Recently Active Mathematics Questions

2 > If a , b are the roots of x2 + px + q = 0 , and they are also the roots of the eqn. x2n + pn xn + qn = 0 , then prove that a / b and b / a are the roots of the eqn. xn + 1 + ( x + 1 )n whenever n is an even integer , a ...

Some very easy quad sums , hope everyone gives a different process ------------- 1 > If ( x - a ) ( x - b ) = k has the roots c , d ; then roots of the eqn. ( x - c ) ( x - d ) + k = 0 are -- ...

Find the greatest common divisor of the following terms . 2mC1 , 2mC3 , 2mC5 ...... 2mC2m - 1 (Hats off to anyone who does this !!!!!! ) ...

I just came across a statement : If |f(x)+g(x)| = |f(x)| + |g(x)| then f(x).g(x) ≥ 0 What does this mean ? ...

Solve for positive reals (x,y,z) z^2+2xyz=1 3x^2y^2+3y^2x=1+x^3y^4 z+zy^4+4y^3=4y+6y^2z It's been a while no -one has really given any elaborate soln for this..... ...

1 ) if iiiiii...∞ = a+ib prove that tan 1/2 pi a = b/a and a2+b2=e-pib... 2) if z1 and z1 are the roots of the equation αz2+βz+γ=0 prove that |z1|+|z2| = 1/|α|[ |-β+√αγ|+|-β-√αγ|] ...

Q. If m=np and p+q=1, then \lim_{n\rightarrow \infty } \; ^{n}C_{r}q^{n-r}p^{r} is equal to (a) e-mmr/r! (b) e-m(m/1)*(m/2)*...(m/r)*(1/r+1) (c) (m/1)(m/2)...(m/r)(1/em) (d) e-mmr/(r+1)! ...

Ques 1) If 0 ≤ x ≤ 3 π , 0 ≤ y ≤ 3 π and cosx . siny = 1 , then the possible number of ordered pairs (x,y) is:- (a) 4 (b) 8 (c) 6 (d) 12 Ques 2) The no. of points inside or on the circle x2 + y2 = 4 satisfying tan 4 ...

Find the sum upto infinite terms giving atleast (bcz i know 2) 2 different methods S = 1+2^2x+3^2x^2+4^2x^3+.... ...

let an be a sequence defined on positive integers by setting a_{n}=\frac{4n+\sqrt{4n^{2}-1}}{\sqrt{2n+1}+\sqrt{2n-1}} then find the value of a_{1}+a_{2}+a_{3}+a_{4}+..............a_{60} ...

Q1. For what values of d is the product of two numbers of the form x2-dy2 and u2-dv2 is also of the same form (d is not a perfect square) Q2. How many solutions does the equation xax = axa, 0<a<1 have in positive real n ...

1) if two regular hexagons are inscribed in a circle of unit radius.....the min area common to the hexagons is ??? 2)if a triangle is inscribed in a rectangular hyperbola then which one of the following is on the curve a) cen ...

→if four points on the curve 2x4+7x3+3x-5 are colinear then find the A.M of the x coordinate of the four numbers? 1>-7/8 2>7/8 3>3/4 4>-3/4 ...

Solve for reals (x,y) 2^{y-x}(x+y)=1 (x+y)^{x-y}=2 ...

They might be simple, But mujhse accurately kabhi nahi hote...in search fr a strategic approach. Find the number of ordered pairs (x,y) (Both x, y are integers) Satisfying- Q1) 2x2 -3xy -2y2 =7 Q2) y- lx2-2xl +1/2 >0 & y+ ...

∞ Σ tan-1(1/2k2) = θ k=1 Find tanθ [7] ...

The number of functions defined from {1,2,3,4,5} ------> {6,7,8,9,10} which is alternatively increasing and decreasing i.e. a local maxima comes between two local minimas, and a local minima comes between two local maximas ...

if sinα ,sinβ,sinγ are in AP and cosα,cosβ,cosγ are in gp then find the value of \frac{cos^{2}\alpha +cos^{2}\gamma -4cos(\alpha)cos(\gamma ) }{1-sin(\alpha )sin(\gamma) } ...

(1) find total no. of Integral point that can be inside or on the circle x^{2}+y^{2}=49 ...

(1) let x be a positive real.Find maximum possible value of y=(x2+2- x4+4 ) / x ...

Let ABC be any triangle with altitudes h1,h2,h3 and inradius r, then find the minimum value of (h1+r)/(h1-r) +(h2+r)/(h2-r) +(h3+r)/(h3-r) = If A,B and C are three non-collinear points in a plane, the area of the greatest equ ...

A bag contains n identical red balls , 2n identical black balls & 3n identical white balls . If probability of drawing n balls of same colour is equal to 1/6 , then minimum no of red balls in the bag is equal to ? ...

Prove that 2^{k}\begin{pmatrix} n\\0 \end{pmatrix}\begin{pmatrix} n\\k \end{pmatrix}-2^{k-1}\begin{pmatrix} n\\1 \end{pmatrix}\begin{pmatrix} n-1\\k-1 \end{pmatrix}+2^{k-2}\begin{pmatrix} n\\2 \end{pmatrix}\begin{pmatrix} n-2 ...

Let f(x) be a function defined as f(x-1)+f(x+1)=f(x) then what iz the period of the function f(x)? (1)8 (2)4 (3)2 (4)12 answer me with explanation ...

find the values of a for which the equation- (x-1)2=|x-a| has exactly 3 solutions ...

1)No of ordered triplets (x,y,z) satisfying (1+sin^{4}x)(2+cot^{2}y)(4+sin4z)\leq 12sin^{2}x 2)Let P be a point on the hyperbola x2-y2=a2,wher a is parameter,such that P is nearest to the line y=2a.The locus of P is _____ 3)s ...

Can anyone explain the difference between 5C3 and 5C1 x 4C1 x 3C1 ?? ...

Q1. Let f(x+y) = f(x).f(y) for all x,y belongs to R and f(5) = 2 and f'(0) = 3. Then f'(5) = ? Q2. Let f(x) be defined in R such that f(1) = 2 and f(2) = 8 and f(u+v) = f(u) + kuv - 2v2 for all u,v belongs to R and k is a fix ...

Q1...................... for 0< \theta <\pi /2 the solutions of \sum_{m=1}^{6}{cosec(\theta +\frac{(m-1)\pi }{4}}).cosec(\theta +\frac{m\pi }{4})=4\sqrt{2} are 1) pi/4 2)pi/6 3)pi/12 4)5pi/12 P.S i want a shorter method ...

Area bounded by the curve y=ex2, x-axis and the lines x=1, x=2 is given to be equal to a sq units. Area bounded by the curve y=√(ln x) , y-axius, and the lines y=e and y=e4 is equal to ? ...