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z has property that |z-5i|=1 & z1 is such that |z1-5|=1 find z1 with the property that |z-z1| is maximum ...
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In how many ways can you put 9 coins of into 2 pockets? Consider the cases as (a) All 9 coins are different (b) all 9 coins are same ...
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if a,b,c,d and p are different real numbers such that (a2+ b2+c2)p2 -2(ab+bc+cd) p +(b2+c2+d2) ≤ 0 then a,b,c and d are in geometric progression ...
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2 frnds after a long time decided to meet at a particular coffee shop between 5:00 pm to 6:00 pm on a specified day.they also decided that the person whho comes earlier will not wait for the second person for more than 10mins ...
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Prove that n*(n+1)*(2n+1) is divisible by 6, for any n>0 ...
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*Image* ...
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Of 3n+1 objects, n are indistinguishable, and the remaining ones are distinct. Find the number of ways to choose n objects from them. ...
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2n players are participating in a tennis tournament. Find the number Permutation of pairings for the ï¬rst round ...
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find the minimum value of th modulus of the sum of all 6 trigo functions.. ...
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\hspace{-16}$Total no. of positive divisers of $\bf{226894500}$ which are is in the form of\\\\ $\bf{(i)\;\;(4n+1)\;\;,}$ Where $\bf{n\in \mathbb{N}}$\\\\ $\bf{(ii)\;\;(4n+2)\;\;,}$ Where $\bf{n\in \mathbb{N}}$\\\\ $\bf{(iii) ...
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(sin4x/2)+(cos4x/3)=1/5 Then... (a)tan2x=(2/3) (b)tan2x=(1/3) (c)(sin8x/8)+(cos8x/27)= 1/125 (d) B and C (e) A and C (f) None ...
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How many 7 digit integers can be formed whose digit sums to 10 and has the digits 1,2 and 3 only (a)66 (b)55 (c)77 (d)88 ...
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\hspace{-16}$Minimum value of $\bf{n\in\mathbb{N},}$ whic has ......\\\\ $\bf{(i)\;\; 16-}$ divisers.\\\\ $\bf{(ii)\;\; 19-}$ divisers.\\\\ $\bf{(iii)\;\; 24-}$ divisers.\\\\ $\bf{(iv)\;\; 25-}$ divisers.\\\\ $\bf{(v)\;\; 26- ...
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\hspace{-16}$Is there is any Natural no. $\bf{n}$ which end with exactly ........\\\\ $\bf{(i)\;\; 2013-}$ zero,s.\\\\ $\bf{(ii)\; 2014-}$ zero,s.\\\\ $\bf{(iii)\; 2015-}$ zero,s.\\\\ ...
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\hspace{-16}$If $\bf{a+b=8}$ and $\bf{ab+c+d=23}$ and $\bf{ad+bc=28}$ and $\bf{cd=12}$.\\\\ Then value of \\\\ $\bf{(i)\;\;\;a+b+c+d=}$\\\\ $\bf{(ii)\;\;ab+bc+cd+da=}$\\\\ $\bf{(iii)\; abcd=}$ ...
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\hspace{-16}$The no. of divisers of the form $\bf{12\lambda+6(\lambda\in \mathbb{N})}$ of the no. $\bf{25200}$ ...
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\hspace{-16}$Let $\bf{S = \{1,2,3,4,5\}}$. Then the no. of unordered pairs $\bf{\{A,B\}.}$\\\\\ of Subsets of $\bf{S}$ such that\\\\ $\bf{(i)\;\;\;\; A\cap B=\phi}$. Where $\bf{A\neq B}$\\\\ $\bf{(ii)\;\;\;\; A\cap B=S}$. Whe ...
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Let U1 and U2 be two urns such that U1 contains 3 white and 2 red balls, and U2 contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from U1 and put into U2. However, if tail appea ...
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2nCn/(n+1) is an integer. ...
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Prove that (a1+a2+...+an)!/a1!a2!...an! is an integer ...
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If f(x)=3x3-13x2+14x-2 and p,q,r are roots of f(x)=0 such that p<q<r,then 1),[q],[r] where [.] denotes greatest integer function,are in A)A.P B)G.P C)H.P D)A.G.P 2) \fn_jvn \lim_{n\rightarrow \infty }(p)^{n!}(q)^{1/n} = ...
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Although some you might have seen this question before give it a try. If p,q are positive integers such that- 1- 1/2 + 1/3 - 1/4 +.........- 1/1318 + - 1/1319 = p/q Show that 1979 divides p. ...
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Four fair dice D1, D2, D3 and D4, each having six faces numbered 1, 2, 3, 4, 5, and 6, are rolled simultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is (A) 91/216 (B) 108/216 (C) 125/216 ...
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Determine all such integers a and b for which one of the roots of 3x3+ax2+bx+12=0 is equal to 1 + Ö3. ...
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The distance between 2 parallel lines is one unit.A point 'A' is chosen to lie between the lines at a distance d from one of them.Triangle ABC is equilateral with B on one line and C on the other parallel line.The length of t ...
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A and B toss a coin each alternatively.The first person to toss 5 heads wins.Find the chances of A winning if he starts the game? ...
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\hspace{-16}$Solve for real $\bf{(x,y,z)}$ in \\\\\\ $\bf{x[x]+z\{z\}-y\{y\}=0.16}$\\\\ $\bf{y[y]+x\{x\}-z\{z\}=0.25}$\\\\ $\bf{z[z]+y\{y\}-x\{x\}=0.49}$ ...
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6 apples and 6 mangoes are to be distributed among 10 boys so that each boy gets atleast 1 fruit.Find the number of ways in which the fruits can be distributed. ...
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x,y belong to R,x2+y2+xy=1,then the minimum value of x3y+y3x+4 is? ...
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If a six digit number abcdef is multiplied with 6,the resulting number is defabc.Find c+f? ...
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