In terms of Bohr radius \( a_0 \), the radius of the 2nd Bohr orbit ofHydrogen is:

Rohit has been given two converging lenses of focal lengths 1.25 cm and 5 cm, respectively to design a compound microscope. If it is desired to have a magnification of 30, what would be the separation between the objective and the eyepiece when the final image is formed at the least distance of distinct vision?

A coil of 400 turns of effective area \(0.05 \text{ m}^2\) is kept perpendicular to a magnetic field of \(5 \times 10^{-3} \text{ T}\). When the plane of coil is rotated by \(90^\circ\) around any of its co-planar axis in 0.2 s in magnetic field, the emf induced in the coil is

White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is b and the screen is at a distance D from the slits. At a point on a screen directly in front of one of the slits, certain wavelength are missing. Some of these wavelengths are :
(A) \( \lambda = \frac{b^2}{D} \)
(B) \( \lambda = \frac{2b^2}{D} \)
(C) \( \lambda = \frac{b^2}{3D} \)
(D) \( \lambda = \frac{2b^2}{3D} \)
Choose the correct answer from the options given below :

The work function for Tungsten and Sodium are 4.2 eV and 2.3 eV, respectively. If the threshold wavelength for Sodium is 5460 \(\text{\AA}\), then that for tungsten is :

A ray is incident normally on the face of an equilateral prism of refracting angle \(60^{\circ}\).
The refractive index of the prism is \(\frac{2}{\sqrt{3}}\).
The angle of deviation will be:

In Young's double slit experiment, the width of one of the two slits is four times the width of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern will be

MONOHYBRID CROSS
The inheritance of flower color in the dog flower (Snapdragon or Antirrhinum sp.) can be understood by crossbreeding between true-breeding red-flowered (RR) and true-breeding white-flowered plants (rr). When they were crossed, F₁ (Rr) was pink. When F₁ was self-pollinated, the F₂ results were Red, Pink and White. Here the genotype ratios were exactly as expected, but the phenotype ratios have been changed. What happened was that R was not completely dominant over r and this made it possible to distinguish Rr as pink from RR (Red) and rr (White).
What was the expected phenotypic ratio in any Mendelian monohybrid cross that had changed when F₁ (Rr) was self-pollinated in this cross?

An electric motor operating at a 100 V D.C. supply draws a current of 12 A. If the efficiency of the motor is 30%, calculate the resistance of its winding.

DNA recombinant technology involves the use of restriction endonucleases. After having cloned the gene of interest and having optimised the conditions to induce the expression of the target protein, one has to consider producing it on a large scale. The cells harbouring cloned genes of interest may be grown on a small scale in the laboratory. In order to link the alien DNA, the vector needs to have very few, preferably single, recognition sites for the commonly used restriction enzymes. Presence of more than one recognition sites within the vector will generate several fragments, which will complicate the gene cloning. In Biolistics or gene gun method cells are bombarded with high velocity micro particles of gold or tungsten coated with DNA. The ligation of alien DNA is carried out at a restriction site present in one of the two antibiotic resistance genes. For example, you can ligate a foreign DNA at the BamH I site of tetracycline resistance gene in the vector pBR322. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA along with other macromolecules such as RNA, proteins, polysaccharides and also lipids. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.
pBR322, which is used in recombinant DNA technology, is a -

The degree of the differential equation \(\left(1+\frac{d y}{d x}\right)^4=\left(\frac{d^2 y}{d x^2}\right)^2\) is:

The relation between species richness and area for a wide variety of taxa (angiosperm plants, birds, bats, freshwater fishes) can be represented by the equation :

If the matrix \(M=\left[\begin{array}{ccc}0 & -1 & 3 \alpha \\ 1 & \beta & -5 \\ -6 & 5 & 0\end{array}\right]\) is skew-symmetric, then