Mathematics

Sets

Notes

1. Introduction
2. Methods of representing a set
3. Types of sets
4. Subset and Proper Subset
5. Subset of set of the real numbers
6. Interval as subset of R Real Number
7. Power Set
8. Universal Set
9. Venn diagram
10. Operation on Sets

Assignment

Assignments

NCERT Solutions

NCERT Solution1

Relations & Functions for Class11

Notes

1. What is Cartesian Sets
2. What is relations?
3. What is Function
4. Algebra of Real Function

Assignments

Assignments

Trigonometry and its function

Notes

Introduction

What is angle

Degree and Radian

Trigonmetric Ratio's

Trignometric functions

Domain and Range of trigonimetric functions

Trigonometrics function of Sum and difference of angless

Trigonometric equations

Mathematical induction

Notes

1. What is Deductive reasoning
2. What is Inductive reasoning
3. The Principle of Mathematical Induction<
4. Solved Examples

Assignments

Assignments

complex numbers

Notes

1. What is complex numbers
2. Properties Of complex Numbers
3. Conjugate of Complex Numbers
4. Modulus of complex numbers
5. Graphical Representation of Complex Number
6. Polar Representation of the complex number
7. Rotation of Complex Number
8. What is the significance of Complex Numbers

NCERT Solutions

NCERT Solution1

Quadratic equation

Notes

1. Flashback of Quadratic equation
2. Complex Roots of quadratic equations

Linear Inequalities

Notes

1. What are inequalities
2. Things which changes the direction of the inequality
3. Linear Inequation in One Variable
4. Linear Inequation in Two Variable
5. Quadratic Inequation
6. Steps to solve the inequalities in one variable
7. Steps to solve the inequality of the another form
8. Steps to solve Quadratic or polynomial inequalities
9. Absolute value equation
10. Absolute value inequation
11. Graphical Solution of Linear inequalities in Two Variable

NCERT Solutions

NCERT Solution1

Permutation

Notes

1. What is factorial
2. Fundamental Principle of counting
3. Permutation
4. Restricted Permutations
5. Another Theorem of Permutation

NCERT Solutions

1. NCERT Solution1
2. NCERT Solution2

Combination

Notes

1. What is combination
2. Combination Formula
3. Properties of Combination Formula

Binomial Expansion

Notes

1. Binomial Theorem
2. Important conclusion from Binomial Theorem
3. General Term in Binomial Expansion
4. Middle Term in Binomial Expansion

Probability for Class11

Notes

1. What is Probability
2. Terms related to Probability
3. Algebra of events operations<
4. Classical Probability
5. How to Solve Probability questions
6. Addition Theorems on Probability
7. Solved examples

Relations and Functions

Notes

1. What is Cartesian Sets
2. What is relations?
3. What is Function
4. Algebra of Real Function
5. Type Of Relations
6. Type Of Functions
7. Composite Function
8. Invertible Function

Vector Algebra

Notes

1. What is vector
2. Difference between Scalar and Vector
3. Type Of Vectors
4. Addition Of vector
5. Subtraction of vectors
6. Scalar multiplication of vectors
7. Components of the vector
8. Multiplication of two vectors
9. Dot product of vectors
10. Cross product of vectors
11. Triple product
12. How to solve vector algebra problems

Vidoes

vector addition and subtraction

Vectors and their properties

Algebra of Matrices

Notes

1. What is Matrix
2. Types of Matrices
3. Equality of Matrices
4. Addition (and Subtraction) of Matrices
5. Properties of Addition
6. Identity Matrix
7. Scalar of  Multiplication/Division Matrix
8. Multiplication Of Matrix
9. Transpose of Matrix
10. Why study the Matrix
11. How to Solve Matrix Problem
12. Solved Examples

Worksheets

Matrices Worksheet-1

Matrices Worksheet-2

Matrices Worksheet-3

Matrices Worksheet-4

Probability

Notes

1. Flashback of Class11 Notes
2. What is Conditional Probability
3. Multiplication Theorem on Probability<
4. Total Probability Law
5. Solved example
6. Bayes Formula
7. Solved examples

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Problems set on motion (Kinematics part 2)

Paragraph type question
(A) A Man X drops a stone from the fifteen floor of the building .A Man Y ascending in an elevator at a  constant speed v=10 m/s passed the Fifteen floor just as the stone is released
Question 1
Find the position, velocity of the stone as seen by the Man X at time t=2 sec
a. (19m ,19m/s)
b. (19.6m,19.6m/s)
c. (10m,10m/s)
d (11m,12m/s)
Question 2
Find the position, velocity of the stone relative to Man Y at 3 sec
a. (39m, 70m/s)
b. (19m, 70m/s)
c. (70m, 39 m/s)
d. (14 m, 29m/s)
Question 3
Find the acceleration of the stone with respect to Man X and Y.
a. (9.8 m/s², 9.8m/s²)
b. (9 m/s², 10 m/s²)
c. (10 m/s², 10m/s²)
d. None of these
(B) A particle moves such a way that

where i and j are unit vectors along x and y direction. A and ω are constant
Question 4
Find the trajectory of the particle

1. Circle
2. Parabola
3. Eclipse
4. None of the above

Question 5
Find the average velocity of the particle from t=0 to 

Question 6
Find the scalar Product of Acceleration and velocity at any point t
a. 1
b. -1
c. 0
d. None of the above
Question 7
Find the tangential acceleration at any point of time t

