Recently Active Algebra Questions

Ques1) The lengths of three unequal rectangular block arein G.P. The volume of the block is 216 cm3 and the total surface area is 252 cm2 . Show that the length of the longest edge is 12 cm. Ques2)Show that 11 2 + 12 2 +13 2 ...

Q. Find the sum : 1 + 5 + 19 + 49 + 101 + 181 + 295 ................. ...

Doubt 1 : What is an increasing function ? Doubt 2 : If b>a then the eqn. (x-a)(x-b)-1=0 has A. both roots in [a,b] B.both roots in (-∞,a) C. both roots in (b,+∞) D. One root in (-∞,a)and the other in (b,+∞) Doubt ...

Let z1, z2, z3 be complex numbers such that 1) |z1| = |z2| = |z3| = 1, 2) z1 + z2 + z3 is not equal to zero, and 3) z12 + z22 + z32 = 0. Then, prove that for all integers n >= 2, the quantity |z1n + z2n ...

Ques1) Show that the sum of the series 1 / 1.3 + 2 / 1.3.5 + 3 / 1.3.5.7 + ........... upto n terms is 1/2. Ques2) Show that the sum of n terms for series 3/4 + 5/36 + 7/144 + 9/400 + 11 / 900 + ......... is 1. Ques3) If the ...

6 dices are thrown together.Find the probability of getting a sum of 15. What is the easiest and quickest way to do it? ...

in a test an examinee either guesses or copies or he knows the answer to a multiple choice question, with more than one answer, and having 4 alternatives. the probabilty that he makes guess is 1/3 and that he copies the answe ...

A bag contains a coin of value M and a number of other coins whose aggregate value is m.A person draws on at a time till he draws coin M Find value of his expectation ...

This question is given in arihant... Prove that the min value of the expression x2+3y2+2xy-6x-3y is -11 Any hints on how to solve this ? ...

( 1+i )n + ( 1- i )n ...

Two n digit integers are said to be equivalent if one is a permutation of the other. for eg. 10075 and 01057 are equivalent. Find the number of 5 digit integers such that no two are equivalent ...

1) Show that the least value of 2 log 100 a - log a 0.0001, for a > 0 is 4. 2) If the equation x 4-4x 3+ax 2+bx+1=0 has four positive roots, then show that a=6 and b=-4 3) If S = a 1+a 2+a 3+..........+an then show that s/ ...

Q.1) prove : (n+1 / 2)n ≥ n! Q.2) prove : 2n + x Cn .2n-x Cn ≤ (2nCn)2 Q.3) If s be the sum of n +ve unequal quantities a,b,c,..... then prove that : s/s-a + s/s-b + s/s-c +...... > n2 / n2-1 ...

Find the coefficient of x50 in (1+x)+2(1+x)2+3(1+x)3+....+1000(1+x)1000 ...

1) If the equation x 4-4x 3+ax 2+bx+1=0 has four positive roots, then show that a=6 and b=-4 2) If S = a 1+a 2+a 3+..........+an then show that s/(s-a1) + s/(s-a2) +s/(s-a3) + ...............+ s/(s-a n) > n2 /( n-1). 3) If ...

Prove that : Any prime number of the form (4k+1) can be expressed as the sum of two perfect squares. [k∈I] ...

In five throws with single die what is the chance of throwing a) three aces exactly b) three aces atleast ...

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f(x+1) ≥ f(x) + 1 f(x+5) ≤ f(x) + 5 g(x) = f(x) + 1 - x find g(2008) ...

well watz sumation of n harmonic terms suppose 1/a 1/a+b 1/a+2b ..........1/a+<n-1>b ie for n terms . wat is sumation.>>>>>>>furmula<<<<<< ...

there is an amoeba....in every minute it has four options : (0) it dies (1) it remains as it is (2) it doubles (3) it triples find the probability that after 2 minutes the amoeba dies ....(.i.e. if it doubles or triples all o ...

1.Find the fallacy :- n+n+n.....(n terms)=n2 differentiating both sides w.t.n 1+1+1....n terms=2n n=2n 1=2 guess: can we differentiate both sides on an identity. 2.find the sum:- 1+(1+a)r+(1+a+a2)r2+..n terms 3.Find the sum 1 ...

If z1 and z2 be two distict complex numbers such that z_1+z_2=\frac{z_1}{\left|z_2 \right|^{2}}+\frac{z_2}{\left|z_1 \right|^{2}} then prove that 1+\left|z_1 \right|\left|z _2 \right|=\frac{z_1}{z_2}+\frac{z_2}{z_1} ...

1) If a>1 , b>1 then show that the min value of log b a + log a b is 2. 2) Show that the least value of 2 log 100 a - log a 0.0001 for a >1 is 4. 3) If x,y,z are positive then show that the min value of X logy - logz ...

a coin is tossed (m+n) times where (m>n). find the probability of exactly n consecutive heads. ...

A stick of length 1 is divided randomly into 3 parts. What is the probability that a triangle can be made with those three parts? ...

Ques1) If a > 0 , b > 0 , c > 0 and the min value of a (b2 + c2) + b(c2 +a2 ) + c(a2+b2) is k abc then prove that k =6. Ques2) If a,b,c are three real numbers such that b+c-a , c+a-b , and a+b-c are positive, then th ...

Find largest possible integer n such that [\frac{na^2b^2c^2}{a^2bc+ab^2c+abc^2}]\leq (a+b)^2+(a+b+4c)^2 for all real positive a,b,c ...

Paragraph Four letter words are formed by using the letters of the word INEFFECTIVE Q1. The number of such words in which all the four letters are different is _____ Q2. The number of such four lettered words in which neither ...

Prove that if coefficients of the quadratic equation ax^2 + bx + c = 0 are odd integers, then the roots of the equation cannot be rational numbers. ...