List of practice Questions

A convex lens has radius of curvature \( R = 40 \, \text{cm} \) for both surfaces and refractive index \( \mu = 1.5 \). Find the focal length.
If \( r_1 \) and \( r_2 \) are the angles of refraction at the first face and second face of a prism, then the angle of the prism is:
The magnifying power of a telescope with tube length 60 cm is 5. Then the focal length of its eye piece is:
A tank is filled with benzene to a height of \(120~\text{mm}\). The apparent depth of a needle lying at the bottom of the tank, as seen through a microscope, is found to be \(80~\text{mm}\). The refractive index of benzene is
An isolated sphere has a capacitance of 60 pF, what is the radius of the sphere?
Two point charges \(q\) and \(-3q\) are kept 12 cm apart. The distance of the point from \(q\) on the line between two charges at which potential due to this system of charges is zero will be:
A dielectric of dielectric constant $ K $ is introduced such that half of its area of a capacitor of capacitance $ C $ is occupied by it. The new capacity is
When $ 10^{19} $ electrons are removed from a neutral metal plate, the electric charge on it is

Let \(f(x)=\frac{sinx+cosx-\sqrt2}{sinx-cosx},x∈[0.\pi]-\left[\frac{\pi}{4}\right]. Then f\left(\frac{7\pi}{12}\right)f^n\left(\frac{7\pi}{12}\right)\)is equal to

Given below are two statements :
Statement I : The decrease in first ionization enthalpy from B to Al is much larger than that from Al to Ga.
Statement II : The d orbitals in Ga are completely filled. In the light of the above statements,
choose the most appropriate answer from the options given below
If A and B are two matrices such that AB=B and BA=A then A2 + B2 =
State and prove the principle of conservation of angular momentum.
Let the lines l1 :  \(\frac{x+5}{3} =\frac{y+4}{1}=\frac{z−α}{−2}\)  and l2 :3x+2y+z–2=0=x–3y+2z-13 be coplanar. If the point P(a, b, c) on l1 is nearest to the point Q(-4,-3, 2), then |a| + |b|+|c| is equal to
Velocity constant for a first order reaction is \( 2 \times 10^{-3} \, \text{s}^{-1} \). The half-life period for this reaction is
A flask contains Hydrogen and Argon in the ratio 2:1 by mass. The temperature of the mixture is 30°C. The ratio of average kinetic energy per molecule of the two gases (K argon/K hydrogen) is:
(Given: Atomic Weight of Ar = 39.9)
Temperature of a reaction with an activation energy value of 15 kcal mol\(^{-1}\) is increased from 300 K to 310 K. If the value of the ideal gas constant (R) is 1.9872 cal mol\(^{-1}\) K\(^{-1}\), the ratio of the reaction rate constants \(\left(\frac{k_{310}}{k_{300}}\right)\) (rounded off to two decimal places) is ____________.
Answer the following questions:
What is the value of resistance for an ideal voltmeter?
ClF5 at room temperature is:
The osmotic pressure of solutions of PVC in cyclohexanone at $300 K$ are plotted on the graph The molar mass of $PVC$ is ____$g \,mol ^{-1}$ (Nearest integer)
The osmotic pressure of solutions of PVC in cyclohexanone at 300K are plotted
( Given : R = 0.083 L atm K-1 mol-1 )
If in a certain language, GRASP is codes as BMVNK, which word could be coded as CRANE?
Given below are two statements: one is labelled as Assertion A and other is labelled as Reason R.
Assertion A: Amniocentesis for sex determination is one of the strategies of Reproductive and Child Health Care Programme.
Reason R: Ban on amniocentesis checks increasing menace of female foeticide.
In the light of the above statements, choose the correct answer from the options given below
Prove that, “Angles inscribed in the same arc are congruent.”
The stable pattern of ‘modern men’ formulated by Alex Inkeles does not include ________________.

In the following given reaction, ' $A$ ' is

In the following given reaction, ' A ' is

Find the differential equation of the family of curves \[ y = a \sin(x + b), \] where \( a \) and \( b \) are arbitrary constants.