What is the force experienced by an electron moving with velocity of \(0.5 c\) in a magnetic field \(\vec{B}\) of \(2 T\) ? The angle between the velocity vector and \(\vec{B}\) is \(90^{\circ}\)
( \(c\) is the velocity of light, \(e=1.6 \times 10^{-19} C\) )

Three resistances of 1 \(\Omega\), 2 \(\Omega\) and 3 \(\Omega\) are given. In order to obtain an equivalent resistance of 11/3 \(\Omega\) they are to be connected as

Choose the correct dimension of \(\varepsilon_0 \frac{d \phi_{ E }}{ dt }\) from the following :
In the given expression symbols have their usual meaning.

A charging capacitor has

A flask contains Argon and Chlorine in the ratio of 2:1 by mass. The temperature of the mixture is \( 27^{\circ}\text{C} \). The ratio of root mean square speed of molecules of two gases will be : (atomic mass of Argon = 40 u and molecular mass of Chlorine = 71 u)

A pure inductor of 70 mH is connected to a source of 220 V. The frequency of the source is 50 Hz. The current in the circuit is:

Which of the following statements are true for the minimum deviation position of a prism?
(A). The angle of the prism is twice the angle of refraction.
(B). The refracted ray is parallel to the base of prism.
(C). The angle of incidence is equal to the angle of emergence.
(D). The angle of deviation is half the angle of a prism.
Choose the correct answer from the options given below:

Arrange the given taxa of invertebrates in terms of their increasing numbers.
(A) Other animal groups
(B) Molluscs
(C) Insects
(D) Crustaceans
Choose the correct answer from the options given below:

If A is a square matrix such that \(A^2=A\) then which of the following statements are TRUE?
(Where I is an identity matrix of same order as A)
(A) \((I+A)^4=I+15 A\)
(B) \((I+A)^2=I+3 A\)
(C) \((I+A)^6=I+30 A\)
(D) \((I+A)^3=I+7 A\)
Choose the correct answer from the options given below:

White phosphorous shows chemiluminescence because it:

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 will be the percentage of progeny in F₁ generation when RR (red flowered plant) is crossed with rr (white flowered plant) in the above passage?

A proton is projected with a speed of \(4 \times 10^6 \text{ m s}^{-1}\) horizontally from east to west. A uniform magnetic field of strength \(3 \times 10^{-3} \text{ T}\) exists in the vertically upward direction. The acceleration of the proton is:
(Given: mass of proton \(1.67 \times 10^{-27} \text{ kg}\); charge on proton \(1.6 \times 10^{-19} \text{ C}\))

A charged particle with charge 0.01 C rotates on a circular path of radius 0.5 m , with velocity \(0.2 m / s\). What is the value of \(B\) at the center of the circle ?