Question 8
Find the radial acceleration at any point of time t

Question 9



(C) A gun is mounted on a train roof .Train is travelling with the velocity v in north direction. A car is also moving on a parallel track with train with velocity w in north direction. Two bullet are fired from the muzzle of the gun .Take north as positive and south as negative
Question 10
 Bullet one is fired in the north direction with the muzzle velocity u. Find the velocity of the bullet as seen from the observer on the earth
a) u+v
b) u-v
c) u
d) v
Question 11
Find the velocity of the bullet as seen from the observer on the moving car
a u+v-w
b u-v-w
c u
d v
Question 12
Bullet one is fired in the south direction with the muzzle velocity u. Find the velocity of the bullet as seen from the observer on the earth
a u+v
b v-u
c u
d v
Question 13
Find the velocity of the second bullet as seen from the observer on the moving car
a u+v-w
b v-u-w
c u
d v
(D) A train is moving in the west direction with a velocity 15m/s.A monkey runs on the roof of the train against its motion with a velocity  5m/s with respect to train .Take the motion along west as positive
Question 14
Velocity of train relative to its driver
a. 0
b. 15 m/s
c. -15 m/s
d. 20 m/s
Question 15
What is the velocity of train with respect to monkey
a. 5m/s
b -5 m/s
c. 15 m/s
d -15 m/s
Question 16
Find the velocty of ground with respect to monkey
a. 5 m/s
b. -5 m/s
c. 10 m/s
d. -10 m/s
(E) Two particles start from the origin of the horizontal x-y plane. Particle A moves along +x axis with uniform velocity u. Particle B moves along -y axis with velocity u. i and j are the unit vectors along x and y direction
Question 17
Find the relative velocity of particle B wrt to A at time t
a -u(i+j)
b u(i+j)
c 0
d none of the above
Question 18
 Find the relative velocity of particle A wrt to B at time t
a -u(i+j)
b u(i+j)
c 0
d none of the above
Question 19
 find the relative position vector of particle A wrt to B at time t
a -ut(i+j)
b ut(i+j)
c 0
d none of the above
Answers

1.  (b)
2. (c)
3. (a)
4.  (a)
5. (a)
6. (c)
7. (b)
8. (b)
9. (a)
10.  (a)
11. (a)
12. (b)
13. (a)
14.  (a)
15. (a)
16. (d)
17.  (a)
18. (b)
19. (b)

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Important Questions on Motion in a plane for JEE Main & JEE Advanced part1

(A) A plank of length L is moving in the direction of x-axis in the X-Y plane. A point A is located on the left hand side of the plank. Position of point A at t=0 is (L,0). The plank is moving in the right direction with velocity v
Question 1
 A person standing at point A at t=0 throws a stone with velocity v and at an angle 60⁰ with X axis. Find the co-ordinates of the maximum height reach by the stone

Question 2  
Find the velocity vector at the maximum height if i and j  are the unit vectors along X and Y axis respectively

Question 3
Find the co-ordinates of the stone where its hit the X-axis

Question 4
Find the velocity vector of the stone when it hits X-axis.

Question 5
Find the co-ordinates of the point A on the plank when the stone hit the X-axis

Question 6
Find the maximum value of velocity v so as to land the stone on the plank

(B) Two ring X and Y are put on two vertical stationary rods AB and A^’B^’. An inextensible thread is fixed at point A^’ and on ring X and is passed through ring Y.
The system is shown below in Figure

Question 7
The ring X moves with constant velocity v downwards. The angle AXY is θ. Find the velocity of the ring Y

Question 8
 Find the velocity of ring Y with respect to ring X

(C) A man X can swim at a speed of 10 m/s with respect to river . He wants to cross the river which is 50 m wide and has a current of 5 m/s
If he wishes to land on the other bank at a point directly across the river from his starting point
Question 9
Velocity of man with respect to the person standing on the bank
a) 5
b) 10
c) 6
d)5√3

Question 10
Find the angle made by the man from the current
a) 120⁰
b) 60⁰
c) 30⁰
d) 90⁰
Question 11
Find the time taken by the man to cross the river

(D)Now if he instead decides to cross the river in shortest possible time
Question 12
what direction it should swim
a) 90⁰ to current
b) 30⁰ to current
c) 60⁰ to current
d) none of these
Question 13 
How much time
a) 5
b) 10
c) 6
d) 4
Question 14
 How much distance it will land from his starting point
a) 30
b) 20
c) 25
d) none of these
(E)The radius vector describing the position of the particle A relative to origin

Question 15
 Find the rectangular components of the average velocity in the time interval between t and t+?t

Question 16
 Which of the following statements are true about the motion
a) The particle is experiencing uniform acceleration motion
b) The particle starts at y axis and touched x axis in 1sec
c) The initial velocity is towards negative Y axis
d) The velocity at t=1 is towards positive x axis
(F) A particle is moving along a parabola given by
  y=x²
So that at any time v_x=3 m/s
Question 17
 Find the magnitude and direction of velocity at x=1/3 m

Question 18
Find the acceleration at x=1/3 (both magnitude and direction)
a) 18 m/sec² ,90⁰
b) 14 m/sec² ,60⁰
c) 18 m/sec² ,60⁰
d) 14 m/sec² ,90⁰
(G)An object is fired up on the inclined place of angle α . The object is fired with velocity v₀ and angle of elevation θ with the horizontal
Question 19
Find the range on the inclined plane

Question 20
Find the relation between  and  α for which object will have maximum range

Answers

1. (c)
2. (a)
3. (b)
4. (b)
5. (a)
6. (b)
7. (a)
8. (b)
9. (d)
10. (a)
11. (a)
12. (a)
13. (a)
14. (c)
15. (a)
16. (a),(b),(c),(d)
17. (c)
18. (a)
19. (b)
20. (a)

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