Ask a Question

Feed

All

Lesson Posted 2 days ago Exam Coaching/Engineering Entrance Coaching Exam Coaching/Math Olympiad CBSE/Class 11

Pulkit

I have rich experience of a decade of guiding and mentoring students across the country who are aspiring...

JEE 2011 Question on Logarithm Let (x0,y0) be the solution of the following equations: (2x)ln2 = (3y)ln3 3lnx = 2lnyThen x0 is(A)1 6(B)1 3(C)1 2(D) 6Answer and Comments: (C). We can treat the data as a system of equations in the unknowns lnx and lny instead of x and y. This is permissible because a... read more

JEE 2011 Question on Logarithm

Let (x0,y0) be the solution of the following equations: (2x)ln2 = (3y)ln3 3lnx = 2lny

Then x0 is

(A)

1 6

(B)

1 3

(C)

1 2

(D) 6

Answer and Comments: (C). We can treat the data as a system of equations in the unknowns lnx and lny instead of x and y. This is permissible because a (positive) real number is uniquely determined by its logarithm. So, taking logarithms, we get

(ln2)2 + (ln2)(lnx) = (ln3)2 + (ln3)(lny) (1) (ln3)(lnx) = (ln2)(lny) (2)

which can be treated as a system of linear equations in the unknowns lnx and lny. Eliminating lny from the two equations gives (ln2)3 + (ln2)2(lnx)−(ln3)2(ln2) = (ln3)2(lnx) (3)

5

which simpliï¬?es to [(ln3)2 −(ln2)2](lnx) =−(ln2)[(ln3)2 −(ln2)2] (4) As (ln3)6= ±(ln2), we cancel the bracketed factor and get lnx = −ln2 (5) which gives x = 1/2. Once the key idea strikes, viz. to take lnx and lny as the variables, the problem is straightforward. The properties of logarithms needed are elementary and standard. Nowhere we have to convert logarithms w.r.t. one base to those w.r.t. another.

Like 0

Comments Lesson Posted on 04 Apr Language/Hindi Language/Hindi Speaking CBSE/Class 1/Maths Exam Coaching/Math Olympiad

Maths Online Tutor, Hindi Online Tutor

Nisha T.

Real time two-way audio and video interactive classes on white board using digital pen tablet. I am...

Real time two-way audio and video interactive classes on whiteboard using digital pen tablet.I am a highly qualified and experienced online tutor, teaching Maths and Hindi. I have taught more than 7000 sessions too and have more than 100 students worldwide. I teach home schooling students also. I teach... read more

Real time two-way audio and video interactive classes on whiteboard using digital pen tablet.

I am a highly qualified and experienced online tutor, teaching Maths and Hindi. I have taught more than 7000 sessions too and have more than 100 students worldwide. I teach home schooling students also. I teach students of all ages from 3 years to 99 years old.

I teach all topics in Maths including Basic maths, pre algebra, algebra, arithmetic, geometry, pre calculus, calculus, probability, statistics etc.

I also teach any curriculum including CBSE, ICSE, IGCSE, IB, KS1, KS2, KS3 etc.

I teach Hindi language (beginner, intermediate, advanced levels).

Teaching and learning on digital whiteboard gives you the benefit of real time interaction. You can write, draw, chat, audio, video etc. in real time. Scheduling of classes can be flexible.

All your sessions are recorded which enables you to review any time at any place.

So, to have a friendly, interactive and encouraging learning experience for Maths and Hindi, Please contact me.

Contacts

Name NISHA THAKUR

Mobile: +91-9821940507

Skype nishathakur4

Email nishathakur04@gmail.com

Fee Structure

read less

Like 0

Comments Lesson Posted on 05 Mar CBSE/Class 8/Maths Exam Coaching/Math Olympiad

Soumi Roy

I am an experienced, qualified tutor with over 5 years of experience in teaching maths and physics across...

1. ABCD is a parallelogram in which ∠A = 110°. Find the measure of each of the angles ∠B, ∠C and ∠D. 2. Two adjacent angles of a parallelogram are equal. What is the measure of each of these angles? 3. Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure... read more

1. ABCD is a parallelogram in which ∠A = 110°. Find the measure of each of the angles ∠B, ∠C and ∠D.

2. Two adjacent angles of a parallelogram are equal. What is the measure of each of these angles?

3. Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each of its angles.

4. Two adjacent angles of a parallelogram are (3x - 4)° and (3x + 16)°. Find the value of x and hence find the measure of each of its angles.

5. The sum of two opposite angles of a parallelogram is 130°. Find the measure of each of its angles.

6. Two sides of a parallelogram are in the ratio 5 : 3. If its perimeter is 64 cm, find the lengths of its sides.

7. The perimeter of a parallelogram is 140 cm. If one of the sides is longer than the other by 10 cm, find the length of each of its sides.

read less Like 1

Comments Looking for Math Olympiad classes

Find best Math Olympiad classes in your locality on UrbanPro.

