Recently Active Mathematics Questions

Prove that n/3+n2/2+n3/6 is an integer for all integers n! ...

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reduce the differential equation *Image* ...

p(x) is a polynomial with integer coefficients. For some positive integer c, none of p(1), p(2), ... , p(c) are divisible by c. Prove that p(b) is not zero for any integer b. (BHATT SIR STAY AWAY) ...

Find [1+\frac{1}{2}+\frac{1}{3}+....\frac{1}{121}] [] ≡ G.I.F ...

If z=iii.....∞=A+iB then find lzl ...

whts the probabbiliy of a coin falling perfectly in one of the squares of a chess bord 6 x 6 .......if diameter of coin n side of small square is same.. ...

Find the total no. of ways in which 6 "+" and 4 "-" signs can be arranged in a line such that no 2 -ve signs occur together. Ans : 7C4 = 35 Why is it not : 6! x 7P4 ...

There is a square of side 4 units... There are 17 points in the square. Prove that there will be 2 points such that the distance between them is less than equal to √2 (Think of where the number 17 could have come from!) ...

an ellipse has major axis and minor axis lengths as 2a , 2b let the foci be x1,y1 and x2,y2 and h,k be its center and if it slides between co-ordinate axes such that it touches the x and y axis at all times i)find the locus o ...

\int _{0}^{1}e^x(x-1)^ndx=16-6e;n\epsilon N,n\leq 5 ...

Ques) Evaluate the following integral:- *Image* for -1 < x <1 ...

Show that there exist infinitely many positive integers A such that (1) 2A is a perfect square ; (2) 3A is a perfect cube ; (3) 5A is a perfect fifth power. ...

Q)there are 4 boys and 3 girls find the no. of ways to seat them in straight chairs such that no girl sits together. a) 7! b) 4!*3! c) 4!*5*4*3 d) 4!*4! ...

what is remainder when 5 power 5 power 5...... 24 times 5 (the base 5 is also included ) is divided by 24 Plz answer in detail ...

A fuction can be written as the sum of an od an even function if: last yr's tst series question a)its continuous b)its continuous and diffrentiable c)it has asymmetric domain about origin d)its ALWAYS obvious that A fuction c ...

In a triangle ABC , find the least value of, cot A/2 * cot B/2 * cot C/2 * cos A/2 * cos B/2 * cos C/2 ...

1) Show that for all positive reals a,b,c,d:- 1/a + 1/b + 4/c + 16/d>= 64/(a+b+c+d) 2) a,b,c are positive reals with abc=1. Prove that, 1/{a^3(b+c)} + 1/{b^3(c+a)} + 1/{c^3(a+b)}>= 3/2. 3) Solve the following inequality ...

\int _{0}^{(2n-1)\pi}[\sin x]dx;n\epsilon N Will this be done in same way as http://www.targetiit.com/iit-jee-forum/posts/find-the-value-11282.html ? :-) ...

Prove the value of integral \int _{0}^{1} \sqrt {1+x^3} is less than 7/2 ...

If the tangent from a point P to the circle x^2+y^2=1 is perpendicular to the tangent from P to the circle X^2+y^2=3.Then find the locus of P.. ...

show that the equation secθ + cosecθ = c has two solutions between 0 and 2π if c2 < 8 and four solutions if c2 > 8. I've tried but didn't get the correct answer. ...

Find all 3 digit numbers with the property that abc=a!+b!+c! ...

In triangle ABC equation of side BC is x-y=0.Circumcentre and Orthocentre of the triangle are (2,3) and (5,8) respectively.Find the equation of circumcircle of the triangle.. ...

∫dx/(1+x^16) i.e; x raised to 16, not the whole raised to 16. ...

iZ3+Z2-Z+i=0 then show that |Z|=1 plz tell me a shortcut for this problem........................ ...

find the range of the function not using differentiation (i.e maxima and minima not allowed ) :- f(x) = (sin2x + sinx - 1) / (sin2x - sinx +2 ) ...

plz explain and draw the graphof [sin2(x/4)+cos(x/4)] ...