A series AC circuit has a resistance \( 8 \, \Omega \) and a reactance of \( 6 \, \Omega \). The impedance of the circuit is :

An LED has a voltage drop of 2 V across it and a current of 10 mA flows when it operates with a 6 V battery through a limiting resistance R. The value of R is :

A series LCR circuit is connected to a 230 V, 50 rad/s source. Given L = 5 H, C = 80 \( \mu \)F and R = 40 \( \Omega \). Impedance of the circuit is

Two concentric coils of radius \( 2\pi \) cm each are placed with their planes at right angles to each other and carry currents of 3 A and 4 A, respectively. The net magnetic field in \( \text{Wb/m}^2 \) at the center of the coils will be

Which of the following is a transducer?

In cyclotron, an ion is made to travel successively along semi circles of increasing radius under the action of magnetic field. Which of the following factor on which angular velocity of the ion is not dependent?

If a capacitor is connected in an ac circuit, what is the phase relationship between current and potential difference applied across the capacitor ?

The probability of a shooter hitting the target in one shot is \(\frac{1}{4}\)
The minimum number of shots needed so that the probability of hitting the target at least once is greater than \(\frac{7}{16}\) is:

Read the paragraph given below and answer the question. Insulin used for diabetes was earlier extracted from slaughtered cattle and pigs. Insulin from an animal source, though caused some patients to develop allergy or other type of reactions. Insulin consists of two short polypeptide chains: chain A and chain B, that are linked bridges. In mammals, including human, insulin is synthesised as a pro-hormone. Patient with diabetes have:

A voltmeter of resistance \( 600 \text{ } \Omega \) is used to measure the potential drop across \( 300 \text{ } \Omega \) resistor. The measured value of potential drop will be

Read the passage carefully and answer the questions:
The degeneracy of the \(d\) orbitals has been removed due to ligand electron-metal electron repulsions in the octahedral complex to yield three orbitals of lower energy, \(t_{2 g}\) set and two orbitals of higher energy, \(e_g\) set. This splitting of the degenerate levels due to the presence of ligands in a definite geometry is termed as crystal field splitting and the energy separation is denoted by \(\Delta_0\). Thus energy of the two \(e_g\) orbitals will increase by \((3 / 5) \Delta_{\circ}\) and that of three \(t_{2 g}\) will decrease by \((2 / 5) \Delta_0\). The crystal field splitting \(\Delta_{ o }\) depends upon the field produced by the ligand and charge on the metal ion. Some ligands are able to produce strong fields, in which case the splitting will be large, whereas others produce weak fields and consequently result in small splitting of \(d\) orbitals. Relative magnitude of crystal field splitting energy \(\Delta_{\circ}\) and pairing energy, \(P\) (energy required for electron pairing in a single orbital) determine the formation of low spin ( \(\Delta_0>P\) ) or high spin ( \(\Delta_0<P\) ) complex. In tetrahedral coordination entity formation, the \(d\)-orbital splitting is inverted and is smaller as compared to the octahedral field splitting. The crystal field theory attributes the colour of the complex to \(d-d\) transition of the electron. The colour of the coordination compounds depends on the crystal field splitting. In the absence of ligand, crystal field splitting does not occur and hence the substance is colourless.
Choose the correct order of the ligands in their increasing crystal field splitting:

If \(\vec{a}, \vec{b}, \vec{c}\) are unit vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}\), then the value of \(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}\) is:

When a ray of light is incident normally with an incident angle (i) on the surface of thin film. What will be the angle of refraction (r) ?