List of practice Questions

The most common oxidation state of Lanthanoid elements is +3. Which of the following is likely to deviate easily from +3 oxidation state?

Following statements related to radioactivity are given below:
(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.
(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.
(C) Slope of the graph of log_e (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time (τ).
(D) Product of decay constant (λ) and half-life time (T_1/2) is not constant.
Choose the most appropriate answer from the options given below:

In the given circuit the input voltage V_in is shown in figure. The cut-in voltage of p–n junction diode
(D₁ or D₂) is 0.6 V. Which of the following output voltage (V₀) waveform across the diode is correct?

A random variable \(X\) has the following probability distribution :

x	0	1	2	3	4
P(x)	k	2k	4k	6k	8k

The value of \(P(1 < X < 4 | x ≤ 2)\) is equal to

The number of distinct real roots of the equation \(x^7 – 7x – 2 = 0\) is

A charge particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charge particle increases to 4 times its initial value. What will be the ratio of new radius to the original radius of circular path of the charge particle

\(lim _{ n → ∞}\bigg (\frac{n^2}{(n^2+1)(n+1)}+\frac{n^2}{(n^2+4)(n+2)}+\frac{n^2}{(n2+9)(n+3)}.....+ \frac{n^2}{(n^2+n^2)(n+n)}\bigg)\)is equal to

The major product of the following reaction is:

Which of the following reactions will yield benzaldehyde as a product?

A body of mass 0.5 kg travels on straight line path with velocity v = (3x²+ 4) m/s. The network done by the force during its displacement from x = 0 to x = 2 m is

Let the maximum area of the triangle that can be inscribed in the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{4} = 1, a>2\), having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the \(y\)-axis, be \(6\sqrt3\). Then the eccentricity of the ellipse is

s-block element which cannot be qualitatively confirmed by the flame test is

The measured BOD values for four different water samples (A-D) are as follows:
A = 3 ppm; B = 18 ppm; C = 21 ppm; D = 4 ppm;. The water samples which can be called as highly polluted with organic wastes, are

A certain amount of gas of volume V at 27°C temperature and pressure 2 × 10⁷ Nm^–2expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use, γ = 1.5)

A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is \(\frac{x}{121}\)%. The value of x is _________.

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of 1 kgs^–1 and at a speed of 10 ms^–1. Then, the initial acceleration of the block, in ms^–2, will be:

A block of metal weighing 2 kg is resting on a frictionless plane

Following statements are given:
(A) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
(B) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
(C) The average kinetic energy of a gas molecule decreases with increase in volume.
(D) Pressure of a gas increases with increase in temperature at constant pressure.
(E) The volume of gas decreases with increase in temperature.
Choose the correct answer from the options given below:

In van der Wall equation

\([P=\frac{a}{V^2}[v-b]=RT;\)

P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants a/b is dimensionally equal to:

Two vectors \(\overrightarrow{A}+\overrightarrow{B}\) have equal magnitudes. If magnitude of \(\overrightarrow{A}+\overrightarrow{B}\) is equal to two times the magnitude of \(\overrightarrow{A}-\overrightarrow{B}\) then the angle between vec A and \(\overrightarrow{B}\) will be

A zener of breakdown voltage V_Z = 8 V and maximum Zener current, I_ZM = 10 mA is subjected to an input voltage V_i = 10 V with series resistance R = 100 Ω. In the given circuit R_L represents the variable load resistance. The ratio of maximum and minimum value of R_L is __________.

The escape velocity of a body on a planet ‘A’ is 12 kms^–1. The escape velocity of the body on another planet ‘B’, whose density is four times and radius is half of the planet ‘A’, is

At a certain place the angle of dip is 30° and the horizontal component of earth’s magnetic field is 0.5 G. The earth’s total magnetic field (in G), at that certain place, is

A longitudinal wave is represented by \(x=10 \,sin⁡\,2π (nt−\frac{x}{λ})cm\). The maximum particle velocity will be four times the wave velocity if the determined value of wavelength 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 \(\frac{7}{5}\), is \(\frac{1}{\alpha}\). The value of \(\alpha\) is _________.

In figure (A), mass ‘2 m‘ is fixed on mass ‘m‘, which is attached to two springs of spring constant k. In figure (B), mass ‘m‘ is attached to two springs of spring constant ‘k‘ and ‘2k‘. If mass ‘m‘ in (A) and in (B) are displaced by distance’ x’ horizontally and then released, then time period T1 and T2 corresponding to (A) and (B) respectively follow the relation.