Recently Active Algebra Questions

If a(70a - 12b + 2c)> 0 and the quadratic equation ax^2 + bx + c = 0 has real roots alpha and beta, then which of the following statement is always false? alpha< beta < -7 alpha < beta<= - 8 alpha > beta> ...

A ball is drawn at random from a bag containing 3 balls and it is found to be black. If it is equally likely that it may contain 1 or 2 or 3 black balls, the probability that the ball drawn is the only black ball is...is the ...

please solve it asap *Image* x ...

It is given that tan A and tan B are the roots of t2-pt+q=0. Find in terms of p and q: i) sin2(A+B) ii)cos 2(A+B) ...

1. If a,b are the roots of x2=x+1 , prove that a5=5a+3 2. Two candidates attempt to solve a quadratic eqn of the form x2+px+q=0 . One starts with a wrong value of p and finds the roots to be 2 and 6. The other starts with a w ...

Q1. Let f(x) = ax^4+bx^3+cx^2+dx+e where a,b,c,d,e\; \; \epsilon \; R , a≠0, b2>8ac/3 and g(x) = lf(lxl)l , then maximum possible no. of points at which g(x) is non-differentiable is _______ Q2. \int_{0}^{\infty }{\left[ ...

\\\texttt{If} \: f_{n}=\sum_{k=0}^{n}\binom{n-k}{k} \\\texttt{evaluate}\\ \\ \begin{vmatrix} f_{n}& f_{n+1}&f_{n+2} \\ f_{n+1}& f_{n+2}&f_{n+3}\\ f_{n+2}&f_{n+3}& f_{n+4} \end{vmatrix} ...

prove: \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{n} is not an integer for any value of n. ...

Solve 1. 4x -3x- 1/2 = 3x+ 1/2 - 22x-1 2. 2x2 : 2x =8:1 ans1 is x=1+- 13 /2 ans 2 is x=3/2 ...

A student appears for test I, II and II. The student is successful if he passes either in tests I and II or test I and III. The probabilities of the student passing in tests I, II and III are p, q and 1/2 respectively. If the ...

The probability that a man aged x years will die in a year is p. The probability that out of n men M1, M2, M3, . . . . . . , Mn each aged x years, M will die and be the first to die is a. 1/n2 b. 1-(1-p)n c. 1/n2[1-(1-p)n] d. ...

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If f(x)=(x-α)n.g(x) then we always have f(α)=f'(α)=f"(α)=...=fn-1(α) where f(x) and g(x) are polynomial functions.Provided that f(x) has rational coefficients Q1 If f(x) is of deg 4 and touches x axis at ( 3 ,0).Find sum ...

Q1. The value of ^{100}C_{0}\; ^{200}C_{100} - ^{100}C_{1}\; ^{199}C_{100} + ^{100}C_{2}\; ^{198}C_{100}-^{100}C_{3}\; ^{197}C_{100}+.......+^{100}C_{100}\; ^{100}C_{100} Q2. If \left|az+b\bar{z}+c \right| = \alpha \left|a \r ...

(1) The No. of (+ve) Integral solution of the equation 7x^{2}-2xy+3y^{2}=27 ans = 1 ,2 0, None. I am very sorry for posting wrong question in my previous post. ...

(1) find all real values of x,y and z in x^{2}-\left|x \right|=\left|yz \right| .......(1) y^{2}-\left|y \right|=\left|zx \right| ........(2) z^{2}-\left|z \right|=\left|xy \right| ........(3) bhatt sir how can i solve these ...

IF a team of 11 players is to b selected from 8 batsmen..6 bowlers..2 wktkipers..4 all ruonders... 1>NO.of selections wen atmost 1 each of wktkipers n alrnder play? 2>NO.of selections wen 2 particular batsmen dont play ...

Find the number of solutions of the system of equations : {x}+y+[z] = 2.3, [y]+{z}+x = 4.5, {y}+[x]+z=6.2 where {} and [] denote the fractional and greatest integer function respectively. Also find the solutions ...

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1> S=1/12+1/22+1/32.......upto ∞ S1=1/12+1/32+1/52.....upto ∞ S2=1-1/22+1/32-1/42......upto ∞ then the value of 486 S1/S2 solution required ...

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find teh greatest value of the expression (a-x)(b-y)(c-z)(ax+by+cz) where a,b,c are known +ve quatities and a-x,b-y,c-z are also +ve. ...

g(k)={4k+√(4k2-1) }/ √(2k+1)+√(2k-1) k belongs to N then find the value of g(1)+g(2)+g(3)........g(60)= ...

Q.(a+2)x2 + 2(a+1)x + a=0..The no.of integral valyes of 'a' for which the roots will be integers? ...

(1) Find (+ve) integral solution of the equation 3x^{2}-2xy+7y^{2}=0 ...

find... \sum_{1}^{\propto }{\frac{1}{(3n-3)!}} . [1][1][1] ...

MULTIPLE ANSWER QUESTIONS: 1. In ΔOAB where O is origin coordinate of A and rational number. AngleAOB = θ, coordinate of B always irrational then θ can take value (A) 30° (B) 15° (C) 60° (D) 45° (2) If θ1, θ2, θ3 an ...

\\1)\: solve\: \frac{x-a}{b}+\frac{x-b}{a}=\frac{b}{x-a}+\frac{a}{x-b}\\ \:\:2)\: if\:f(n)=\sum_{r=1}^{n}\frac{1}{r}...then \:show \:that\:\frac{n}{2}<f(2^n-1)<n\\ 3)\:if\:(1+x)^n=\sum_{r=0}^{n}^{n}C_{r}x^r\:find \:teh\ ...

1)If a>0>b>c & the system of eqn ax+by+cz,bx+cy+az=0,cx+ay+bz=0 has a non trivial soln,then find nature of roots of (b+c)t2+(c+a)t+a+b=0 . From first 3 eqns i got a+b+c=0 what next ?? 2) Let (1+x)2n=a0+a1x+....+a2nx2 ...

In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is : a. At least 30 b. At most 20 c. Exactly 25 d. None of the above ...