Lesson Posted on 06 Feb Exam Coaching/NTSE exam Coaching Exam Coaching/Math Olympiad

Find The Ratio AE: EC (Important For NTSE Olympiad)

Sujoy D.

1. Strong concept building classes. 2. Weekly tests in weak areas for students to improve their confidence. 3....

Question given below: Solution 1: Solution 2: Solution 3: Solution 4: Draw a line from D... read more

Question given below:

Solution 1:

Solution 2:

Solution 3:

Solution 4:

Draw a line from D parallel to BE cutting AC at P.

CDP and CBE are similar.

EP/EC = BD/BC = 3:5

Also, AFE and ADP are similar.

AE/EP = AD/FD = 2:1

Multiply both the equation from the top, so AE/EC = 6:5.

read less Like 2

Comments Answered on 16/09/2017 Exam Coaching/Math Olympiad

PRAMIT JANA

Tutor

1)3/13,2)4/13

Like 0

Answers 16 Comments Lesson Posted on 28/06/2017 Tuition/Class VI-VIII Tuition Tuition/Class IX-X Tuition Tuition/Class VI-VIII Tuition/Mathematics

Padmini R.

I am an experienced, qualified teacher and tutor with over 15 years of experience in teaching Maths and...

Factorising: 1. Factorising - Expanding Bracket: This section shows you how to factorise and includes examples. Brackets should be expanded in the following ways:a. For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything... read more

1. Factorising - Expanding Bracket:

This section shows you how to factorise and includes examples.

Brackets should be expanded in the following ways:

a. For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket (e.g. 2*x*(*x* + 3) = 2x² + 6x [remember x × x is x²]).

b. For an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.

Example:

Expand (2x + 3)(x - 1):

(2x + 3)(x - 1)

= 2x² - 2x + 3x - 3

= 2x² + x - 3

2. Factorising: Factorising is the reverse of expanding brackets, so it is, for example, putting 2x² + x - 3 into the form (2x + 3)(x - 1). This is an important way of solving quadratic equations.

The first step of factorising an expression is to 'take out' any common factors which the terms have. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1) .

3. Factorising Quadratics: There is no simple method of factorising a quadratic expression, but with a little practise it becomes easier. One systematic method, however, is as follows:

Example:

Factorise 12y² - 20y + 3

= 12y² - 18y - 2y + 3 [here the 20y has been split up into two numbers whose multiple is 36. 36 was chosen because this is the product of 12 and 3, the other two numbers].

The first two terms, 12y² and -18y both divide by 6y, so 'take out' this factor of 6y.

6y(2y - 3) - 2y + 3 [we can do this because 6y(2y - 3) is the same as 12y² - 18y]

Now, make the last two expressions look like the expression in the bracket:

6y(2y - 3) -1(2y - 3)

The answer is (2y - 3)(6y - 1)

Example:

Factorise x² + 2x - 8

We need to split the 2x into two numbers which multiply to give -8. This has to be 4 and -2.

x² + 4x - 2x - 8

x(x + 4) - 2x - 8

x(x + 4)- 2(x + 4)

(x + 4)(x - 2)

Once you work out what is going on, this method makes factorising any expression easy. It is worth studying these examples further if you do not understand what is happening. Unfortunately, the only other method of factorising is by trial and error.

4. The Difference of Two Squares: If you are asked to factorise an expression which is one square number minus another, you can factorise it immediately. This is because a² - b² = (a + b)(a - b) .

Example:

Factorise 25 - x²

= (5 + x)(5 - x) [imagine that a = 5 and b = x]

Like 1

Comments Looking for Math Olympiad classes

Find best Math Olympiad classes in your locality on UrbanPro.

Lesson Posted on 03/06/2017 Tuition/Class IX-X Tuition Exam Coaching/Math Olympiad Exam Coaching/Bank Clerical Exam Coaching

Fast Calculations In Mathematics: (Multiplication Module 1: Part a - Multiplication By 11)

Anshuman singh

1. Worked in IT for 2 years. 2. Worked in family business of stone crushers for 4 years. 3. Overall...

Multiplication Of Any Two-Digit Number (Let Say Ab) By 11: A) WHEN (A+B) IS BETWEEN 0 TO 9: A (A+B) B EXAMPLES: 1) 11 X 42 = 4 ( 4+ 2) 2 = 462 2) 11 X 53 = 5 ( 5+3) 3 = 583 3) 11 X 12 = 1 (1+2)... read more

