Two electrons are moving with different kinetic energies. If 1st electron is moving with kinetic energy \( k \) and the 2nd electron with kinetic energy \( 4k \), the ratio of their de Broglie wavelengths will be respectively:

Two identical capacitors are joined in parallel, charged to a potential V and then separated and connected in series, i.e., negative plate of first is connected to positive plate of second :

Match List I with List II

LIST I	LIST II
A. Cyclotron frequency	I. \(\frac{N A B}{K R}\)
B. Magnetic field due to a circular coil	II. \(\frac{q B}{2 \pi m}\)
C. Magnetic field inside a toroid	III. \(\frac{\mu_0 N I}{2 \pi R}\)
D. Voltage sensitivity	IV.\(\frac{\mu_0 I}{2 R}\)

Choose the correct answer from the options given below:

A charged particle with charge 0.01 C rotates on a circular path of radius 0.5 m , with velocity \(0.2 m / s\). What is the value of \(B\) at the center of the circle ?

Which of the following statement is not true for the electromagnetic waves?

In an AC circuit, the current leads the voltage by \(\pi/2\). The circuit is :

In the given circuit when steady current flows, the potential drop across the capacitor is:

From the given standard reduction potentials, arrange the metals in decreasing order of their reducing power.
(A) \(E_{ Zn ^{2+} / Zn _{ n }}^0=-0.76 V\)
(B) \(E_{ Mg ^{2+} / Mg }^0=-2.37 V\)
(C) \(E_{ Al ^{3+} / Al }^0=-1.67 V\)
(D) \(E_{ Ag ^{+} / Ag }^0=+0.80 V\)
Choose the correct answer from the options given below:

Who popularised the term 'Biodiversity' that intends to describe the combined diversity at all the levels of biological organisation?

Consider two lines \(l_1\) and \(l_2\) with cartesian equations \(\frac{x}{2}=\frac{1-y}{-2}=\frac{z}{1}\) and \(\frac{2 x-5}{16}=\frac{y-2}{-1}=\frac{z-5}{4}\) respectively. Which of the following is/are true?
(A) Direction ratio of \(l_1\) are \(2,2,1\)
(B) Direction cosines of \(l_1\) are \(\frac{2}{3}, \frac{-2}{3}, \frac{1}{3}\)
(C) Direction ratio of \(l_2\) are \(16,-1,4\)
(D) Angle between \(l_1\) and \(l_2\) is \(\cos ^{-1}\left(\frac{38}{3 \sqrt{273}}\right)\)
Choose the correct answer from the options given below:

Points of discontinuity of the greatest integer function \(f(x)=\lfloor x\rfloor\), where \(\lfloor x\rfloor\) denotes integer less than or equal to \(x\), are

Answer the question on the basis of passage given below :
Formaldehyde is the first member of the aldehydic series. It is present in green leaves of plants where its presence is supposed to be due to the reaction of \(CO_2\) with water in the presence of sunlight and chlorophyll. Commercially, formaldehyde is obtained by the controlled oxidation of methane in the presence of molybdenum oxide (\(MoO\)) acting as a catalyst. Formaldehyde is a constituent of a number of polymers also called resins. These are non volatile solids or semi solids which are obtained directly from certain plants and can be synthesized in the laboratory.
What is formalin ?

The equation of the tangent to the curve \(y=\frac{x-5}{(x-3)(x+2)}\) at the point where it cuts the \(x\)-axis is :