List of practice Questions

The sum of the series \(\frac{1}{x+1} + \frac{2}{x^2+1} + \frac{2^2}{x^4+1} + \dots + \frac{2^{100}}{x^{2^{100}}+1}\) when \(x = 2\) is :

The \(OH^-\) concentration in a mixture of 5.0 mL of 0.0504 M \(NH_4Cl\) and 2 mL of 0.0210 M \(NH_3\) solution is \(x \times 10^{-6}\) M. The value of \(x\) is _________. (Nearest integer)
[Given \(K_w = 1 \times 10^{-14}\) and \(K_b = 1.8 \times 10^{-5}\)]

The number of 4f electrons in the ground state electronic configuration of \(Gd^{2+}\) is _________. [Atomic number of Gd = 64] (Integer answer)

The polymer formed on heating Novolac with formaldehyde is :

Given below are two statements :
Statement I : In the titration between strong acid and weak base methyl orange is suitable as an indicator.
Statement II : For titration of acetic acid with NaOH phenolphthalein is not a suitable indicator.
In the light of the above statements, choose the most appropriate answer from the options given below :

Which one of the following when dissolved in water gives coloured solution in nitrogen atmosphere ?

The conversion of hydroxyapatite occurs due to presence of \(F^-\) ions in water. The correct formula of hydroxyapatite is :

Which one of the following is correct for the adsorption of a gas at a given temperature on a solid surface ?

Given below are two statements.
Statement I : The choice of reducing agents for metals extraction can be made by using Ellingham diagram, a plot of \(\Delta G\) vs temperature.
Statement II : The value of \(\Delta S\) increases from left to right in Ellingham diagram.
In the light of the above statements, choose the most appropriate answer from the options given below :

Which one of the following methods is most suitable for preparing deionized water ?

What are the products formed in sequence when excess of \(CO_2\) is passed in slaked lime ?

The incorrect statement is :

Two short magnetic dipoles \(m_1\) and \(m_2\) each having magnetic moment of \(1 \text{ Am}^2\) are placed at point O and P respectively. The distance between OP is 1 meter. The torque experienced by the magnetic dipole \(m_2\) due to the presence of \(m_1\) is _________ \(\times 10^{-7} \text{ Nm}\).
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An amplitude modulated wave is represented by \(C_m(t) = 10(1 + 0.2 \cos 12560 t) \sin(111 \times 10^4 t)\) volts. The modulating frequency in kHz will be _________.

Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3 s with the same initial velocity of 35 m/s, then these balls collide at a height of _________ m.
(take \(g = 10 \text{ m/s}^2\))

A source and a detector move away from each other in absence of wind with a speed of 20 m/s with respect to the ground. If the detector detects a frequency of 1800 Hz of the sound coming from the source, then the original frequency of source considering speed of sound in air 340 m/s will be _________ Hz.

If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula \(P = E L^2 M^{-5} G^{-2}\) are :

A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is _________ cm.

The material filled between the plates of a parallel plate capacitor has resistivity 200 \(\Omega\)m. The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is : (given the value of relative permittivity of material is 50)

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 \(ms^{-2}\). The gases come out at a relative speed of 500 \(ms^{-1}\) with respect to the rocket : [Use \(g = 10 \text{ m/s}^2\)]

In a photoelectric experiment ultraviolet light of wavelength 280 nm is used with lithium cathode having work function $\phi = 2.5$ eV. If the wavelength of incident light is switched to 400 nm, find out the change in the stopping potential. ($h=6.63 \times 10^{-34}$ Js, $c=3 \times 10^8$ $ms^{-1}$)

The rms speeds of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are $V_H$, $V_O$ and $V_C$ respectively then :

A particular hydrogen like ion emits radiation of frequency $2.92 \times 10^{15}$ Hz when it makes transition from n=3 to n=1. The frequency in Hz of radiation emitted in transition from n=2 to n=1 will be :

In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular observation the reading on the main scale is 5 mm and the 20th division of the circular scale coincides with reference line. Calculate the true reading.

Two bodies of masses 8 kg are placed at the vertices A and B of an equilateral triangle ABC. A third body of mas 2 kg is placed at the centroid G of the triangle. If AG = BG = CG = 1 m, where should a fourth body of mass 4 kg be placed so that the resultant force on the 2 kg body is zero?