Recently Active Fundamentals Questions

Prove that for any " x , y > 0 " , x x + y y ≥ x y + y x ...

two planes 1 and 2 hit a plane in succession . the probability of 1 and2 scoring hit correctly is 0.3 and 0.2 respectively. The second plane will bomb only if 1misses it. probability the target is hited by 2nd one ans-0.32 ...

A four-digit number has the following properties: (a) It is a perfect square; (b) Its first two digits are equal (c) Its last two digits are equal. Find all such four-digit numbers. (RMO '91) ...

A rectangular sheet of paper is folded so that two diagonally opposite corners come together. If the crease formed is the same length as the longer side of the sheet, what is the ratio of the longer side of the sheet to the s ...

What digit is the least frequent between the numbers 1 and 1,000? ...

Find the sum of all four digit palindromes. ...

two planes 1 and 2 hit a plane in succession . the probability of 1 and2 scoring hit correctly is 0.3 and 0.2 respectively. The second plane will bomb only if 1misses it. probability the target is hited by 2nd one ans-0.32 ...

two planes 1 and 2 hit a plane in succession . the probability of 1 and2 scoring hit correctly is 0.3 and 0.2 respectively. The second plane will bomb only if 1misses it. probability the target is hited by 2nd one ans-0.32 ...

two planes 1 and 2 hit a plane in succession . the probability of 1 and2 scoring hit correctly is 0.3 and 0.2 respectively. The second plane will bomb only if 1misses it. probability the target is hited by 2nd one ans-0.32 ...

Given a cyclic quadrilateral with side lengths a,b,c,d the area K can be found as: K=\sqrt{(s-a)(s-b)(s-c)(s-d)} ...

I was going through Play with graphs. There the graph of \sin^{-1} sinx is given . Though the graph happens to be okay. I got one problem. IT SUGGESTS students to learn defination of it like x+2Î ; -5Î /2<= x<= -3Î /2 - ...

Find the remainder when 599 is divided by 13? ...

*Image* which concept is involved here? ...

which concept is involved here? *Image* ...

Find the maximum number of sides of a n-sided polygon, the sum of all the angles of which is less than 2011° and hence find the sum of all the interior angles of the polygon. ...

Does there exist a power of 2, such that its digits (in decimal representation) can be permuted to form a different power of 2? ...

i have ml khanna,arihant objective approach and TMH for mathematics but they dont have proofs of various theorems,properties. please suggest a book which has theory as well as proofs of all the theorems,properties of the chap ...

I wiill put up some good questions of AM GM inequality only... So that you all can try them.. some of themwill be very very easy.. others will be a bit more tough... So try them all one by one.. I will try to post them in ord ...

A circle is given by the following eqn x^2+y^2=a^2 . Also given a is any real no. Which of the following options may represent the total number of integral points inside the circle? a) 11008 b) 11009 c) 11010 d) 11011 ...

A nice problem ;) (who am i to rate ? :P) If u choose 5 distinct real numbers there must exist some a and b for which the following inequality is valid |ab+1| > |a-b| Prove it!! source : ISI workbook ...

Prove that the number nm(n-m) is even for any integers n & m ...

The greatest integer n such that (42)n divides 2011! is (A)330 (B)331 (C)332 (D)333 ...

prove the expression is non zero if p≠q≠r pq(p-q) + qr(q-r) + rp(r-p) sort of doubt actually :) ...

*Image* In the above figure we see four line segments intersecting at A,B,C and D respectively. LA = 900, LC = 900. Surely, LB = LD = 900. So how can we prove it theoretically...! Practically its true and obvious but can that ...

Which mathematics book(s) are best for concept clearance for IIT-JEE which explains every topic from the zero level ? ...

*Image* There are six circles of equal radius and are arranged as an equilateral triangle. Find the radius of the circle. ...

*Image* Can we say that it is a function? "of form x = f(y) " ...

why is the total number of real numbers equal to thenumber of numbers between 0 n 1?? ...

This question might seem silly but this is my doubt. we use mod. function for x2=9 i.e. x=±3 But if we just calculate the √9, we dont write ±3, though both +3 or -3 when squared equal 9. ...

1.Find the number of positive unequal integral solutions of the equation a+b+c+d=20. 2.A five digit number divisible by 3 is to be formed using the number 0,1,2,3,4,5,without repetition.The total number of ways this can be do ...