An electric dipole of dipole moment \(p\) is rotated in an electric field of magnitude \(E\) from the most stable orientation to most unstable orientation. The work done in the process is:

A thin infinite line charge has linear charge density of \( 2.0 \times 10^{-9} \text{ C/m} \). The electric field intensity at a distance of 3 m from the line charge is : (\( \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \))

An ac source of variable angular frequency and constant amplitude is connected in series with a capacitance C and an electric bulb of resistance R. When angular frequency is increased then :

Two Polaroids are placed in such a way that their axes make an angle of 60° with each other. If an unpolarized light is incident on a system of these Polaroids, the fraction of transmitted light to the incident light will be

An LCR series circuit consisting of resistance 45 \( \Omega \), inductive reactance 4 \( \Omega \) and capacitive reactance 4 \( \Omega \) is connected to an alternating source of emf 90 V. The readings of the ammeter connected to the circuit would be

In a meter bridge experiment null point is obtained at 20 cm from one end when resistance X is balanced against resistance Y, where \( X < Y \). Then, the new position of the null point from the same end if X is replaced by 4X will be:

The correct sequence A, B, C, D, E with reference to atomic spectral series is :
(A) Lyman series \(\frac{1}{\lambda}=R\left(\frac{1}{A^2}-\frac{1}{n^2}\right)\)
(B) Balmer series \(\frac{1}{\lambda}=R\left(\frac{1}{B^2}-\frac{1}{n^2}\right)\)
(C) Pfund series \(\frac{1}{\lambda}=R\left(\frac{1}{C^2}-\frac{1}{n^2}\right)\)
(D) Brackett series \(\frac{1}{\lambda}=R\left(\frac{1}{D^2}-\frac{1}{n^2}\right)\)
(E) Paschen series \(\frac{1}{\lambda}=R\left(\frac{1}{E^2}-\frac{1}{n^2}\right)\)
Choose the correct answer from the options given below :

Match List-I with List-II

List-I ( Matrix A )	List-II ( Determinant of adj A )
(A) \(\left[\begin{array}{cc}2 & 1 \\0 & -1\end{array}\right]\)	(I) 6
(B) \(\left[\begin{array}{cc}0 & 1 \\4 & -1\end{array}\right]\)	(II) 5
(C) \(\left[\begin{array}{cc}1 & 2 \\-3 & -1\end{array}\right]\)	(III) \(-4\)
(D) \(\left[\begin{array}{cc}4 & -2 \\3 & 0\end{array}\right]\)	(IV) \(-2\)

Choose the correct answer from the options given below :

If the slope of the tangent to the curve \(y=y(x)\) at any point \((x, y)\) is \(\frac{2 x}{y^2}\) and the curve passes through the point \(\left(\frac{1}{\sqrt{3}}, 1\right)\), then the equation of the curve is :

If the relation \(R: A \rightarrow B\), where \(A=\{2,3,4\}\) and \(B=\{3,4,5\}\) is defined by \(R=\{(x, y): x < y, x \in A, y \in B\}\), then

We use microbes and microbially derived products almost every day. Bacteria called lactic acid bacteria (LAB) grow in milk to convert it into curd. The dough, which is used to make bread, is fermented by yeast called Saccharomyces cerevisiae. Microbes are used to produce industrial products like lactic acid, acetic acid and alcohol, which are used in a variety of processes in the industry. However, certain bacteria, which grow anaerobically on cellulosic material, produce large amount of methane along with CO2 and H2. These bacteria are collectively called methanogens, and one such common bacterium is Methanobacterium. These bacteria are commonly found in the anaerobic sludge during sewage treatment. Microbes are also used for commercial and industrial production of certain chemicals like organic acids, alcohols and enzymes.
Examples of acid producers are Aspergillus niger (a fungus) of citric acid. You are familiar with the commonly used antibiotic Penicillin. Do you know that Penicillin was the first antibiotic to be discovered, and it was a chance discovery? Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol.
Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by:

A system has two charges, \( q_A = 5 \times 10^{-7} \, \text{C} \) and \( q_B = -5 \times 10^{-7} \, \text{C} \), located at points \( A : (0, 0, -10 \, \text{cm}) \) and \( B : (0, 0, +10 \, \text{cm}) \), respectively. Which of the following are true?
(A) The electric field of dipole at point (0, 0, -15 cm) is \( 1.73 \times 10^6 \, \text{NC}^{-1} \)
(B) Electric field intensity is zero at origin (0, 0, 0)
(C) dipole moment \( (p) = 5 \times 10^{-8} \, \text{C-m} \)
(D) direction of the dipole moment is along the negative z- axis
Choose the correct answer from the options given below:

If \(y=(\log x)^{\log x}, x>1\) then \(\frac{d y}{d x}\) is equal to