
(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 ...

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 ...

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. ...

2nCn/(n+1) is an integer. ...

Prove that (a1+a2+...+an)!/a1!a2!...an! is an integer ...

If f(x)=3x313x2+14x2 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} = ...

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 ...

Q1:The teacher of a class having a large number of students decides to take a test.After the test ended the teacher took the papers from the students and randomly distributed them among the students to check. Prove that the p ...

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 ...

Determine all such integers a and b for which one of the roots of 3x3+ax2+bx+12=0 is equal to 1 + Ö3. ...

If A=\begin{bmatrix} 4 & 6 & 6\\ 1& 3 & 2\\ 1& 4 &3 \end{bmatrix} and A^{1}=\alpha A^{2}+\beta A+\gamma I,then \alpha +\beta +\gamma is ...

x,y belong to R,x2+y2+xy=1,then the minimum value of x3y+y3x+4 is? ...

\hspace{16}$Calculate The Remainder When $\bf{2^{2009}}$ is divided by $100$ ...

\hspace{16}$Solve for real $\bf{(x,y,z)}$ in \\\\\\ $\bf{x[x]+z\{z\}y\{y\}=0.16}$\\\\ $\bf{y[y]+x\{x\}z\{z\}=0.25}$\\\\ $\bf{z[z]+y\{y\}x\{x\}=0.49}$ ...

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. ...

If a six digit number abcdef is multiplied with 6,the resulting number is defabc.Find c+f? ...

A class contains 3 girls and four boys. Every Saturday five students go on a picnic, a different group of students is being sent each week. During the picnic, each girl in the group is given a doll by the accompanying teacher ...

Is there any shorter way to solve this ques. Consider the equation x2+y2 = 2007. How many solutions (x; y) exist such that x and y are positive integers? (A) None (B) Exactly two (C) More than two but nitely many (D) In fitel ...

This has been discussed before but it is important... a+b+c=4 a2+b2+c2=6 a3+b3+c3=8 Find [a4+b4+c4] where [] denotes G.I.F? P.s:I know a method but i'm not sure if it's the shortest one to do this problem....thus sharing this ...

Find the least number which when divided by 24,32 and 36 leaves the remainder 19,27,31 respectively. ...

The grid is 4X3 rectangular Determine the number of paths from the lowerleft corner of the left grid to the upperright corner. ...

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. The number of ways in which we can place the balls in the boxes ( order is not considered in the box) so th ...

The total number of three digit numbers, the sum of whose digits is even, is equal to: (A) 450 (B) 350 (C) 250 (D) 325 ...

Find the least number which when divided by10987654321 leaves remainder9876543210 ...

Prove that if 3 prime numbers greater than are in AP then common difference is divisible by 6. ...

Suppose n is a natural number such that i + 2i^2 + 3i^3 +................+ ni^n=18√2,where i is √1.Then n is... ...

Let a,b,c be three distinct real numbers such that the expression ax2+bx+c, bx2+cx+a, and cx2+ ax+b is positive for each x belongs to R and let α =(bc+ca+ab)/(a2+b2+c2) Then (a) α<4 (b) α<1 (c) α>1/4 (d) α>1 ...

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

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 ...

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