List of practice Questions

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height Choose the correct statement out of the following (Assume negligible air friction)

The wavelength of the radiation emitted is $\lambda_0$ when an electron jumps from the second excited state to the first excited state of hydrogen atom If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will be $\frac{20}{x} \lambda_0$ The value of $x$ is
For differentiable function f: R-{0}⟶ R, let 3f(x)+2f(\(\frac{1}{x}\))-\(\frac{1}{x}\)-10, then |f(3)+f(\(\frac{1}{4}\))| is equal to
Identify the correct order of reactivity for the following pairs towards the respective mechanism
pairs towards the respective mechanism
pairs towards the respective mechanism
pairs towards the respective mechanism
pairs towards the respective mechanism
Choose the correct answer from the options given below :

Given below are two statements: One is labelled as Assertion $A$ and the other is labelled as Reason $R$

Assertion (A) : The beam of electrons show wave nature and exhibit interference and diffraction 

Reason (R) : Davisson Germer Experimentally verified the wave nature of electrons

In the light of the above statements, choose the most appropriate answer from the options given below :

Molar mass of the hydrocarbon (X) which on ozonolysis consumes one mole of O3 per mole of (X) and gives one mole each of ethanal and propanone is _______ g mol-1  
(Molar mass of C : 12 g mol-1 , H : 1 g mol-1)

A bowl filled with very hot soup cools from $98^{\circ} C$ to $86^{\circ} C$ in 2 minutes when the room temperature is $22^{\circ} C$. How long it will take to cool from $75^{\circ} C$ to $69^{\circ} C$ ?

A bar magnet with a magnetic moment 50 $Am ^2$ is placed in parallel position relative to a magnetic field of 0.4T. The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is

The integral \(∫^∞_0  \frac{6}{(e^{3x} + 6e^{2x} + 11e{x} + 6)}dx\)
A closed circular tube of average radius 15 cm, whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fit inside the tube. The speed of block is 22 m/s, when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The work done by the tube on the block is J. (Given: g = 10 ms−2)
closed circular tube of average radius 15 cm,
\(max\\{0≤x≤π}\) \(\{x−2\,\, sin. x \,\,cos+\frac{1}{3} sin\,\, 3x \}=\)
The titration curve of weak acid vs. strong base with phenolphthalein as indictor is shown below. The Kphenolphthalein = 4 × 10-10 . 
Given: log2 = 0.3
The titration curve of weak acid vs. strong base with phenolphthalein
The number of following statements which is/are correct about phenolphthalein is______
A. It can be used as an indicator for the titration of weak acid with weak base.
B. It begins to change colour at pH = 8.4
C. It is a weak organic base
D. It is colourless in acidic medium.

The initial speed of a projectile fired from ground is $u$ At the highest point during its motion, the speed of projectile is $\frac{\sqrt{3}}{2} u$ The time of flight of the projectile is :

If 1000 droplets of water of surface tension 0.07 N/m, having same radius 1 mm each, combine to from a single drop In the process the released surface energy is - (Take π=\(\frac {22}{7}\))
 

Let a =\(\^i+4\^j​+2\^k,b=3\^i−2\^j​+7\^k \,\,\,\,and\,\,\.\ c=2\^i−\^j​+4\^k\). Find a vector d satisfies \(\overrightarrow{d}\times{\overrightarrow{b}}=\overrightarrow{c}\times{\overrightarrow{b}}\) and \(\overrightarrow{d}.\overrightarrow{a}=24\), then \(|\overrightarrow{d}|^2\) is equal to
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 $=6400 \,km$ )