A) *WHEN (A+B) IS BETWEEN 0 TO 9: *A (A+B) B

EXAMPLES: 1) 11 X 42 = 4 ( 4+ 2) 2 = 462

2) 11 X 53 = 5 ( 5+3) 3 = 583

3) 11 X 12 = 1 (1+2) 2 = 132

4) 11 X 23 = 2 (2+3) 3 = 253

B) *WHEN (A+B) IS GREATER THAN 9*: A ( A+B) B

⇓

CARRY OVER A

Examples: 1) 11 X 57 = 5 (5+7) 7 ⇒ 5 (12) 7 ( Here carry 1 over 5) ⇒ (5+1) (2) 7 = 627

2) 11 X 93 = 9 ( 9+3) 3 ⇒ 9 (12) 3 ( Here carry 1 over 9) ⇒ (9+1) (2) 3 = 1023

3) 11 X 59 = 5 ( 5+9) 9 ⇒ 5 (14) 9 ( Here carry 1 over 5) ⇒ (5+1) (4) 9 = 649

4) 11 X 78 = 7 (7+8) 8 ⇒ 7 (15) 8 ( Here carry 1 over 7)⇒ (7+1) (5) 8 = 858

Problems: Find Out The Following Multiplications Mentally :

1) 11X27, 11X62, 11X71, 11X80, 11X33 , 11X45, 11X90, 11X10, 11X11, 11X42.

2) 11X58, 11X46, 11X79, 11X88, 11X65, 11X89, 11X77, 11X29, 11X56, 11X48.

read less Like 1

Comments Lesson Posted on 06/05/2017 Tuition/Class IX-X Tuition Exam Coaching/Math Olympiad

Shiva Chary

What is a polynomial... In general 'poly' means many and 'nomials' means terms. That means polynomial means having many terms. But this is not the definition, it's just the meaning of the word. Now we will define what is a polynomial, Before going to define, first we define what do we mean by an... read more

What is a polynomial... In general 'poly' means many and 'nomials' means terms. That means polynomial means having many terms. But this is not the definition, it's just the meaning of the word.

Now we will define what is a polynomial,

Before going to define, first we define what do we mean by an algebraic expression. It's an important word which we use in maths.

ALGEBRAIC EXPRESSION :

Its a mathematical statement which has combination of variables and constants connected by some or all the arithmetic operations like +,-,x, / etc.

Ex. x+2, y^2-2x+√x etc

**POLYNOMIALS:**

**It's an algebraic expression in which the powers of the variables are non negative integers(whole numbers).**

**Ex. x^2+2x^2.y^2-6 it is a polynomial **

** x^-2 +x-2 it is not a polynomial, because the power of the variable X is negative. **

******For an algebraic expression to be a polynomial

1.The exponent of the variable should be a whole number.

2.There should be no variable in the denominator.

3.A polynomial may contact in n any number of terms but it should have definite number of terms.

read less Like 0

Comments Lesson Posted on 05/02/2017 Tuition/Class I-V Tuition Tuition/Class VI-VIII Tuition Exam Coaching/Math Olympiad

Ipsita Chaudhury

I teach Maths through Cuemath Programme. Cuemath is a sophisticated after-school maths program designed...

Can your child solve this puzzle? What is the 4th number in the following series - 2B 9D 30F 93H ?

Like 0

Comments Looking for Math Olympiad classes

Find best Math Olympiad classes in your locality on UrbanPro.

Lesson Posted on 06/01/2017 Tuition/Class IX-X Tuition Tuition/Class VI-VIII Tuition Exam Coaching/Engineering Entrance Coaching/GATE Coaching

Ch 1- Mutliplication short tricks by Ashish Vastri..

Ashish Vastri

I am teaching Maths since 4 years and I have taught from Basics to advance mathematics. I am an avid...

1. HOW TO MUTLIPLY 2 digit number by 11? Example 1. 35 * 11 = 385 Step 1. Add both digits of the two digit number. 3+5 = 8. Step 2. Place the result in between both the digits. 3_8_5 = 385 Example 2. 78 * 11 = 858 Step 1. Add both digits of the two digit... read more

**1.** HOW TO MUTLIPLY 2 digit number by 11?

**Example 1. 35** * 11 = 385

**Step 1. **Add both digits of the two digit number.

*3+5 = 8.*

**Step 2. **Place the result in between both the digits.

*3_ 8_5 = 385*

**Example 2. *** 78 ** 11 = 858

**Step 1. **Add both digits of the two digit number.

*7 + 8 = 15*

**Step 2. **Carry "1" when result is greater than 9, and add it to the preceding digit.

*7 + 1 = *

**Step 3.** Place the result in between both the digits...

*8_ 5_8 = 858*

Like 0

Comments UrbanPro.com helps you to connect with the best Math Olympiad classes in India. Post Your Requirement today and get connected.

x

Ask a Question