# Solving Quadratic Equations

Many students find solving Quadratic equation problems tough, but students who subscribed to TCYonline solve the toughest of Quadratic equation problems mentally. Let us see how simple it is.

The most frequent question from this topic could be to find whether the roots are

1. Real or Imaginary

2. Rational or Irrational(if they are real)

3. Equal or Unequal

The nature of roots is always dependent on DETERMINANT (D).

Let us consider a Quadratic equation ax²+bx+c=0. Then the determinant would be b²-4ac.

Attempt more questions to practice and prepare for NTSE exam.

Keep visiting TCYonline.com blog for more tips and strategies on NTSE exam.

Remember, we here at TCY are committed to your success.

# NTSE Study Tips on Free Fall Equations - Part-2

Once we have mastered the art of calculating time of flight (refer to part-1), we just need two more principles to calculate total distance mentally as STEPS students do.

Principle 3: the time required to reach max height is half the time of flight.

Principle 4: The average velocity under uniform acceleration is average of initial and final velocities. Since the final velocity is zero, the average velocity is simply half of initial velocity.

Now let us calculate the maximum height of a ball projected up with a speed of 30 m/s which is just the distance travelled up by the projectile before it stops.

Time taken to reach max height =3 s

Average speed is 15 m/s

Max height = 45 m

Isn’t that COOL STUFF! We will cover the case of projectiles in 2-D in the third part.

Attempt more questions to practice and prepare for NTSE exam @ https://www.tcyonline.com/exam-preparation-ntse-olympiad-preparation-and-practice-test/100194/ntse-nsejs-kvpy

Keep visiting TCYonline.com for more Tips and Strategies on NTSE exam.

# NTSE Study Tips on Free Fall Equations - Part-1

Many a student find free fall equations tough, but the students at STEPS (A program run by TCY in Ludhiana, Ambala, Jammu, Karnal and Kurukshetra for NTSE and NSEJS aspirants) just solve the toughest of free fall problems mentally. I would like to share their secret with you.

The first basic principle is the time taken for a change in velocity under uniform acceleration is given by, “change in velocity/acceleration”

The second principle is that when you throw a ball up with a velocity of say 20 m/s, then it returns back with a velocity -20 m/s. So the change in velocity is 40 m/s in the direction of acceleration. To simplify things the change in velocity is simply double the initial velocity.

Using these two principles let us try to calculate time of flight of a ball thrown up with a speed of 25 m/s.

Change in velocity =50 m/s

Acceleration = 10 m/s^^{2}

Time = 5 s

Now isn’t that easy!

Attempt more questions to practice and prepare for NTSE exam @ https://www.tcyonline.com/exam-preparation-ntse-olympiad-preparation-and-practice-test/100194/ntse-nsejs-kvpy

Keep visiting TCYonline.com for more Tips and Strategies on NTSE exam.

# NTSE: Punjab State Level-2013 Analysis of Question Paper

NTSE- State Level -2013 in Punjab was a real dampener. The levels of the questions were not such that the students who qualify the state level would have a good chance of clearing the second level too. Thankfully we didn’t come across any wrong or misprinted questions this year, though some questions in the English section were quite ambiguous. Here is a detailed analysis of the paper.

**Mental Ability Section:**

The mental ability section looked like the author picked 2 questions each from all the chapters of some popular reasoning book. All questions were standard type and there weren’t any innovative problem on the lines of NTSE National 2013. The paper doesn’t provide any advantage to creative problem solvers. Any student can score 100% in this paper through sheer practice.

The Topic Coverage was as under:

Verbal Reasoning |
No of Qns |
Non- Verbal Reasoning |
No of Qns |

Coding -Decoding | 2 | Counting Triangles | 1 |

Number Series | 2 | Water/Mirror Images | 4 |

Words and letter arrangement | 4 | Completing figure matrix | 2 |

Direction sense | 2 | Paper folding | 2 |

Logical ordering | 2 | Analogy figures | 2 |

Inserting missing characters | 3 | Classification of Figures | 2 |

Dice Problems | 2 | Series of Figures | 2 |

# Forceful way to solve the Force Problems: The Free Body Diagram Approach

**What do you do when you realize that a Force problem has popped up in your test? Try this problem and we will discuss what to do.**

**Problem:** In a two-dimension tug-of-war, three person Mr. A, Mr. B & Mr. C pull horizontally on an automobile tire at the angles shown in the over head view of figure(a) below. The tire remains stationary in spite of the three pulls. Mr. A pulls with a force Fa of magnitude 220N, and Mr. C pull with a force F_{c }of magnitude 170 N. The direction of F_{c }is not given. What is the magnitude of Mr. B’s force Fb ?

This is an ideal question where I can give a lot of insight into, how to read a problem, break it down and analyze it.

What’s your first step? Let’s use this problem as an opportunity to practice the Process.

**Reading Force Problems**

Read the problem statement several times until you have a good mental picture of what the situation is, what data is given, and what is required. If you know what the problem is about but don’t know what to do next, put the problem side and reread the text. If you are hazy about Newton’s Second Law, reread that section. Study the sample problems. And remember, solving physics problems (like repairing cars and designing computer chips) takes training- you were not born with the ability.