List of practice Questions

If $\alpha, \beta$ are zeroes of the polynomial $8x^2 - 5x - 1$, then form a quadratic polynomial in x whose zeroes are $\frac{2}{\alpha}$ and $\frac{2}{\beta}$.

Two point charges, 4 µC and -3 µC (with no external field) are placed at (-6 cm, 0, 0) and (6 cm, 0, 0), respectively. The amount of work required to separate the two charges infinitely away from each other will be

A current carrying circular loop of area A produces a magnetic field $ B $ at its centre. Show that the magnetic moment of the loop is $ \frac{2BA}{\mu_0} \sqrt{\frac{A}{\pi}} $.

Two slits 0.1 mm apart are arranged 1.20 m from a screen. Light of wavelength 600 nm from a distant source is incident on the slits. How far apart will adjacent bright interference fringes be on the screen?

One term in the given number series is wrong. Find out the wrong term.

A mouldboard plough is operated by a 2WD tractor with 6.0 kN pull. The ratio of lateral component to the longitudinal component of soil forces is 0.30, and the ratio of the vertical component to the longitudinal component of soil forces is 0.50. If the diameter of the driving wheels is 1.2 m and the rear axle rotates at 10 rpm, the drawbar power produced at 20% wheel slip is _________ kW. (Rounded off to 2 decimal places)

Calculate the value of Net Value Added at Factor Cost (NVA\textsubscript{FC}):

S. No.	Particulars	Amount (in ₹ crore)
(i)	Operating Surplus	3,740
(ii)	Increase in unsold stock	600
(iii)	Sales	10,625
(iv)	Purchase of raw materials	2,625
(v)	Consumption of fixed capital	500
(vi)	Subsidies	400
(vii)	Indirect taxes	1,200

Match List-I with List-II \[ \begin{array}{|l|l|} \hline \textbf{Product} & \textbf{Producer} \\ \hline (A) \; \text{Citric Acid} & (I) \; \text{Trichoderma polysporum} \\ \hline (B) \; \text{Ethanol} & (II) \; \text{Monascus purpureus} \\ \hline (C) \; \text{Statins} & (III) \; \text{Saccharomyces cerevisiae} \\ \hline (D) \; \text{Cyclosporin A} & (IV) \; \text{Aspergillus niger} \\ \hline \end{array} \]

$\textit{Statement I:}$ In case of non-financial enterprises, payment of interest and dividends are classified as financing activities, whereas receipt of interest and dividends are classified as investing activities.
$\textit{Statement II:}$ Investing and financing transactions that require the use of cash or cash equivalents, should be excluded from cash flow statement.
Choose the correct alternative from the following:

The following question is based on pollination. Study the figures carefully and answer the questions that follow.

Give the scientific terms for the processes taking place in Figures A and B respectively.
Mention two conditions necessary for the process occurring in Figure B.
- [(i)] State one advantage and one disadvantage of the process occurring in Figure B.
  OR
- [(ii)] Name one plant where, in some flowers only, the process in Figure B takes place and give the reason responsible for it.

A closed organ and an open organ tube filled by two different gases having the same bulk modulus but different densities $ \rho_1 $ and $ \rho_2 $, respectively. The frequency of the 9th harmonic of the closed tube is identical with the 4th harmonic of the open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is $ \rho_1 : \rho_2 = 1 : 16 $, then the length of the open tube is:

A sub-atomic particle of mass $ 10^{-30} $ kg is moving with a velocity of $ 2.21 \times 10^6 $ m/s. Under the matter wave consideration, the particle will behave closely like (h = $ 6.63 \times 10^{-34} $ J.s)

In a resonance tube experiment at one end, resonance is obtained at two consecutive lengths $ l_1 = 100 \, \text{cm} $ and $ l_2 = 140 \, \text{cm} $. If the frequency of the sound is 400 Hz, the velocity of sound is:

Two plane polarized light waves combine at a certain point, whose "E" components are: \[ E_1 = E_0 \sin \omega t, \quad E_2 = E_0 \sin \left( \omega t + \frac{\pi}{3} \right) \] Find the amplitude of the resultant wave.

A composite sound wave is represented by $ y = A \cos \omega t \cdot \cos \omega' t $. The observed beat frequency is:

The amplitude and phase of the wave when two travelling waves given as $ y_1(x, t) = 4 \sin(\omega t - kx) $ and $ y_2(x, t) = 2 \sin\left(\omega t - kx + \frac{2\pi}{3}\right) $ are superimposed.

Two ropes of the same material of radius $ R $ and $ \frac{R}{2} $, what will be the ratio of wave speed in the second rope to the first? (They both are with the same tension)

The displacement $ x $ versus time graph is shown below.

The displacement $ x $ is plotted against time $ t $. Choose the correct answer from the options given below:

Displacement of a wave is expressed as $$ x(t) = 5 \cos \left( 628t + \frac{\pi}{2} \right) \, \text{m}. $$ The wavelength of the wave when its velocity is 300 m/s is:

The equation of a wave travelling on a string is $ y = \sin[20\pi x + 10\pi t] $, where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

A light wave is propagating with plane wave fronts of the type $ x + y + z = \text{constant} $. The angle made by the direction of wave propagation with the $ x $-axis is:

Reactant ‘A’ underwent a decomposition reaction. The concentration of ‘A’ was measured periodically and recorded in the table given below:

Based on the above data, predict the order of the reaction and write the expression for the rate law.

The magnetic field of an E.M. wave is given by: \[ \vec{B} = \left( \frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j} \right) 30 \sin \left( \omega \left( t - \frac{z}{c} \right) \right) \] The corresponding electric field in S.I. units is:

A plane electromagnetic wave of frequency 20 MHz travels in free space along the +x direction. At a particular point in space and time, the electric field vector of the wave is $ E_y = 9.3 \, \text{V/m} $. Then, the magnetic field vector of the wave at that point is:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Electromagnetic waves carry energy but not momentum.
Reason (R): Mass of a photon is zero. In the light of the above statements.
choose the most appropriate answer from the options given below: