List of practice Questions

A physical quantity P is related to four observables a, b, c, and d as \( P = \frac{\sqrt{ab}.d^\alpha}{\sqrt{C}} \) (\(\alpha\) is constant). The percentage errors in a, b, c and d are 0.5% in each. If the percentage error in P is 2%, then \(\alpha\) is
Light of wavelength 1 nm belongs to the following class of waves
An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm–1. Choose the correct equations for electric and magnetic field if the EM wave is propagating in vacuum:
A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is tan-1(3/4). Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is

Let f be a differential function satisfying
f(x) =\(\frac{ 2}{√3} \)\(∫^{√30} f(\frac{λ2x}{3})dλ,x>0 and f(1) = √3.\)
If y = f(x) passes through the point (α, 6), then α is equal to _____

In a Young’s double slit experiment, an angular width of the fringe is 0.35° on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is 1/α. The value of α is _________.

In the given circuit, the magnitude of VL and VC are twice that of VR. Given that f = 50 Hz, the inductance of the coil is 1/(Kπ) mH. The value of K is ________.

Fig.

All resistances in figure are 1 Ω each. The value of current ‘I‘ is (a/5) A. The value of a is _______.

Fig.

A capacitor C1 of capacitance 5 μF is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C2 of capacitance 10 μF as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C2 is ____ μC.

Fig.

A tuning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ____ cm.
(Velocity of sound in air is 340 ms–1)

A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is _____ N.
(Take g = 10 ms–2)

Fig.
High purity (>99.95%) dihydrogen is obtained by

A car covers AB distance with first one-third at velocity v1 ms–1, second one-third at v2 ms–1 and last one-third at v3 ms–1. If v3 = 3v1, v2 = 2v1 and v1 = 11 ms–1 then the average velocity of the car is ____ ms–1.

Fig.
The correct order of density is
\(lim_{n→∞} \frac1{2^n}(\frac1{\sqrt{1-1/2^n}} +\frac1{\sqrt{1-\frac2{2^n}}}+\frac1{\sqrt{1-\frac3{2^n}}}+...+\frac1{\sqrt{1-\frac{2^n-1}{2^n}}})\) is equal to
If A and B are two events such that \(P(A)=\frac1{3},P(B)=\frac1{5}\)  and \(P(A∪B)=\frac1{2}\) then \(P(\frac{A}{B'}) + P(\frac{B}{A'})\) is equal to

A common tangent T to the curves
\(C_1:\frac{x^2}{4}+\frac{y^2}{9} = 1\)
and
\(C_2:\frac{x^2}{4^2}\frac{-y^2}{143} = 1\)
does not pass through the fourth quadrant. If T touches C1 at (x1, y1) and C2 at (x2, y2), then |2x1 + x2| is equal to ______.

Match List I with List II.
 

List-IList-II
A. Benzene sulphonyl chlorideI. Test for primary amines
B. Hoffmann bromamide reactionII. Anti Saytzeff
C. Carbylamine reactionIII. Hinsberg reagent
D. Hoffmann orientationIV. Known reaction of Isocyamates

Choose the correct answer from the options given below:

20 mL of 0.02 M K2Cr2O7 solution is used for the titration of 10 mL of Fe2+ solution in the acidic medium. The molarity of Fe2+ solution is ______×10–2 M. (Nearest integer)
2NO + 2H2 → N2 + 2H2O
The above reaction has been studied at 800 °C. The related data is given in the table below.
The order of the reaction with respect to NO is ___.

2sin(\(\frac{\pi}{22}\))sin(\(\frac{3\pi}{22}\))sin(\(\frac{5\pi}{22}\))sin(\(\frac{7\pi}{22}\))sin(\(\frac{9\pi}{22}\)) is equal to

Amongst the following, the number of oxide(s) which are paramagnetic in nature is
Na2O, KO2, NO2, N2O, ClO2, NO, SO2, Cl2O
The molar heat capacity for an ideal gas at constant pressure is 20.785 J K–1 mol–1. The change in internal energy is 5000 J upon heating it from 300 K to 500 K. The number of moles of the gas at constant volume is _____. (Nearest integer)
(Given : R = 8.314 JK-1mol-1).
According to MO theory, number of species/ions from the following having identical bond order is ___.
CN-, NO+, O2, O+2, O2+2
At 310 K, the solubility of CaF2 in water is 2.34 ×10–3 g/100 mL. The solubility product of CaF2 is _____ × 10–8 (mol/L)3.
(Given molar mass : CaF2 = 78 g mol–1).