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Your point seems to be correct hemant.

Wait let me think on it.

What do you think about my explanation?

Aby oye,

Tumne likha hai (since powers are equal, base can be equated)

This is no property.

The real property is-when bases are equal, powers can be equated.

According to what you have written it is also true that 1²=2²=3²=.........=n².

Which is not true.

Now I think you should give me a salute as you promised.

Kislay,
I have the solutions of IRODOV. In those solutions, the question is solved with the help of coriolis force which is not in our JEE syllabus.
Remember that when you are doing IRODOV, you do only those questions which are relevent to JEE so that you don't end up wasting ur time.

First of all I want the questions from the point of view of competetions ,that is, objective questions.
Secondly I want them on the internet. I am not going to buy a book just to do one chapter.

Priyesh,
your solution seems to be correct, But my doubt is that total number of numbers are coming out to be 15625 and ur answer is 1405,
Can there be such a large difference??????
Because only a few cases are neglected w.r.t to total numbers in this question. Only those cases are neglected which have every number only once.
SO are there as many cases as 14220?????
I don't think so.

Yes Rahul, this question is from RMO-2007.

DId anyone give the Regional Maths Olympiad held on 7 oct? Organised be Homi Bhabha centre for science education.

Do you know about the cut-offs? When will the results of Delhi region be announced. In the site of HBCSE, the results of Greater Mumbai region are given.

Its an easy question.

Let

1=@

Then

3=@ (AC=AP)

Now as AB=AC,

1=

(2+4) = @

2=180-2@

Therefore,

4 = 3@-180

But as AP=AQ,

Therefore,

6=3@-180

Now

5=540-6@ (Sum of angles in a triangle =180)

Therefore,

7=5@-360 (linear angle=180)

As QP=QB,

8=5@-360

Now

8+

1+

2+

4=180

Solving we get, @=540/7

But

B= 5@-360

Therefore

B=180/7

Rate me if satisfied,

Nudge me if not understood.

Answer must be (d).

Let the radius of first circle be R
Then the radius of second circle is coming out to be Rsin@.

Now 0Case 1- when both circles are same, then the angle between tangents at a point will be 180.
Case 2- when the second cirlce is inside the first, no tangent can be drawn from outer circle to inner.

Hence the answer is (d).
Rate me if I am correct.
Nudge me if not understood.

Rajat,
your answer is right but the solution not satisfactory.
How can you prove that min is reached when a=b=c=d?

Find all the pairs (a,b) of real numbers such that whenever

is a root of x²+ax+b=0,

² - 2 is also a root of the equation.

I don't know the answer so please post solution along with the answer.

Rates assured.

I am studying salt analysis these days. I want to practice more & more questions on this topic.

Can you please provide some website which has good questions of salt analysis? Its really important for me.

Rates assured.

How many 6 digit numbers are there such that any digit that appears in the number appears at least twice.

(Example-225252 is an admissible number while 222133 is not)

Numbers are to be chosen from the set {1,2,3,4,5}

I don't know the answer. Please post ur solutions.

Rates assured.

Rate me if you think the question was useful and challenging.