Recently Active Fundamentals Questions

You have 2 balls. Both are identical in size and mass, but one is made of gold and is hollow,the other is not hollow and made from titanium. Find out which is which ball, and lets say both are covered with a black paint that ...

There is a machine with 8 toys in it that each cost between 25 cents and 2 dollars, with each toy being 25 cents more expensive than the next most expensive one. Each time Sam presses the big red button on the machine, the ma ...

Which of these is true? Infinity a perfect square? Infinity is a Real Number Infinity is a Even number It is an odd number It is both even and odd It is neither even nor odd It is a Integer It is a rational number It is an ir ...

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits,1,2 and 3 only,is: a)55 b)66 c)77 d)88 I got b)66 as the answer but tata mcgraw hill says that c)77 is the answer.who is ri ...

Just tell me this. When we have an inequality a < x < b where b > a, does it imply that x > a AND x < b or x > a OR x < b? Put in set theory, is it a union or an intersection? ...

Is zero (0) a positive no., negative or both? Why is the set of non-negative reals defined as [0,∞) and negative reals as (-∞, 0)? ...

Find an 8 digit no. whose 1st digit tells how many zero(s)are there, 2nd tells how many one(s)are there, 3rd digit tells how many two(s) are there and so on in the number. ...

There are 5 ships in a port. 1. The Greek ship leaves at six and carries coffee. 2. The ship in the middle has a black chimney. 3. The English ship leaves at nine. 4. The French ship with a blue chimney is to the left of a sh ...

Three boxes contain 600 balls each. The first box contains 600 identical red balls, the second box contains 600 identical white balls and the third box contains 600 identical blue balls. From these three boxes, 900 balls are ...

If a circle of radius r is inscribed in a n-sided regular polygon,and the perimeter is 2p,find the polygon's area. ...

A triangle,a circle,and a square are isoperimetrical.Arrange the areas in increasing way. Please urgent. ...

1.How many 4 digit numbers divisible by 4 can be made with the digits 1,2,3,4,5 if repitition of the digits is not allowed? 2.Determine the number of natural numbers smaller than 104,in the decimal notation of which all the d ...

\large \\ f=\left\{\left(1,3 \right),(2,5),(3,7) \right\} \newline g=\left\{\left(3,7 \right), (5,9), (7,10) \right\} \newline\newline \:give\: reasons\: why\: fog\: is\: not\: possible ...

Prove:::::::: If gcd(a,n)=1,then the integers c,c+a,c+2a,c+3a,...........................,c+(n-1)a form a complete set of reidues modulo n, for any c. ...

Prove that any integer of the form 3k+2 also has a prime factor of the form 3k+2............ ...

this thread is mainly intended to give some insight into congruences and how to solve various jee related problems using that concept.. definition of congruent: A number `a` is said to be congruent to `b` modulo `m` if `m` di ...

*Prove that every integer of the form n^4+4 is always composite......... ...

Fifteen boys are standing on a field, and each of them has a ball. No two distances between two of the boys are equal. Each boy throws his ball to the boy standing closest to him. (a) Show that one of the boys does not get an ...

1) Let S=1+\frac{1}{2}+\frac{1}{3}+...\frac{1}{2^n-1} . S lies between a) 0 & n/2 b) n/2 & n c) n and 2n d) none. 2) IIT-1996. Let f(x) be evn. Given f(x) satisfies f(x)=f\left(\frac{x+1}{x+2} \right) find all possible values ...

1.Prove that 24 divides 2.7^n+3.5^n-5.(n>=1) 2.Prove that the sum of the squares of two odd integers cannot be a perfect square. 3.If there exists x and y for which ax+by=gcd(a,b),then gcd(x,y)=1.(a,b are integers) 4.Prove ...

what is the highest power of 30! that divides 3000! ? ...

Using binomial theorem, the value of (0.999)3 correct to 3 decimal places is (A) 0.999 (B) 0.998 (C) 0.997 (D) 0.995 ...

If the rate of increase of the radius of a circle is 5 cm/.sec., then the rate of increase of its area, when the radius is 20 cm, will be (A) 10Ï€ (B) 20Ï€ (C) 200Ï€ (D) 400Ï€ ...

The number of points on the line x + y = 4 which are unit distance apart from the line 2x + 2y = 5 is (A) 0 (B) 1 (C) 2 (D) Infinity ...

Angle between y2 = x and x2 = y at the origin is ...

How many odd integers from 1000 to 8000 have distinct digits a)2520 b)1736 c)1680 d)1920 ...

A very simple one... specially the 2nd one... a) if x+y+z=0, x3+y3+z3=3xyz b) Prove that if x, y, z are positive, x3+y3+z3≥3xyz ...

The last 3 digits of 79999 are a)523 b)143 c)343 d)263 ...

it is in my belief that we live in a 3d world and we require a different level of mind to understand a 4d world.if there are certain creatures which live in a 4 d world,they will have a totally different conditions of living ...

If A is a non empty set, then R ⊂ A × A is said to be a relation on A. A relation R on 'A' is said to be (i) Reflexive if aRa, i.e. (a, a) ∈ R ≠a ∈ A. (ii) Symmetric if aRb then bRa i.e. if (a, b) ∈ R then (b, a) â ...