the nature of alcohol.
Pyridinium chlorochromate is used for:

Arrange the evolutionary human species in their occurrence from recent to the oldest order.
(A) Australopithecus
(B) Homo erectus
(C) Homo sapiens
(D) Neanderthal man
Choose the correct answer from the options given below:

Genetic disorders in the developing foetus can be detected by:

The Western Ghats have a greater number of amphibian species than the Eastern Ghats. This is an example of :

Which of the following statements are true?
(A) If \(\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}\), then \(x, y, z\) are called direction ratios of \(\vec{r}\).
(B) For any two vectors \(\vec{a}\) and \(\vec{b}, \vec{a}+\vec{b}=\vec{b}+\vec{a}\).
(C) \(\vec{a} \perp \vec{b}\) if and only if \(\vec{a} \times \vec{b}=\overrightarrow{0}\).
(D) Projection of \(\vec{b}\) on \(\vec{a}\) is \(\frac{\vec{a} \cdot \vec{b}}{|\vec{a}|^2}\).
Choose the correct answer from the options given below :