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

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

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

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 xyzâ‰¤10 ...

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 mâ‰¥1.Show that âˆ©(nCk)=F[m+1] for all mâ‰¥1. where nâ‰¥kâ‰¥0 and n+k=m ...

Prove that if the equation a_{0}x^{n} + a_{1}x^{n1} + ... + a_{n1}x = 0 has a positive root x0 then the equation na_{0}x^{n1} + (n1)a_{1}x^{n2} + ... + a_{n1} = 0 has a positive root less than x0 ...

How many integers between 1 & 1000000 have the sum of the digits equal to 18? ...

C0/2+2C1/3+3C2/4+...+(n+1)Cn/(n+2) ...

We know that Î£nCr*r2= n*2n1 + n*(n1)*2n2 (see "http://www.targetiit.com/discuss/topic/21790/solvethisbinomialquestion/" for the proof) Further we can find Î£nCr*r3 = n*2n1 + 3*n(n1)*2n2 + n(n1)(n2)*2n3 However on ...

Find the general formula for: 1k+2k+3k+..........+nk ...

Find Î£ r2*Cr ...

(x2x+1)4  6 x2(x2x+1)2 +5x4= 0 of multiplicity (a)2 (b)3 (c)4 (d)6 ...

left[ {frac{1}{4}} ight] + left[ {frac{1}{4} + frac{1}{{200}}} ight] + left[ {frac{1}{4} + frac{1}{{100}}} ight] + .....left[ {frac{1}{4} + frac{{199}}{{200}}} ight] is ...

If a,b,c Îµ R are distinct then the condition on a,b,c for which the equation 1/xa + 1/xb + 1/xc + 1/xbca =0 has real roots is (a)a+b+câ‰ 0,aâ‰ 0 (b)abcâ‰ 0,aâ‰ 0 (c)2a=b+c (d) none of these ...

âˆš(3x2+6x+7) + âˆš(5x2+10x+14) = 42xx2 Find the no of real roots... ...

The number of irrational roots of the equation ?? (x23x+1)(x2+3x+2)(x29x+20)= 30 ...

limxâ†’0 {(1+3x)1/31x} / {(1+x)101 1101x} has the value equal to? ...

Suppose a,b,c are positive integers and f(x) = ax2bx+c =0 has two distinct roots in (0,1) m then (a) aâ‰¥5 (b) bâ‰¥5 (c) abcâ‰¥25 (d) abcâ‰¥5 2 ...

Let f(x) = ax2+bx+c where a,b,c Îµ R. Suppose f(x) â‰¤ 1 for all x Îµ [0,1],then (a) aâ‰¤8 (b) bâ‰¤8 (C) câ‰¤1 (d) a+b+câ‰¤17 ...

Let Î± be a repeated root of p(x) = X3+ 3ax2 +3bx+c =0 , then (a) Î± is a root of x2+2ax+b=0 (b) Î± =(cab)/2(a2b) (c) Î±=(abc)/(a2 b) (d) Î± is a root of ax2+2bx+c =0 ...

Let a,b,c,d be four integers such that ad is odd and bc is even,then ax3+bx2+cx+d = 0 has (a) at least one irrational roots (b) all three rational roots (c) all three integral roots (d) none of these ...

Let a,b,p,q Îµ Q and suppose that f(x) = x2 +ax+b=0 and g(x)= x3 + px + q = 0 have a common irrational root , then (a) f(x) divides g(x) (b) g(x) â‰¡ x f(x) (c) g(x) â‰¡ (xbq)f(x) (d) none ...

If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pÎµR,then the value of bc+ca+ab is? ...

If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pÎµR,then the value of bc+ca+ab is? ...

If three distinct real numbers a,b,c satisfy a2(a+p)=b2(b+p)=c2(c+p) where pÎµR,then the value of bc+ca+ab is? ...

Let f(x)= ax2+bx+c ,a,b,c Îµ R.If f(x)takes real values for real values of x and non real values for non real of x,then (a) a=0 (b) b=0 (c) c=0 (d) nothing can be said about a,b,c ...

If x is real,then the maximum value of y=2(ax)[x+âˆš(x2+b2] ...

Let a,b,c be nonzero real numbers such that 0 âˆ« 1 (ex +ex )(ax2+bx+c)dx = 0 âˆ« 2 (ex+ex)(ax2+bx+c)dx Then the quadratic equation ax2 +bx+c = 0 has (a) no root in (0,1) (b)at least one root in (1,2) (c) a double root in ...