List of top Questions asked in CBSE Class XI

Evaluate the Given limit: \(\lim_{x\rightarrow 0}\)\(\frac{sin\,ax}{bx}\)

Arrange the following types of radiations in increasing order of frequency: 
(a) radiation from the microwave oven 
(b) amber light from a traffic signal 
(c) radiation from FM radio 
(d) cosmic rays from outer space and (e) X-rays.

Nitrogen laser produces radiation at a wavelength of 337.1 nm. If the number of photons emitted is 5.6 × 10²⁴, calculate the power of this laser.

Neon gas is generally used in the sign boards. If it emits strongly at 616 nm, calculate 
(a) the frequency of emission
(b) distance traveled by this radiation in 30 s 
(c) the energy of quantum and 
(d) number of quanta present if it produces 2 J of energy.

Draw appropriate Venn diagram for each of the following: 
(i) (A ∪ B)' 
(ii) A' ∩ B'
(iii) (A ∩ B)'
(iv) A' ∪ B'

Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1^)th to (2n) ^th term is \(\frac{1 }{ r^n}.\)

Let f, g:R\(\to\)R be defined, respectively by f(x) = x+1, g(x) = 2x-3. Find f+g, f-g and \(\frac fg\).

State, for each of the following physical quantities, if it is a scalar or a vector: 
Volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.

Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \(\frac{sin\,ax}{sin\,bx}\) ,a,b ≠0

Pick out the two scalar quantities in the following list:
Force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.

If a, b, c and d are in G.P. show that (a ² + b ² + c ² ) (b 2 + c ² + d ² ) = (ab + bc + cd)².

Pick out the only vector quantity in the following list:
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.

Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

Let f = {(1, 1), (2, 3), (0, -1), (-1, -3)} be a function from Z to Z defined by \(f(x) = ax+ b\), for some integers a, b. Determine a, b.

Read each statement below carefully and state with reasons, if it is true or false:
(a) The magnitude of a vector is always a scalar.
(b) each component of a vector is always a scalar
(c) the total path length is always equal to the magnitude of the displacement vector of a particle.
(d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time,
(e) Three vectors not lying in a plane can never add up to give a null vector

Establish the following vector inequalities geometrically or otherwise:
a) |a + b| ≤ |a| + |b|
b) |a + b| ≥ ||a| − |b||
c) |a − b| ≤ |a| + |b|
d) |a − b| ≥ ||a| − |b||
When does the equality sign above apply?

A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity ? Are the two equal ?

Find the value of n so that \(\frac{a^{n+1}+b^{n+1}}{a^n+b^n }\)n may be the geometric mean between a and b.

A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone ?

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio (3+2√2) : (3-2√2).

Read each statement below carefully and state, with reasons and examples, if it is true or false : A scalar quantity is one that
(a) is conserved in a process
(b) can never take negative values
(c) must be dimensionless
(d) does not vary from one point to another in space
(e) has the same value for observers with different orientations of axes.

Answer the following :
(a) You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means ?
(b) An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity ?
(c) If you compare the gravitational force on the earth due to the sun to that due to the moon, you would find that the Sun’s pull is greater than the moon’s pull. (you can check this yourself using the data available in the succeeding exercises). However, the tidal effect of the moon’s pull is greater than the tidal effect of sun. Why ?