The charge flowing in a conductor varies with time as \(q(t) = (8t^2 - 4t + 5)C\). Then the current changes at the rate of :

Kirchhoff's second law for an electric network is based on:

One student has to make an electromagnet using a coil of copper wire. He needs a ferromagnetic material to make its core. This core material should have

Two polaroid \( P_1 \) and \( P_3 \) are placed such that their pass-axis are mutually perpendicular. Another polaroid \( P_2 \) is rotated between \( P_1 \) and \( P_3 \). For what angle \( \theta \) between \( P_1 \) and \( P_2 \) the intensity of light emerging from \( P_3 \) will be maximum ?

A galvanometer has a resistance of 8 \( \Omega \). It is shunted by a wire of resistance 2 \( \Omega \). If the total current is 2 A, the current passing through the shunt is

A charged particle moving with a certain velocity enters a uniform electric field perpendicular to its direction. In this context, which of the following statements are correct?
(A) Force acting on the particle is constant
(B) Acceleration of the particle is constant
(C) Velocity of the particle is constant
(D) Displacement of the particle follows a parabolic path
Choose the correct answer from the options given below:

A 10 V battery of negligible internal resistance is being charged by a 200 V battery with a resistance of \( 38 \Omega \) in series. The value of the current in the circuit is

If the matrix \(\left[\begin{array}{ccc}-1 & x-y & 4 \\ 2 & 0 & 5 \\ x+y & z & 6\end{array}\right]\) is symmetric, then \(x+3 y+2 z\) is equal to

Read the following passage carefully and answer the given questions.
Plasmodium, a tiny protozoan is responsible for the disease malaria. Different species of Plasmodium (P. vivax, P. malaria and P. falciparum) are responsible for different types of malaria. Of these, malignant malaria caused by Plasmodium falciparum is the most serious one and can even be fatal. Innate immunity consist of four types of barriers. These are – (i) Physical barriers- skin on our body is the main barrier which prevents entry of the micro-organisms. (ii) Physiological barriers- Acid in the stomach, saliva in the mouth, tears from eyes-all prevent microbial growth. (iii) Cellular barriers- Certain types of leukocytes (WBC) of our body like polymorpho-nuclear leukocytes (PMNL-neutrophils) and monocytes and natural killer (type of lymphocytes) in the blood as well as macrophages in tissues can phagocytose and destroy microbes. (iv) Cytokine barriers- virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Allergy is due to the release of chemicals like histamine and serotonin from the mast cells. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Drugs like barbiturates, amphetamines, benzodiazepines, and other similar drugs, that are normally used as medicines to help patients cope with mental illnesses like depression and insomnia, are often abused.
Which one of the following drugs is not used as medicine to help patients cope with mental illnesses like depression and insomnia?

Read the passage carefully and answer the questions
The speed at which a chemical reaction takes place is called the rate of reaction. The rate of reaction depends on various factors like concentration of the reactants, temperature, etc. The relation between the rate of reaction and the concentration of reacting species is represented by the equation r = k[A]^x[B]^y, where x and y are the order of the reaction with respect to the reactants A and B, respectively. The overall order of the reaction is x + y. The rate of reaction can also be increased by the use of a catalyst which provides an alternate pathway of lower activation energy. It increases the rate of forward and backward reaction to an equal extent. It does not alter the Gibbs energy of the reaction.
The role of a catalyst is to change

Given that \(\text{E}^{\circ}_{\text{Ni}^{2+}/\text{Ni}} = -0.25 \text{ V}\) and \(\text{E}^{\circ}_{\text{Cu}^{2+}/\text{Cu}} = +0.34 \text{ V}\).
The EMF of the cell containing nickel and copper electrodes in 1 M solution is

A problem in mathematics is given to three students whose chances of solving it are \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\) respectively. The probability that the problem is solved is

Two charges of -2 \(\mu C\) and +2 \(\mu C\) are placed at the point A (0, 2, 0) m and B (0, -2, 0) m located in an electric field \(E = 0.5i\) V/cm. The magnitude of torque acting on the dipole is: