Two large plane parallel sheets with equal but opposite surface charge densities +\(\sigma\) and -\(\sigma\). A point charge q placed at points \(P_1, P_2,\) and \(P_3\) experiences forces \(F_1, F_2,\) and \(F_3\) respectively. Then :

Choose the correct statements:
A. In uniform electric field E, the net force on electric dipole is zero.
B. The torque on dipole in electric field is \( \tau = PE \cos \theta \), where \( \theta \) is angle between \( \vec{P} \) and \( \vec{E} \).
C. In non uniform Electric field, when dipole moment P is parallel to E, the dipole has a net force in the direction of decreasing field.,
D. The direction of torque is perpendicular to both \( \vec{P} \) and \( \vec{E} \).
E. The net torque is zero if E is not uniform.
Choose the correct answer from the options given below:

The correct arrangement of electromagnetic spectrum in decreasing order of wavelength is :

A parallel plate capacitor with air between the plates has a capacitance of 6 pF. What will be the capacitance if the distance between the plates is reduced to half and the space between them is filled with a substance of dielectric constant 5?

A transformer with turns ratio \( \frac{N_1}{N_2} = \frac{100}{1} \) is connected to a 240 V ac supply. If the primary and secondary resistance are \( 1.0 \text{ k}\Omega \) and \( 1 \ \Omega \) respectively, then find the output power ?

For a series LCR circuit, \( R = X_L = 3X_C \). The impedance of the circuit and the phase difference between voltage V and current I, respectively, will be:

Which of the following statements are correct?
A. Dipole field depends on the distance r and also on the angle between the position vector and the dipole moment P
B. A comb runs through dry hair acquires charge through friction
C. If surface charge density of a plate is positive, the electric field is directed towards the plate.
D. Electrostatic field lines cannot form closed loops.
E. In a uniform electric field, a dipole experiences a torque and a net force also.
Choose the correct answer from the options given below:

Data available for profit (₹ Thousands) of a company as

Year	2004	2005	2006	2007	2008	2009	2010
Profit(000)	114	130	126	144	138	156	164

Based on the above data using least square method the trend value for the year ‘2007’ is

In a reaction :
\(MnO _4^{-}+8 H ^{+}+5 e^{-} \rightarrow \underline{ A }+ H _2 O\)
A stands for :

Read the passage carefully and answer the questions
Biomolecules are the organic compounds present as an essential constituents of living organisms in different cells.The molecules are generally termed as macromolecules, which are carbohydrates, enzymes, nucleic acids, amino acids and proteins etc. Carbohydrates are classified as sugars and non-sugars include sucrose, glucose, fructose, starch and cellulose. Enzymes are coordinated with various chemical reactions in nucleic acid. Nucleic acids are found in living organisms made up of proteins and natural polymers. Two types that are generally found in biological systems are DNA and RNA nucleic acid. Amino acids are bifunctional groups of carboxyl and amino groups. Proteins are a class of biologically important compounds. They are crucial to virtually all processes in living systems. Some of them are hormones, which serve as chemical messengers that coordinatecertain biochemical activities.
Glucose when treated with Bromine water forms

MTP is considered safe up to _________ weeks of pregnancy.

Motion of a charged particle having velocity v in a uniform magnetic field B is circular, if v is

A 100 W bulb working on 200 V and a 200 W bulb on 100 V, have their resistances in the ratio