List of practice Questions

Two identical long conducting wires AOB and COD are placed at right angle to each other, with one above other such that 'O' is their common point for the two. The wires carry I₁ and I₂ currents, respectively. Point 'P' is lying at distance 'd' from 'O' along a direction perpendicular to the plane containing the wires. The magnetic field at the point 'P' will be:

A conducting sphere of radius R is given a onducting charge Q. The electric potential and the electric field at the centre of the sphere respectively are:

A thermodynamic system undergoes cyclic process ABCDA as shown in Fig. The work done by the system in the cycle is:

Copper of fixed volume 'V' is drawn into wire of length 'l'. When this wire is subjected to a constant force 'F', the extension produced in the wire is 'Δl'. Which of the following graphs is a straight line?

If n₁, n₂ and n₃ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is given by:

The resistances in the two arms of the meter bridge are 5Ω and RΩ, respectively. When the resistance R is shunted with an equal resistance, the new balance point is at 1.6 l₁. The resistance 'R', is:

Two thin dielectric slabs of dielectric constants K₁ and K₂ (K₁ < K₂) are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field 'E' between the plates with distance 'd' as measured from plate P is correctly shown by:

For the reaction:
\(X_2O4(l) → 2XO_2(g)\)
△U = 2.1 k cal, △S = 20 cal K^–l at 300 K.
Hence △G is

Identify \(Z\) in the sequence of reactions:
\(CH_3CH_2CH=CH_2  \xrightarrow{HBr/H_2O_2}Y \xrightarrow{C_2H_5ONa}Z\)

In the following reaction, the product (A) is :

Using the Gibbs energy change, \(△G° = + 63.3\  kJ\), for the following reaction,
\(Ag_2CO_3 (g) ⇋ 2Ag+ (aq) + CO_3^{2–} (aq)\)
the \(K_{sp}\) of \(Ag_2CO_3 \)(s) in water at \(25°C\) is :
\((R = 8.314\ J K^{–1} mol^{–1})\)

Which of the following will not be soluble in sodiumhydrogen carbonate?

A gardener is digging a plot of land. As he gets tired, he works more slowly. After $' t '$ minutes he is digging at a rate of $\frac {2} {\sqrt {t}} $square metres per minute. How long will it take him to dig an area of $40$ square metres ?

A steady current flows in a long wire. It is bent into a circular loop of one turn and the magnetic field at the centre of the coil is $ B $ . If the same wire is bent into a circular loop of $ n $ turns, the magnetic field at the centre of the coil is

Two concentric hollow spherical shells have radii $ r $ and $ R \left(R\,>>\,r\right) $ . A charge $ Q $ is distributed on them such that the surface charge densities are equal. The electric potential at the centre is

A balloon with mass m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration $a$?

Which of the following will be most stable diazonium salt $(R\, N^{+}_{2}\,X^{-})$ ?

Which property of colloids is not dependent on the charge on colloidal particles?

Which of the following will not be soluble in sodium hydrogen carbonate?

If the function $f(x)$ defined by $\frac {x^{100}}{100}+\frac {x^{99}}{100}+\dots \frac {x^2}{100}+x+1$ then $f'(0)$ is equal to

If $x+y\leq2,x \geq 0,y \geq 0$ the point at which maximum value of $3x + 2y$ attained will be

The general solution of the differential equation $\frac {dy}{dx}+\frac {y}{x}=3x$ is

Given $0 \leq x \leq \frac {1}{2}$ then the value of $\tan \left[\sin^{-1}\left\{\frac{x}{\sqrt {2}}+\frac {\sqrt {1-x^2}} {\sqrt {2}}\right\}-\sin^{-1}x\right]$ is

A stone of mass $0.05 \,kg$ is thrown vertically upwards. What is the direction and magnitude of net force on the stone during its upward motion ?

Energy of one mole of photons of radiation whose frequency is $ 5\times 10^{14}\,Hz $ is