List of top Questions asked in CBSE Class XI

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.

State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:

(a) adding any two scalars, 

(b) adding a scalar to a vector of the same dimensions, 

(c) multiplying any vector by any scalar, 

(d) multiplying any two scalars, 

(e) adding any two vectors, 

(f) adding a component of a vector to the same vector

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 position of a particle is given by r = 3.0t i -2.0t2 j + 4.0 k m.  where t is in seconds and the coefficients have the proper units for r to be in metres.
(a) Find the v and a of the particle? 

(b) What is the magnitude and direction of velocity of the particle at t = 2.0 s ?

A particle starts from the origin at t = 0 s with a velocity of 10.0 j m/s and moves in the x-y plane with a constant acceleration of (8.0 i + 2.0j ) m s-2.

(a) At what time is the x- coordinate of the particle 16 m? What is the y-coordinate of the particle at that time? 

(b) What is the speed of the particle at the time ?

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 ?
Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true?
  1. (a, a) ∈ R, for all a ∈ N
  2. (a, b) ∈ R, implies (b, a) ∈ R
  3. (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.
Justify your answer in each case.
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A±√(A+G)(A-G).

Choose the correct alternative : 
(a) Acceleration due to gravity increases/decreases with increasing altitude.
(b) Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density).
(c) Acceleration due to gravity is independent of mass of the earth/mass of the body.
(d) The formula –G Mm  \(\frac{1}{r_2 }– \frac{1}{r_1}\)  is more/less accurate than the formula mg(r2 – r1) for the difference of potential energy between two points r2 and r1 distance away from the centre of the earth.

Suppose there existed a planet that went around the Sun twice as fast as the earth. What would be its orbital size as compared to that of the earth?

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour ?

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true?
  1. f is a relation from A to B.
  2. f is a function from A to B.
Justify your answer in each case.