Recently Active Algebra Questions

If a,b,c,d are diff. pos. real nos. in HP,then A. ab>cd B. ac>bd C. ad>bc D. none of these ...

Find all real values of parameter a for which the equation in x \[ 16x^{4}-ax^{3}+(2a+17)x^{2}-ax+16 = 0 \] has four solutions which form an arithmetic progression. ...

if (9+4√5)n=p+β where n and p are postive integers and β is a positive proper fraction, prove that (1-β)(p+β)=1 ? ...

The rational number which equals to the number 2. 3 5 7 with recurring decimal is-- A. 2355/1001 B. 2370/997 C. 2355/999 D. none of these. ...

WRITE THE FOLLOWING RELATION ON THE SET {1,2,3,4,5,6,7}AS THE SET OF ORDERED PAIR- R={(X,Y):X IS RELATIVELY PRIME TO Y} SOLUTION: R={(2,3),(2,5),(2,7),(3,2),(3,4),(3,5),(3,7),(4,3),(4,5),(4,7),(5,2),(5,3),(5,4),(5,6),(5,7), ( ...

1. a, b, c, p, q, r are real nos. such that ax2 + bx + c ≥ 0 and px2 + qx + r ≥ 0 for all x ε R. Prove that apx2 + bqx + cr ≥ 0 for all x. I know c, r, a and p > 0 and Discriminant ≤ 0 but im not able to prove it ...

A sequence of positive integers is constructed as follows: the first term is 1, the following two terms are 2, 4, the following three terms are 5, 7, 9, the following four terms are 10, 12, 14, 16, etc. Find the n-th term of ...

Prove that for positive real numbers a, b, c, d, we have \[ \frac{1}{\frac{1}{a}+\frac{1}{b}}+\frac{1}{\frac{1}{c}+\frac{1}{d}}\le\frac{1}{\frac{1}{a+c}+\frac{1}{b+d}} \] ...

Q. Find the first non-zero digit from the right when 25 ! is written in base 5 notation. Q. There are 3 circular coins each with different radii … They are placed touching each other externally. The distance from the centre ...

three straight lines r drawn thru a pt lying in a triangle abc ,parallel to its side.the area of the resulting triangles are 1,4,9 sq cm..then area of triangle abc???? ...

i am really confused about COMPLEX NUMBERS i dont know how to begin that and complete that! anybody there , plz help me out on how to go about complex numbers i missed my classes during this topic....plz help! ...

solve the equation 1 - x + x(x-1)/1.2 - x(x-1)(x-2)/1.2.3 + ...... +(-1)nx(x-1)(x-2)....(x-n+1)/n! = 0 putting x=n in the equation, it becomes nC0-nC1+nC2.........+ (-1)n nCn = 0 so x=n is a solution. how can we say that no o ...

prove that \frac{1}{15}<\frac{1}{2}.\frac{3}{4}.\frac{5}{6}.\frac{7}{8}........\frac{99}{100}<\frac{1}{10} ...

here's a nice one i came across while reading a book yesterday prove for all positive integers m, the integer next greater than (\sqrt{3}+1)^{2m} contains 2^{m+1} as a factor ...

an 8 x 8 array consists of the numbers 1,2,3,.............,64 . consecutive numbers are adjacent along a row or coloumn. what is the minimum value of sum of numbers along a diagonal ? ...

1] Let a,b,c be non-negative real numbers such that a+b+c=3. Prove that \frac a{a+2bc}+\frac b{b+2ca}+\frac c{c+2ab}\ge1 ...

what is the coefficient of x99 in (x-1)(x-2)(x-3)......(x-100) is 1. -5050 2. 5050 ...

29. The number of permutations of the word HINDUSTAN such that none of the three patterns HIN, DUS, TAN occurs is (1) 169194 (2) 166680 (3) 169190 (4) 166670 ...

(12x-1)(6x-1)(4x-1)(3x-1)=5 SOLVE ...

1! + 2! + 3! ............. + n! = k! where kεI+ find all solutions ...

Find all polynomial P(x) with real coefficients satisfying P^2(x)+P^2(x-1)=2(P(x)-x)^2 ...

A frnd of mine gave me this sum to solve but i am not being able to do so...(cant match the ans)... the q is: x2+y2+z2=27 then x3+y3+z3 has: a) min value 81 b)max value 81 c)min value 27 d) max value 27 ans: b) ...

(A):22225555+55552222 is divisible by 7. (R):xn-an is divisible by x-a,n is even or odd and xn+an is divisible by x+a if n is odd. answer is A.............jus tell me how is reason explainin the assertion part?? ...

here is a typical number theory problem. i hav tried this but was unable to solve this sum. i figured out the answer but could not proceed in any logical method. could you please tell me some logical step-by-step method for r ...

1) Show that if a diagonal matrix is commutative with every matrix of the same order, then it is necessarily a scalar matrix. 2)Find the possible square roots of the two rowed unit matrix I. 3) If M is a 3x3 matrix where |M|= ...

There are n stones in a line , the distance betwen the consecutive stones being 1m ,3m,5m etc. There is a basket fixed at the first stone.A man starting from the baskets collects all the stones in the basket one by one . Find ...

1. The solution of the inequality 2x-5/|x-3|>-1 is a)(2,∞) b)(3,∞) c) (2,3) 4) (8/3,∞) ...

A square of n units by n units is divided into n2 squares of 1 sq. unit each. find the number of ways in which 4 points ( out of (n+1)2 points) be selected so that they form the vertices of a square. i was able to count the n ...

we all know that 0<={x}<1 .. is also, 0<={-x}<1????? i think yes... but saw recently in a practice paper whch says the reverse,,...!!! MAY DAY!! ...

Q) Two rectangles are given.The Area of the 1st rectangle is double the area of the 2nd rectangle.The Perimeter of 2nd rectangle is double the perimeter of the 1st rectangle.Then Find the Sides of the 2 rectangles? Plz give t ...