Recently Active Mathematics Questions

Q 2n girls are randomly divided into 2 subgroups contaitning n girls each.The probablity that two tallest girls are in diff groups... Ans given is n/2(2n-1) ..but i am getting (n-1)/2n ...

For how many values of "a" will the following equation have two equal roots: x^3 + (a^2++a-1)x^2 + (a^3-a^2-a)x -a^3 =0 i got 4 as ans.... plz verify... ...

I know this has been done before here...but I couldnt understand soln there or at goiit..where bhatt sir did it So posting it again.... If f(x).f'(x).f"(x)>0 for all xεR.Then prove that f(x) is increasing function ...

Prove that n= 5125-1/525-1 is a composite number. ...

Q1 graph of x2+y2=0 in 3D is ?? Q2 Locus of xy+yz=0 in 3D is ??? ...

Q1. 9 persons enter a lift from the ground floor of a building which stops at 10 floors exulding the ground floor ,if its known that persons will leave in groups of 2,3,4 in different floors ..In how many ways can this happen ...

Prove or disprove that sin A/A + sin B/B + sin C/C ≥ 9 (4 - 3 - 3 .25 )/2 Πwhere A,B,C are the angles of a triangle in radian. ...

if a>b>0 n→N prove that an -bn>=n(a-b)(ab)(n-1) /2 ...

locus of center of circle which touches (x+2)^2 + y^2 =4 nd (x-1)^2 + y^2=1 externally. let A is d vertex of its locus. An isosceles triangle is constructed such dat its vertex is at A nd base touches d circle. what is d area ...

A car will hold 2 in the front seat and 1 in the rear seat.If among 6 persons 2 can drive,then what is the number of ways in which the car can be filled? ...

If x = {1,2,3,..............., 100} and let S = {(a,b,c) | a,b,c belongs to a < b and a <c }, then the number of elements in S are : (a) 328250 (b) 328450 (c)328350 (d) none ...

if the circle C1 touches x-axis and the line y = x tanθ (tan θ >0) in frist quadrant and circle C2 touches the line y = x tan θ, y - axis and circle C1 in such a way that ratio of radius of C1 and C2 is 2:1 then the val ...

ques. There are 5 boxes of 5 different colors. Also there are 5 balls of colors same as those of the boxes. In how many ways we can place 5 balls in 5 boxes such that a) all balls are placed in the boxes of colors not same as ...

Hi T IIT IIANS !!! ...

Number of quadrilaterals which can be constructed by joining the vertices of a convex polygon of 20 sides, if none of the side of the polygon is also the side of the quadrilateral is : (a) 17C4 – 15C2 (b) 15C3 .20/4 (c) 227 ...

find the sum (nC1)2 + 2(nC2)2 + ...+ n(nCn)2 ...

a+b+c=1 then prove (1+1/a)(1+1/b)(1+1/c) >= 64 ...

In a town of population of n,a person sends 2 letters to 2 separate persons,each of whom is asked to repeat the procedure.Thus for each letter recieved,2 letters are sent to 2 separate persons chosen at random, Let P1,P2,..., ...

Fermat's Little theorem states taht .... If p is prime, then P divides ap-a A good question for congruences.... To understand and implement it.... I am giving the guidelines on how to approach and solve.. see if it fits your ...

unit vectors a and b are perpendicular to each other and unit vector c is inclined at angle θ to both a and b.If c=m(a+b)+n(axb) and m,n are real.Find range of θ I have found m=cosθ...and nothing else..help me out ...

Find vector which is orthogonal to vector 3i+2j+6k and is coplanar with 2i+j+k and i+j-k ...

Given that x^3-3xy^2 = 10 and y^3-3x^2y = 30 find the value of x^2+y^2 ...

If |z-25i|≤15 then |max Arg. (z)-min Arg. (z)| equals to..? ...

Prove that if n >3 , then *Image* = 0 ...

A is a point on circumference of a circle, chords AB and AC divide circle area in three equal parts, f(x)=0 is an equation whose root is angle BAC, then f(x) is equal (A) x-sinx+ \pi /3 (B) x+sinx+ \pi /3 (C) 2[x-sinx+ \pi /3 ...

find the remainder wen a)...1399 is divided by 81 b)....22225555 +55552222 is divided by 7 ...

If y=[tan-1 1/(1+x+x2) + tan-1 1/(x2+3x+3) + tan-1 1/(x2+5x+7) +....] upto n terms,then y'(0) is equal to: a)-1/(n2+1) b)-n2/(n2+1) c)n2/(n2+1) d)none of these ...

Prove: \prod_{k=1}^{n}{\left[ 1+2\cos\frac{2\pi.3^k}{3^n+1}\right]}=1 Source: Titu Andreescu's Book.. ...

(\frac12+cos\frac{\pi}{20})(\frac12+cos\frac{3\pi}{20})(\frac12+cos\frac{9\pi}{20})(\frac12+cos\frac{27\pi}{20})=\frac1{16} This is another problem again from Titu Andreescu's book... (Hint: Chapter: Telescopic products and P ...

A circle of radius 5 units has diameter along the angle bisector of the lines x+y = 2 and x - y = 2. If chord of contact from origin makes an angle of 45° with the positive direction of x axis then the equation of the circle ...