Recently Active Algebra Questions

*Image* In the given figure, u have the road plan of a city. A man standing at X wants to reach the cinema hall at Y by the shortest path. (i) Find the no. of different paths that he can take. (ii) Find the no. of shortest ro ...

1) Last two digits of 3100 are .... 2)Last three digits of 17256 are... 3)The remainder when (a) 597 is divided by 52 (b) (106)85 - (85)106 is divided by 7 (c) 3100 is divided by 100 ...

Be sure to read the problem clearly. A bag contains 6 balls of different unknown colors. Probability for A and B speaking truth are p and q respectively. A ball is drawn and both cofirm it to be RED. What is the probability t ...

Please can anyone please show me a detailed explanation of the method to find the co-eff. of x11 in the expansion : (1+x+x2+x3+.......+x6)3 ...

If - Z= \frac{1}{^nC_0} + \frac{1}{^nC_1} +....+ \frac{1}{^nC_n} Then, find the value of - Z= \frac{1}{^nC_1} + \frac{2}{^nC_2} + \frac{3}{^nC_3}+....+ \frac{n}{^nC_n} in terms of "n" and "Z". ...

The no. of irrational solutions of the equation - \sqrt{x^2 + \sqrt{x^2 + 11}} + \sqrt{x^2 - \sqrt{x^2 + 11}} = 4 are - a) 0 b) 2 c) 4 d) Infinite ...

The remainder when ... .^5 x= .^. 5^5 (24 times 5 ) is divided by 24 is _______ . ...

Let f : A-->B be an onto function where A={1,2,3,4} B = {x,y,z} also f(!) = x Let M be total such functions then find value of M/2 ...

First look this might seem an olympiad problem that may scare some of you... but try this problem to get an insight on how to solve such problems... x+y+z = w 1/x + 1/y + 1/z = 1/w Solve for x, y and z... (Not that you have t ...

√(1+1/12+1/22) + √(1+1/22+1/32) +....√(1+1/20072+1/20082) ...

A sequence is defined as a1 = a2 = 1 and an = an-1 + an-2 for all n ≥ 3 then { an } is an increasing sequence TRUE / FALSE ...

If a,b,c be the three consecutive coefficients in the expansion of a power of (1+x), prove that the index of the power is 2ac + b(a+c)/b2 - ac ...

if (1+2x+2x2)n=a0+a1x+a2x2+........a2n2n then prove that : ar=nC0.2nCr + nC1.2n-2Cr-2 +nC2.2n-4Cr-4+..................... ...

183 + 73 + 3.18.7.25/36 + 6.243.2 + 15.81.4 + 20.27.8 + 15.9.16 + 6.3.32 + 64 Find the value of the expression. ...

Q1 A_x=\begin{bmatrix} a_{11}+x & a_{12}+x & a_{13}+x\\ a_{21}+x & a_{22}+x &a_{23}+x \\ a_{31}+x & a_{32}+x & a_{33}+x \end{bmatrix} Prove A_x=A(0)+x\sum_{k=1}^{3}{\sum_{l=1}^{3}{A_{lk}}} Q2 If a,b>0 and a3+b3=a-b,then pr ...

If t1, t2, t3,...tn are the roots of the equation - xn +px + q =0 , then (t1- t2)(t1- t3)(t1- t4) ... (t1- tn) = ? (a) n.p (b) n.t1n +p (c) n.t1n-1 +p (d) n.t1 +p ...

Paper 2 Let x1,x2,....,xn be a sequence of integers such that -1 ≤ xi ≤ 2 for all i belongs to {1,2,...n} ; x1 +x2 + x3 + ....+ xn = 19 x12+x22 +...+xn2 = 99 Let m,M be the least and greatest values of x13 + x23 +...+xn3 ...

There are 2 irreducible polynomials f and g with rational coeff.Now let there be 2 complex numbers a and b s.t. f (a) = g (b) = 0. Prove that if a+b is rational number, then f and g must have same deg. ...

find the digit in tenth place of the sum1!+2!+3!+...........+49! ...

Hey guys , hope you are not too bored with maths . I found some good questions which I think don’t require pen and paper , yet are interesting . So please try --- 1 > If xy = 281 . 378 . 534 ( x + y ) , then find the num ...

Hey guys , hope you are not too bored with maths . I found some good questions which I think don’t require pen and paper , yet are interesting . So please try --- 1 > If xy = 281 . 378 . 534 ( x + y ) , then find the num ...

if \alpha _{1},\alpha _{2} are the roots of equation: ax2+bx+c=0 and \beta _{1},\beta _{2} be roots of equation : px2+qx+r=0.if \alpha _{1}y+\alpha_{2}z=0 \beta_{1}y+\beta_{2}z=0 have a non trivial(nonzero solutions) then pro ...

Solve logx2log2x2.log24x>1 ...

if x=1 is a real root of ax2+bx+c=0 then show that 4ax2 +3bx +2c =0 has real roots ...

find t: t=n+1Cn +n+2Cn +..............+2nCn ...

(p + q)(p + r) ≥ p+ qr ...

Well , how about some good questions to wake you up all night ? I think these are quite intriguing to attempt , so I will definitely post the solutions after a day or two ---- 1> ( a , 1 / a ) , ( b , 1 / b ) , ( c , 1 / c ...

PROVE : 2<f(n)<3 if n→N n ≥ 2 and f(n)=(1+1/n)n ...

Solve for x : (x+3)^{5}-(x-1)^{5}\geq 244 PS: the ans given is x \in (-infinity,-2] U [0,infinity) i thought of solving by taking x +1 = y ...so dat we can get some symmetry ...but ans nahi match hora ....pls see f any 1 can ...

A polynomial f(x) of n-th degree satis es f(k) = 2k for k = 0, 1, 2,.... n Find f(n + 1) (I was wondering if I should put it in the olympiad section.. but then with the last few discussions on polynomials that we have.. I tho ...