Recently Active Algebra Questions

Sum of all the solutions in [0, 4π] of the equation- tanx + cotx +1 = cos(x + π/4) is ?? ...

Find the sum of all integral values of P for which the equation \left|x+\frac{1}{x} -3\right| = P-3 has exactly two distinct roots. ans-----------21 ...

Q1. (T/F) If the complex nos. z1, z2, z3 represent the vertices of an equilateral triangle such that |z1| = |z2| = |z3|, then z1+z2+z3 ≠0 (ans given: T) Q2. No. of ways to Arrange letters of the word INTERMEDIATE such that ...

If \begin{vmatrix} p & b & c\\ a & q & c\\ a& b & r \end{vmatrix}=0 find the value of p/p-a + q/q-b + r/r-c where a≠p. b≠q , and c≠r ans---- 2 ...

a lot contain 20 articles.the probability that the lot contains exactly 2 defective articles is 0.4 and the probality of exactly three defective is 0.6.articles are drwan without replacement till all defective articles are dr ...

4 sin2 θ - 8 sin θ + 3 ≤ 0 Find the interval of θ from 0 to 2π. Ans: [ π/6 , 2π/6 ] ...

Let x, y are positive integres such that the LCM of x,y is 1000. If the no. of ordered pairs (x,y) is k , then the no. of divisors of 'k' of the form 6n+1, n belogs to N, is A) 10 B) 2 C) 6 D) 8 ...

q1 S=\sum_{r=0}^{n-1}{\frac{1}{(n-r)^2}}(\frac{C_{r+1}}{C_r})^2 q2 S=\frac{C_0}{n(n+2)}-\frac{C_1}{(n+1)(n+3)}+\frac{C_2}{(n+2)(n+4)}......(n+1) terms ...

Came in roorkee mains. Find the coefficient of x49 in the polynomial \left(x-\frac{C_{1}}{C_{0}} \right)\left(x-2^{2} \frac{C_{2}}{C_{1}}\right)\left(x-3^{2}\frac{C_{3}}{C_{2}} \right).....\left(x-50^{2}\frac{C_{50}}{C_{49}} ...

show that \frac{C_{0}}{1}-\frac{C_{1}}{5}+\frac{C_{2}}{9}-\frac{C_{3}}{13}+.........+(-1)^{n}\frac{C_{n}}{4n+1} = \frac{4^{n}n!}{1.5.9....(4n+1)} ...

find the value of sin\left(\textrm{log} \left ( \textup{i}^\textup{i} \right ) \right) ...

Q1. Let the function f(x) = x2+x+sinx-cosx+log(1+|x|) be defined on the interval [0,1]. The function g(x) on [-1,1] satisfying g(-x) = -f(x) is ans given: -x2+x+sinx-cosx+log(1+|x|) (wrong naa?) Q2. If f:R-->R is defined b ...

\sum_{s=0}^{n}{(1)} = ( n + 1 ) how is it coming.... or shud we just remember it [12][12][12][12][12][12][12][12][12] ...

\sum_{s=0}^{n}{(1)} = ( n + 1 ) how is it coming.... or shud we just remember it [12][12][12][12][12][12][12][12][12] ...

P.T: (n c 0) (2n c n) - (n c 1) (2n-1 c n) +.... [(-1)^n] (n c n) (n c n)] =8 ...

1. A bag contains "W" white and 3 black balls. Balls are drawn one by one without replacement till all the black balls are drawn. What is the probability that this procedure for drawing the balls will come to an end at the r ...

A is an orthogonal matrix of odd ordeer such that |A|(x2+x+1) > 0, x belongs R. If I is a unit matrix of the same order as of A then value of |A(I+A2)-(I+A)(I+A2-A)| is equal to A) 1 B) -1 C) 0 D) 2 ...

QUES : A BAG CONTAINS 3 WHITE, 3 BLACK AND 2 RED BALLS. ONE BY ONE ,THREE BALLS ARE DRAWN WITHOUT REPLACING THEM. FIND THE PROBABILITY THAT THIRD BALL IS RED. ...

Q1. The equation Z3+ i Z -1 =0 has how many real roots ? The answer given is 0. BUT IF WE DO IT LIKE THIS : multiplying both sides by Z' [ Z conjugate ]... |Z|2 Z2 + i|Z|2 - Z' =0 then by inspection we get num of real roots a ...

Q1 if n postiive integers are taken at random and multiplied together and pn is probablity that last digit of product is 2,4,6,8.Find pn and p4 Q2 2 integers r,s are drawn one at a time without relacememnt from set 1,2,3...n. ...

q1 Let an=5n+7n and \Delta =\begin{vmatrix} a_{n+1} &a_{n+2} &a_{n+3} \\ a_{n+4} &a_{n+5} &a_{n+6} \\ a_{n+7} & a_{n+8} & a_{n+9} \end{vmatrix} then Δ= ? q2 Let \ f_k(x)=\int_{0}^{x}{(a_kt^2+b_kt+c_k)dt} \ for \ 1\leq k \leq ...

A triangle with vertices at 3+i, i(1+ 3 ) , and i(1- 3 ) is rotated about its circumcentre through an angle of Î /3 in anticlockwise direction.Find the new positon of the vertices. Pls post the method and method to find circu ...

1.Remainder when 22003 is divided by 17.. 2.If n is a positive integer.. then value of \sum_{i=0}^{n}{(-1)^{n} } 10^{n} C^{2n}_{n} divided by 81^{n} ...

Q1. \textup{If A=}\begin{bmatrix} a & b & c\\ b & c & a\\ c & a & b \end{bmatrix}\textup{, where a,b,c}\; \epsilon \; R^{+}\textup{ and abc=1,}\; A^{T}A=I\textup{, then }a^3+b^3+c^3\textup{ is} (a) a+b+c (b) a+b+c+3 (c) 3 (d) ...

Find the no. of integer solutions of x+y+z = 24 such that x is even and +ve , y>2 and z > -2 ? A) 110 B) 96 C) 120 D) 121 ...

let l l l 1 0 0 l l l A= l 3 w 0 l l l l 0 3-i w^2 l l l then a) A^105 is a lower triangular matrix b) A^106 is a upper triangular matrix c) trace of A^109 is zero d) trace of A^108 is w^108 w, w^2 are cube oots of unity A is ...

1.. *Image* ...

Find the co-efficient of x59 in the expansion : (x-1)(x2-2)(x3-3)(x4-4).........(x11-11) EXPERT'S HELP PLEASE !!! ...

q1)let A={x1,x2,...,xm},B={y1,y2,...,yn} and f:A→B,n>=m 1.number of increasing function from A to B: a)mCn b)nCm c)mn d)nC1+nC2+.....+nCn 2.number of non decreasing functions from A to B 3.number of onto functions from A ...

let A be the set of all 3X3 determinant having entries +1 or -1. if a determinant D from set A is chosen randomly, then probability that product of elemrnts of any row or any column is -1 is a) 1/32 b) 1/8 c)1/16 d) none ans ...