Recently Active Algebra Questions

If a,b,c and d are real positive such that : a + b + c + d = 1 Show that : 4a+1 + 4b+1 + 4c+1 + 4d+1 < 6 ...

Prove that [√n + √(n+1)] = [√(4n+1)] = [√(4n+2)] [.] here is used to denote greatest integer/floor function. ...

Find the sum of [x]+[x+ 1/n ]+[x+ 2/n ]+......+[x+ n-1/n ] if 'x' is real and 'n' is natural. [.] represents the greatest integer function. ...

Sorry. Mistakes that the question repeated ...

Q: Given a,b,c and d ε R satisfying a+b=8 ; ab+c+d=23 ; ad+bc = 28 ; cd = 12 , Find a) a+b+c+d b) ab+cd c) ac+bd d) ab (It's matrix type but I didn't wrote the options as it was taking more time) Q: The no. of values of ' k ...

PROVE: n!/r! (n-r)! + n!/(r-1)!(n-r+1)! = (n+1)!/r! (n-r+1)! ...

1.find the number of ways in which m boys and n girls may be arranged in a row so that no two girls are together . given that m>n 2. In an exam,10 candidates have to appear. 4 candidates are to appear in maths and rest in ...

1. A= \begin{bmatrix} 1& 0 &1 \\ 0 & 1 &1 \\ 0& -2 & 4 \end{bmatrix} 6A-1=A2+cA+dI,then c,d = [a nice method will do,without working a lot] 2. Assertion and Reason: Consider the system of equations: x-2y+3z=-1;x-3y+4z=1;-x+y- ...

1. Prove that (n!)! is divisible by (n!)^{(n-1)!} . 2. Show that 1!+2!+3!+ \dots + n! cannot be a perfect square for any n \in \mathbb{N}, \: n\geq 4 . ...

let P1(x)= ax^2-bx-c, P2(x)=bx^2-cx-a,P3(x)= cx^2-ax-b, be 3 quadritic polynomials where a,b,c are non zero real numbers suppose there exists a real number k such that P1(k) = P2(k)= P3(k). then prove that a=b=c. please do it ...

Little Einstein writes the numbers 2 , 3 , … N on a blackboard. He chooses any two of them, say X and Y, scratches both of them and replaces them by the single number T given by the relation : T = XY – X – Y + 2 He repe ...

\hspace{-16}$\textbf{Solve System of Equations.}\\\\ $\begin{matrix} \bold{x^4+y^2-xy^3-\frac{9}{8}x=0} & \\\\ \bold{y^4+x^2-x^3y-\frac{9}{8}y=0} & \end{matrix}\right. ...

sum the following to n terms and infinity... 1/4 + 1.3/4.6 + 1.3.5/4.6.8 ...... please dont use binomial.....this is a pure progressions sum.... ...

I am having arihant algebra and TMH algebra books.. do i have to complete both books to get a good rank? Or if any one is enough ? which one is better?(and not too much time consuming !?) ...

two arithmetic progressions are a1, a1, a1 ........ and b1, b2 , b3 ......... such that a1 + b1 = 100. also a22 - b21 = b99 - b100. find the sum of 100 terms of the progression (a1 + b1) , (a2 + b2) .......... ...

The minimum value of x2 + 2xy + 3y2 – 6x – 2y, where x, y are Real , is equal to (a) –9 (b) –11 (c) –12 (d) –10 ...

find the consecutive terms in the binomial expansion of (3+2x)^7 whose coefficients are equal.. ...

Find the remainder when [(2 × 4 × 6 × 8 × 10 ×…× 200) – (1 × 3 × 5 × 7 × 9 ×…× 199)] is divided by 201. do not take more than 2 min..... ...

1) Find all natural n's for which n4 + 2n3 + 2n2 + 2n + 1 is a perfect square. 2) If [a] is the grestest integer not exceeding a and a = 2 + √3 then the value of an + a-n + [an] for any positive integer n is 3) Find the num ...

Let A = [aij] , where aij = uij , 1 ≤ j ≤ n , 1≤ i ≤ n and ui , vj belongs to R satisfies A5 = 16 A , find tr(A). ...

\hspace{-16}$\textbf{If $\mathbf{x^{10}+(13x+1)^{10}=0}$ has a roots $\mathbf{r_{1}\;,r_{2}\;,\;r_{3}\;,r_{4}\;,r_{5}}$ and $}\\\\ \mathbf{\bar{r_{1}}\;,\bar{r_{2}}\;,\;\bar{r_{3}}\;,\bar{r_{4}}\;,\bar{r_{5}}}.$Then find $\ma ...

If n is greater than 5, then 2n/3 is greater than √2n dont take more than 5 mins for this ...

What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3? ...

List all solutions of the system of equations with positive real numbers: x2+y4=16 x2+z2=4+xz y2+z2=4+yz√3 Please give a legitimate solution. ...

*Image* ...

\hspace{-16}(1)::\;$Solve for $\mathbf{x\in\mathbb{R}$ in $\mathbf{\mid x^3-1\mid +\mid 2-x^3\mid = 1}} ...

\large \dpi{100} $\mathbf{Solve for $x\in \mathbb{R}$ in x = 6\left[\sqrt{x}\;\right]+1}$\\\\ $Where $[\;.\;]=$ Greatest Integer function. ...

If 6n tickets numbered 0,1,2,...,6n-1 are placed in a bag, and three are drawn out , show that the chance that the sum of the numbers on them is equal to 6n is \frac{3n}{(6n-1)(6n-2)} Looking for simpler and better ways ...

Let a , b , c possitive real numbers : Show that : a/(b+c)2 + b/(c+a)2 + c/(a+b)2 ≤ 9/4(a+b+c) ...

given, x + xy + y = 2 + 3√2 and, x2 + y2 = 6 Then find the value of |x + y + 1| options are : 1) 1 + √3 2) 2 - √3 3) 2 + √3 4) 3 - √2 5) 3 + √2 This is a good question no doubt...!! ...