
If Î± be the number of solns of the equation [sin x]=x, (where [.] represents greatest integer function) and m be the greatest value of cos(x2+xex[x]) in the interval [1,1], then what is the relation between Î± and m (Î± ...

For all real numbers a; b; c prove the following chain inequality 3(a2 + b2 + c2) â‰¥ (a + b + c)2 â‰¥ 3(ab + bc + ca): ...

What are the roots of x3+px2+q=0 in terms of p and q ...

If a, b, c, d are unequal +ve numbers then the roots of the equation x/xa + x/xb + x/xc +x+d=0 are necessarily a)all real b)all imaginary c)2 real 2 imaginary d)atleast 2 real ...

If Cr=nCr,the sum of the series 2[( n/2 )fact)2]/nfact [C022C12+3C22......(1)n(n+1)2Cn2] where n is even integer,is (a)0 (b)(1) n/2 .(n+1) (c)(1)n.(n+2) (d)(1)n.n (e)none of these Ans is (e)..however..pls provide the so ...

The circle x2+y2+2kx=0,k belongs to R,touches the parabola y2=4x externally.Then (a)k>0 (b)k<0 (c)k>1 (d)none of these Ans is (a). i have put y2=4x in the eq.of the circle.and in the quad.of x,i put b2=4ac.i got k=2 ...

If cos Î¸ + cos2 Î¸ = 1, then sin12 Î¸ + 3 sin10 Î¸ + 3 sin8 Î¸ + sin6 Î¸ + 2 sin4 Î¸ + 2 sin2 Î¸ â€“ 2 = (A) 0 (B) 1 (C) 2 (D) 3 Thanx in advance... ...

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

For the given regular hexagon, find the perimeter and the area of the hexagon. *Image* ...

pls give the shortest method to solve this quickly *Image* ...

What shoud be the minimum thickness of a coin of radius 'r' so that there is a 1/3 probability that the coin will stand straight? ...

if D = diag(a1 , a2 , a3 , ...... an), where ai â‰ 0 for all i = 1,2....,n, then show that D1 = diag(a11 , a21 , a31 , .......... an1). ...

*Image* ...

The number of 5 digit numbers such that the sum of their digits is even is? ...

âˆ«(a2b2 *x2))3/2 dx ...

All the values of m for which both roots of the equation x2 â€“ 2mx + m2 â€“ 1 = 0 are greater than â€“ 2 but less than 4 lie in the interval : ...

Number of permutations of 1,2,3,4,5,6,7,8 and 9 taken all at a time ,such that the digit 1 appearing somewhere to left of 2 3 appearing to the left of 4 and 5 somewhere to the left of 6 (e.g.815723946 would be one such permut ...

*Image* [x]=Greatest Integer function ...

lim n >âˆž 1/2n log(2nCn) ...

the number of four digits having only two consecutive digits identical is ?? ...

Find the coefficient of x99 and x98 in the polynomial (x1)(x2)(x3).........(x100). ...

Represent m6+n6 as a sum of 2 squares other than (m3)2+(n3)2. Think its easy....give it a try!:P ...

x1, x2, x3, x4 are real nos. x1 < x2 < x3 < x4. Product of any three chosen at a time + the remaining = 130. Find the sum of all possible values of x4 rounded to the nearest decimal place. ...

If a0, a1, a2,... are the coefficients in the order of expression of (1+x+x2)n, prove that a02a12+a22.....+(1)n1an12=(1/2)an(1(1)nan) ...

A 10digit number has one 1, two 2's, three 3's and four 4's as its digits in some order. Prove that it can never be a perfect square. ...

In a Î”ABC if cosA+cosB+cosC=3/2 then prove that the Î” is equilateral. ...

all possible three digits even numbers which can be firmed with the condition that if 5 is one of the digit,then 7 is the next digit is? ...

The number of ways in which 2 boys can take 4 subjects if each boy takes atleast one subject is? ...

Let abcd is 4 digit number which satisfy the equation 4*abcd=dcba find the abcd ...

number of 9 digits numbers divisible by 9 using the digits from 0 to 9 if each digit is used atmost once is K.8!, then k has value equal to? ...