Time period of oscillation of a bar magnet in a uniform magnetic field is \( T_o \). The magnet is cut into 3 equal parts transverse to its length. The new time period of oscillation of one part will be :

Kinetic energies of four particles a, b, c, d of equal masses are given below. Arrange them in order of their decreasing de-Broglie wavelengths.
(A) \((KE)_a = 1 \text{ eV}\)
(B) \((KE)_b = 0.01 \text{ eV}\)
(C) \((KE)_c = 4 \text{ eV}\)
(D) \((KE)_d = 16 \text{ eV}\)
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If \( n_h \) is the number of holes per unit volume and \( n_e \) is the number of conduction electrons per unit volume in an extrinsic semiconductor. The relation between \( n_h, n_e \) and \( n_i \) is (\( n_i \) is intrinsic carrier concentration):

Identify the incorrect statement.
(A) Power meters work on the principle of Eddy currents.
(B) Induction furnace uses eddy currents to produce heat.
(C) Eddy currents can be used to produce braking force in moving trains.
(D) Eddy currents are produced in a steady magnetic field.
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If \(I=I_0 \sin \left(\omega t-\frac{\pi}{2}\right)\) and \(E=E_0 \sin \omega t\), then the AC power consumed is

The property of a medium which determines the electric force between two charges situated in the medium is

The capacitance of a parallel plate capacitor with air as medium between the plates is 1 nF. When a material of dielectric constant 5 is filled between the plates, the new capacitance becomes -

If the lines \(\frac{1-x}{3}=\frac{y-2}{2 \lambda}=\frac{z-3}{2}\) and \(\frac{x-1}{3 \lambda}=\frac{y-1}{1}=\frac{6-z}{5}\) are perpendicular, then the value of \(\lambda\) is:

Choose the correct statements regarding infra red waves from the following.
(A) Infra red waves produced by hot bodies and molecules.
(B) This radiation is trapped by greenhouse gases such as \( CO_2 \) and water vapour.
(C) These waves are used in earth satellites.
(D) Exposure to these radiation induces the production of more melanin.
(E) These radiations are used in eye surgery.
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For the differential equation \(y d x-\left(x+3 y^2\right) d y=0\), which of the following statements are true?
(A) It is a linear differential equation
(B) It is a homogenous differential equation
(C) Its general solution is \(x=3 y^2+C y: C\) is an arbitrary constant
(D) If \(y(0)=1\), then its particular solution is \(x=3 y^2-1\)
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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.
Malignant malaria is caused by _____ is the most serious one and can even be fatal.

In agarose gel electrophoresis, the separated DNA fragments can be visualised by staining the DNA with a compound, known as

Match List-I with List-II

List-I (Formula)	List-II (Physical quantity)
(A) \( neAv_d \)	(I) Mobility
(B) \(\frac{v_d}{E}\)	(II) Current
(C) \(\frac{n e^2 \tau}{m}\)	(III) Conductivity
(D) \(\frac{m}{n e^2 \tau}\)	(IV) Resistivity

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