Recently Active Algebra Questions

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 ...

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 ...

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 ...

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

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

How many 1s are there in the result of 1 + 11 + 111 + ... + 11..111 (which is 2002 ones) ...

for what values of "m" is y=0,if y=x2+(2m+1)x+m2-1?x is a real number. ...

a problem similar to a few posted so far.... (Just for practice) What are the last digits of ? a) 22222222 10 times b) 333333 6 times c) 44444 5 times d) 7777777...... 8 times e) 888888 8 times... ...

What is the minimum distance between circle x2+y2=9 and curve 2x2+10y2+6xy=1? this was earlier done by kaymant sir in a way which didn't strike me,so get an easier method sir.. ...

1) Express the complex number 1 / [1 - (cos θ + i sin θ )] in the cartesian form. 2) Prove that [(1 + cos θ + i sin θ) / (1+cos θ)] n = cos n θ + i sin n θ. 3)(a)If c2+s2=1 ,then evaluate (1 + c + i s) / (1+c- i s) (b) ...

If l log1/ 3 lzl2-lzl+1/2+lzl l<2 then find all possible values of lzl ...

Find value of (a+ib)m/n +(a-ib)m/n ...

Prove that the determinant -- sin 2A sin C sin B sin C sin2B sin A sin B sin A sin2C =0 where A,B,C are the angles of a triangle. ...

Let 3 points A,B,C with affixes z1,z2,z3 respectively lie on unit circle lzl=1.AD is perpendicular to BC and AD is produced to a point E on circle lzl=1 Q1 Find orthocentre of ΔABC Q2 Find the affix of point E ...

Considr ΔABC in argand plane.Let A(0),B(1),C(1+i) be its vertices and M be mid point of CA.Let z be variable complex number in the plane.Let u be another variable complex number u=z2+1 Q1Find locus of u when z is on BM Q2FIn ...

i am excited to see the solution: (a-b)(b-c)(c-a)=a^{2}+b^{2}+c^{2} ...

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Q1If ω is non real complex cube root of unity tehn find value of \frac{\prod_{p=1}^{4}{(\omega +\alpha ^p)}}{\prod_{q=1}^{7}{(\omega ^2-\alpha ^q)}} Q2 If n beolgns to N then value of \prod_{r=1}^{n-1}{\sin(r\pi /n)} ...

When to take permutation and when combi ? Suppose there are 11 places and 7 people have to be distributed in these places. How many ways ? Pls explain. Also pls explain the prime difference between permu and combi and when to ...

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If 2cosθ=x + 1/x,2cosφ=y + 1/y,find values of 1)xmyn + 1/xmyn 2)xm/yn + yn/xm ...

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Provided n^3 unit cubes, n > 1 which are numbered from 1 to n^3. All these unit cubes are put together to form a cube with side length n. In this cube two unit cubes will be neighbors if they share at least one vertex. As ...

(A) if x,y,z are 3 positive numbers in AP, then 3x+y/2y-x + 3z+y/2y-z ≥ In column II options were (p) 3 (q) 5 (r) 2 (s) 12 (t) 8 I got ≥8 So should i write the answer as 't' or pqrt ?? ...

If x1,x2...xn are roots of equation xn+p1xn-1+p2xn-2+...+pn-1x+pn=0 where p1,p2..pn real, Prove that(1+x12)(1+x22)(1+x32)..(1+xn2)=(1-p2+p4-p6+...)2+(p1-p3+p5-....)2 ...

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Six people sit around a circular table. In how many ways can three pairs of people shake hands so that no arms cross (nobody shakes hands with two people at the same time)? ...

A coin has probability p of showing head when tossed.It is tossed n times.Let pn denote the probablity that no two(or more) consecutive heads appear. Prove taht pn=(1-p)pn-1 +p(1-p)pn-2 for n≥3 ...