A capacitor of unknown capacitance is connected with a battery of V volts. The charge stored in it is \( 200 \, \mu\text{C} \). When the potential of the capacitor is reduced by 100 volts, the charge stored in it becomes \( 150 \, \mu\text{C} \). The unknown capacitance is:

An ordinary light of intensity \(I_0\) is passed through a polaroid \(P_1\) which is crossed with another polaroid \(P _{ 2 }\). Now a third polaroid is placed in between \(P _1\) and \(P _2\) with its pass aris making an angle \(\beta\) with the pass axis of \(P_1\). The value of \(\beta\) for which the intensity of light from \(P_2\) is \(\frac{I_0}{8}\) is :

A conducting circular loop is placed in a uniform magnetic field, B = 0.025 T with its plane perpendicular to the magnetic field. The radius of the loop is made to shrink at a constant rate of 2 mm \( s^{-1} \). The induced emf when the radius is 2 cm, is

Which of the following is necessary to use to achieve half wave rectification of an alternating current?

A proton has double the kinetic energy of an \( \alpha \)- particle. The ratio of the de-Broglie wavelength of the proton to that of \( \alpha \)- particle will be

Arrange the following in increasing number of quantum number when coming from excited energy state:
A. Lyman Series
B. Balmer Series
C. Paschen Series
D. Brackett Series
E. Pfund Series
Choose the correct answer from the options given below:

The electric field component of an electromagnetic wave in vacuum is \( \vec{E} = 3 \cos(1.8y + 5.4 \times 10^8 t) \, \text{N/C} \), where y is in meter and t is in seconds. The frequency of the wave is (approximately)

A specific characteristic of a sample is known as a:

Which of the following statements are correct for a transistor action ?
(A) The input resistance depends upon the current \( I_e \) in the transistor
(B) Collector currents is equal to the sum of base current and emitter current
(C) The emitter junction is forward biased
(D) The collector junction is reverse biased
(E) Both the emitter junction as well as the collector junction are forward biased
Choose the correct answer from the options given below :

In a college, 30 % students fail in Physics, 25 % fail in Mathematics and 10 % fail in both. One student is chosen at random. The probability that she fails in Physics if she has failed in Mathematics is

Reproductive capacity of a flowering plant can be appreciated by finding out the:
(A) Size of the embryo sac in the ovule
(B) Number of eggs in the embryo sac
(C) Size of eggs in the embryo sac
(D) Number of ovules in the ovary
Choose the most appropriate answer from the options given below:

Two inductor coils of self inductance \( L_1 \) and \( L_2 \) having same length and same area of cross-section are placed so close that effective flux in one coil is completely linked with the other. The mutual inductance between them is, is equal to:

Werner was the first to describe the bonding features in coordination compounds. But his theory could not answer basic questions like :
(i) Why only certain elements possess the remarkable property of forming coordination compounds ?
(ii) Why the bonds in coordination compounds have directional properties ?
(iii) Why coordination compounds have characteristics magnetic and optical properties ?
Many approaches have been put forth to explain the nature of bonding in coordination compounds viz. Valence Bond Theory (VBT), Crystal Field Theory (CFT), Ligand Field Theory (LFT) and Molecular Orbital Theory (MOT).
We shall focus our attention on elementary treatment of the application of VBT and CFT to coordination compounds.
According to this theory, the metal atom or ion under the influence of ligands can use its ( \(n -1\) )d, ns np or ns, np, nd orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on.
These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding.
The formula which correctly represents Potassium tetra hydroxo zincate (II) is :