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limx→0 {(1+3x)1/3-1-x} / {(1+x)101- 1-101x} has the value equal to? ...

easy one... Find the minimum value of the sum of squares of all trigonometric ratios? Hint:Integer-type answer... :P ...

ATTENTION Q7 ) added i'm weak in algebra Pleasse help.So Posting the questions VERY VERY WEAK Q1) Prove that 22225555 + 55552222 is divisible by 7 Q2) If 7 divides 323232 then find the remainder . ans is 4 Q3) Show that 19921 ...

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x2+y2= 2013 How many solutions (x,y) exist such that x and y are positive integers? ...

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show that ∫[sspi][/ss0]|(sin nx)/x|dx ≥ (2/pi)|1+(1/2)+(1/3)+.......(1/n)| ...

A drop with initial mass M falls under the action of the force of gravity and evaporates uniformly losing a mass m each second.What is the work performed by the force of gravity during the time interval from the start to the ...

The number of points in space (x, y, z), whose each coordinate is a negative integer such that x+y+z+12=0 is ...

In the periodic table,note that for the main group elements,if the periodic group of the element is even,the monoatomic ion and the oxyanions of the element have charges that are even numbers,while if the periodic group numbe ...

43. The number of times the function f (x) = 2009 Σ x/x-r vanishes is r=1 (A) 0 (B) 2008 (C) 2010 (D) 1 ...

If you rub a piece of gold, Au, vigorously, you can rub off 2.00 moles of gold atoms in a century. How many minutes are needed to rub off 1.50 micrograms of gold? ...

If a,b,c are integers and are the sides of a right angle triangle,where c is the largest,prove that the area of that triangle is divisible by 6. ...

Find the number of ordered triplets of natural numbers (x, y, z) satisfying xyz≤10 ...

Newton's 3rd law states that to every action there is an equal and opposite reaction on two different bodies.... But, A ball has mass m. it goes and hits a wall with f=ma. let this force be f1. now change the frame of referen ...

What is the difference between aqueous and alcoholic K(OH) ? ...

The equations of the common tangents to the circles x2 + y2-2x-6y+9=0 and x2+y2+6x-2y+1=0 is/are ? ...

let a1,a2,........an be integers.Show that there exists integers k and r such that the sum ak,ak+1,ak+2+.........ak+r is divisible by n. ...

let nCk denote the binomial coefficient and F[m] be the mth fibonaki number given by F[1]=F[2]=1 and F[m+2]=F[m]+F[m+1] for m≥1.Show that ∩(nCk)=F[m+1] for all m≥1. where n≥k≥0 and n+k=m ...

Prove that if the equation a_{0}x^{n} + a_{1}x^{n-1} + ... + a_{n-1}x = 0 has a positive root x0 then the equation na_{0}x^{n-1} + (n-1)a_{1}x^{n-2} + ... + a_{n-1} = 0 has a positive root less than x0 ...

let f(x)=∫(0 to 1)|t-x|tdt for all real x. What is the minimum value of f(x). ...

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Which of the following substances is a strong electrolyte? ...

A uniform cylinder of steel of mass M, radius R is placed on frictionless bearings and set to rotate about its vertical axis with angular velocity ω0.After the cylinder has reached the specified state of rotation it is heate ...

Let the range of the function f: R→ R f(x) = | x-1| + |x - a| + | x| + |x+1| + |x+ 2a - 21 | a being a real parameter given by [α,∞).Then find the no. of integral values of a for which there is exactly one x0ε R such th ...

A container (both side open is kept inverted as shown in the figure. Dimensions are given in the picture itself. The container is completely filled with a liquid. Find the minimum mass of the container so that it can stay on ...

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How does bleaching powder bleaches water? ...