List of practice Questions

In Young's double slits experiment, the position of $5^{\text {th }}$ bright fringe from the central maximum is $5 \,cm$ The distance between slits and screen is $1 \,m$ and wavelength of used monochromatic light is $600 \,mm$ The separation between the slits is:
The number of following statement/s which is/are\(\text{\underline{ incorrect}}\) is______  
(A) Line emission spectra are used to study the electronic structure  
(B) The emission spectra of atoms in the gas phase show a continuous spread of wavelength from red to violet  
(C) An absorption spectrum is like the photographic negative of an emission spectrum  
(D) The element helium was discovered in the sun by spectroscopic method.

Three bulbs are filled with CH4, CO2 and Ne as shown in the picture. The bulbs are connected through pipes of zero volume. When the stopcocks are opened and the temperature is kept constant throughout, the pressure of the system is found to be_______atm. (Nearest integer)
A message signal of frequency $5 \,kHz$ is used to modulate a carrier signal of frequency $2\, MHz$ The bandwidth for amplitude modulation is:
In chromyl chloride, the number of d-electrons present on chromium is same as in (Given at no. of Ti : 22, V : 23, Cr : 24, Mn : 25, Fe : 26)
\((S1) : lim_{n→∞}\frac{1}{ n ^2} ( 2 + 4 + 6 + . . . . + 2n) = 1\)
\((S2):  lim_n→∞\frac{1}{n^{16}}( 1^15 +2^15 +3^15 + . . . . + n^15 ) = \frac{1}{16} \)
The root mean square velocity of molecules of gas is
A parallel plate capacitor has plate area $40\, cm ^2$ and plates separation $2\, mm$ The space between the plates is filled with a dielectric medium of a thickness $1 \,mm$ and dielectric constant $5$ The capacitance of the system is :
Let s1, s2, s3,…..,s10 respectively be the sum to 12 terms of 10 A.P.s whose first terms are 1,2,3, …. ,10 and the common differences are 1, 3, 5, …. , 19 respectively. Then  \(10∑^{10}_{i=1} s_i\) is
Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth It is found that when a particle is released in this tunnel, it executes a simple harmonic motion The mass of the particle is $100 \,g$ The time period of the motion of the particle will be (approximately)(Take $g=10 \, m s ^{-2}$, radius of earth $=6400 \,km$ )
A Carnot engine with efficiency $50 \%$ takes heat from a source at $600 \,K$ In order to increase the efficiency to $70 \%$, keeping the temperature of sink same, the new temperature of the source will be :
For the system of linear equations  
2x+4y+2az=b
x+2y+3z=4 
2x-5y+2z=8 
which of the following is NOT correct ?  
"Konark Samman" is given for the significant contribution in the field of
20 mL of calcium hydroxide was consumed when it was reacted with 10 mL of unknown solution of H2SO4. Also 20 mL standard solution of 0.5 M HCI containing 2 drops of phenolphthalein was titrated with calcium hydroxide the mixture showed pink colour when burette displayed the value of 35.5 mL whereas the burette showed 25.5 mL initially. The concentration of H2SO4 is_____M (Nearest integer)
Let \( \alpha_1, \alpha_2, \dots, \alpha_7 \) be the roots of the equation \( x^7 + 3x^5 - 13x^3 - 15x = 0 \) and \( |\alpha_1| \geq |\alpha_2| \geq \dots \geq |\alpha_7| \). Then \( \alpha_1 \alpha_2 - \alpha_3 \alpha_4 + \alpha_5 \alpha_6 \) is equal to:
An organic compound on combustion gives 0.22 g of CO2 and 0.126 g of H2O. If the percentage of C in given organic compound is 40%, the percentage of H will be?
Let \({a_k}\) and \({b_k}\), \(𝑘∈N\), be two G.P.s with common ratios \(r_1\) and \(r_2\) respectively such that \(a_1= b_1=4\) and \(r_1<r_2\). Let \(c_k=a_k+b_k\), \(k∈N\). If \(c_2=5\) and \(c_3=\frac {13}{4}\), then \( \displaystyle\sum_{k=1}^{∞ }c_k−(12a_6+8b_4)\) is equal to _____ .
Bob P is released from the position of rest at the moment shown. If it collides elastically with an identical bob Q hanging freely then velocity of Q, just after collision is (g = 10 m/s2).
In Young's double slit experiment, two slits $S_1$ and $S_2$ are ' $d$ ' distance apart and the separation from slits to screen is $D$ (as shown in figure) Now if two transparent slabs of equal thickness $0.1 \,mm$ but refractive index $1.51$ and $1.55$ are introduced in the path of beam $(\lambda=4000 \mathring {A})$ from $S_1$ and $S_2$ respectively, The central bright fringe spot will shift by ______ number of fringes
Young's double slit experiment, two slits S1 and S2 are ' d ' distance apart and the separation from slits to screen is D
A metal surface of 100 cm2 area has to be coated with nickel layer of thickness 0.001mm. A current of 2A was passed through a solution of Ni (NO3)2 for 'x' seconds to coat the desired layer. The value of x is_____ (Nearest integer)
 (PNi (density of Nickel) is 10 gmL-1, Molar mass of Nickel is 60 gmol-1 F = 96500 C mol-1)
A thin uniform rod of length $2 m$, cross sectional area ' $A$ ' and density ' $d$ ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$ If value of $\omega$ in terms of its rotational kinetic energy $E$ is $\sqrt{\frac{\alpha Ad }{ Ad }}$ then value of $\alpha$ is _____ .
Let \(A\) be a symmetric matrix such that \(|A|=2\) and \(\begin{bmatrix} 2 & 1 \\[0.3em] 3 & \frac 32 \\[0.3em] \end{bmatrix}𝐴−\begin{bmatrix} 1 & 2 \\[0.3em] α & β \\[0.3em] \end{bmatrix}\). If the sum of the diagonal elements of \(A\) is \(s\), then \(\frac {βs}{α^2}\) is equal to ____ .
A point source of light is placed at the centre of curvature of a hemispherical surface The source emits a power of $24\, W$ The radius of curvature of hemisphere is $10\, cm$ and the inner surface is completely reflecting The force on the hemisphere due to the light falling on it is ______ $\times 10^{-8} N$

In the following circuit, the magnitude of current $I _1$, is ______ A

If the gravitational field in the space is given as $\left(-\frac{K}{r^2}\right)$ Taking the reference point to be at $r =2\, cm$ with gravitational potential $V =10 \,J / kg$ Find the gravitational potential at $r =3\, cm$ in SI unit (Given, that $K =6 \,Jcm / kg$)