List of practice Questions

Two media A and B are separated by a plane boundary surface. The speed of light in medium A and B are 2 x 108 m/s and 2.5 x 108 m/s respectively. The critical angle for which a ray of light going from A to B will have total internal reflection is A
Energy needed in breaking a liquid drop of radius \( R \), into \( n \) smaller drops each of radius \( r \), is
[ \( T \) - Surface tension of the liquid ]
An object of mass \(10 \, \text{kg}\) is released from rest in a liquid. If the object moves a distance of \(2 \, \text{m}\) while sinking in a time duration of \(1 \, \text{s}\), then the mass of the liquid displaced by the submerged object is (Given: Acceleration due to gravity \( g = 10 \, \text{m/s}^2 \))
Consider the following statements:
(A) Whentemperature increases, the viscosity of gases increases and viscosity of liquids decreases.
(B) Water does not wet an oily glass because the cohesive force of oil is less than that of water.
(C) A liquid will wet a surface if the angle of contact is greater than 90◦.
Which of the following is true?
The movable cylindrical pistons \( P_1 \) and \( P_2 \) of a hydraulic lift are of radii 2 m and \( R \) respectively. A body of mass 32 kg on piston \( P_2 \) is supported by a body of mass 2 kg placed on piston \( P_1 \). The value of \( R \) is
A liquid of density \( \rho \) flows steadily. At point 1, area = \( 2A \), speed = \( \sqrt{2}\ \text{m/s} \); at point 2, area = \( A \), height difference = 10 cm, pressure difference = 100 N/m\(^2\). Find \( \rho \).
Aliquidofdensityρflowssteadily
If the equation of the parabola, whose vertex is at \((5, 4)\) and the directrix is \(3x + y – 29 = 0\), is \(x^2 + ay^2 + bxy + cx + dy + k = 0\), then \(a + b + c + d + k\) is equal to
An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be
[If, g = 10 ms–2 and radius of earth = 6400 km]
The correct structure of C is
structure of C

Let ℝ → ℝ be function defined as
f(x) = αsin(\((\frac{π[x]}{2})\)+[2-x],α∈R
where [t] is the greatest integer less than or equal to t.
If lim x→1 f(x) exists, then the value of\(∫_0^4\) f(x)dx
is equal to

\(250\) \(g\) solution of \(D-glucose\) in water contains 10.8% of carbon by weight. The molality of the solution is nearest to (Given: Atomic Weights are, \(H, 1 u; C, 12 u; O, 16 u\))
The disproportionation of MnO42- in acidic medium resulted in the formation of two manganese compounds A and B. If the oxidation state of Mn in B is smaller than that of A, then the spin-only magnetic moment (μ) value of B in BM is _______. (Nearest integer)
Given below are two statements.
Statement I: \(O_2, Cu^{2+}, \;and\; Fe^{3+}\) are weakly attracted by magnetic field and are magnetized in the same direction as magnetic field.
Statement II: \(NaCl\) and \(H_2O\) are weakly magnetized in opposite directions to the magnetic field.
In the light of the above statements, choose the most appropriate answer from the options given below.
Which of the following methods are not used to refine any metal?
  1. Liquation
  2. Calcination
  3. Electrolysis
  4. Leaching
  5. Distillation
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: Energy of 2s orbital of hydrogen atom is greater than that of 2s orbital of lithium.
Reason R : Energies of the orbitals in the same subshell decrease with increase in the atomic number.
In the light of the above statements, choose the correct answer from the options given below.

Match List-I with List-II

Choose the correct answer from the options given below:
 

Given below are two statements.
Statement I : Hydrogen peroxide can act as an oxidizing agent in both acidic and basic conditions.
Statement II : Density of hydrogen peroxide at 298 K is lower than that of \(D_2O\).
In the light of the above statements, choose the correct answer from the options given below :
Given below are two statements.
Statement I : The chlorides of Be and Al have Cl-bridged structure. Both are soluble in organic solvents and act as Lewis bases.
Statement II : Hydroxides of Be and Al dissolve in excess alkali to give beryllate and aluminate ions.
In the light of the above statements, choose the correct answer from the options given below.
Write the classification of aliphatic ketones with example. What is the action of sodium hypoiodite on acetone?
Let S = {4, 6, 9} and T = {9, 10, 11, …,1000}. If A = {a1 + a2 + … +ak :k∈N, a1, a2, a3, …, ak∈S}, then the sum of all the elements in the set T – A is equal to ____________.
The value of the integral \(\begin{array}{l} \displaystyle\int\limits_0^{\frac{\pi}{2}}60\frac{\sin\left(6x\right)}{\sin x}dx \end{array}\) is equal to ______.

An electron (mass m) with an initial velocity
\(\vec{v}=v_0\hat{i}(v_0>0)\)
is moving in an electric field
\(\vec{E}=E_0\hat{i}(E_0>0)\)
where E0 is constant. If at t = 0 de Broglie wavelength is
\(λ_0=\frac{ℎ}{mv_0}\)
, then its de Broglie wavelength after time t is given by

Which oxoacid of phosphorous has the highest number of oxygen atoms present in its chemical formula?
An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm. The density of the element is 6.0 g cm–3. The number of atoms present in 180 g of the element is ______× 1023. (Nearest integer)
What is the half-life period of a radioactive material if its activity drops to 1/16 th of its initial value in 30 years?