Recently Active Mathematics Questions

prove that 1*2* nCr-- 2*3* nCr-2 + 3*4*nCr-2-.............+(-1)r(r+1)(r+2) = 2* n-3Cr ...

*Image* how is it done ? ...

Q1 \lim_{m\rightarrow infinity}[(\frac{e^{-100}.100^{100}}{100!})^{m}+5^{m}]^{1/m} ...

Statement 1: and Statement 2: 1. Statement 1 is True, statement 2 is True; statement 2 is a correct explanation for statement 1. 2. Statement 1 is True, statement 2 is True; statement 2 is not a correct explanation for statem ...

Statement 1: If z1 and z2 are two complex numbers such that their product is a real number, then they are conjugate to each other and Statement 2: (x + iy) (x - iy) = x2 + y2, x, y R. 1. Statement 1 is True, statement 2 is Tr ...

x^3\frac{dy}{dx}-4x^2coty=e^xcosecy solve the de....and find solution given that y(1)=0 ...

find .... [ k = 1Σ80( 1/√k ) ] .. where [.] denotes greatest integer function ... ...

please give detailed solution ... find the orthocentre of triangle whose vertices are z1 z2 z3 ... ...

2 different lines meet a circle |z| =r in the points p , q , r ,s lines are not parrallel . then prove that these lines meet in the point z given by \frac{p^{-1} + q^{-1} -r^{-1}-s^{-1}}{p^{-1}q^{-1} -r^{-1}s^{-1} } =z ...

f(x) is a bijective function .. g(x) is inverse of that function .. f '(x) = 1/ (1 + x2009) find g ' (x) in terms of g(x) ? ...

please give a detailed solution... dont give me hints i tried it many times before editing [2] can u please tell me equation of line perpendicular to az + \bar{a}\bar{z}+b=0 yaar actually i cant make out difference b/w two eq ...

Let a and b be 2 non collinear unit vectors . u=a-(a.b)b and v = a x b,then |v| = ? (in terms of u , a,b) ...

1. let f(x)=x2+bx+c,where b,c ε R.if f(x) is a factor of both x4+6x2+25 and 3x4+4x2+28x+5,then least value of f(x) is a. 2 b. 3 c. 5/2 d. 4 2. the number of ordered pair of positive integers x,y such that x2+3y and y2+3x are ...

Statement 1 *Image* Stat2 *Image* ...

suppose that f(x) is properly integrable over [a,b] and g(x) properly integrable over [a,b+d], d>0. then prove that \lim_{\delta \rightarrow +0}\int_{a}^{b}{}f(x)g(x+\delta )dx=\int_{a}^{b}{f(x)g(x)}dx ...

integrations: q1)∫(2x12 + 5 x9) / ((x5 + x3 +1) dx Q2)∫x4/(1-x2)3/2 dx ...

find the number of the natural numbers less than or equal to 2985984,which are neither perfect squares nor perfect cubes . ...

*Image* try d 7th and 8th one ...

WATS DA SHORTEST WAY to find da circumcenter and INCENTRE of a triangle if the 3 vertices are known? How bout ORTHO-Center?? ...

if \Theta is the angle subtended at P(0,2) by the circle 4x2+4y2-4x-12y+9=0 then a)tan \Theta /2=1/2 b)tan \Theta =4/3 c) \Theta =90 d) \Theta =45 ...

The straight line whose equation is ax+by=1 where ab>0passes through (3,4) and makes a triangle of area S with the co-ordinate axis. then the least value of S is a)12 b)24 c)6 d)7 ...

1)\lim_{x->0}xlogsinx \; 2) \lim_{x->0} (cosecx)^{^{1/logx}} 3)\lim_{x->0} ((1+x)^{^{1/x}}-e)/x 4)\lim_{x->0}[(sinx)^{1/x}+ (1/x)^{sin x}] ...

find the centre and the radius of the smaller of the two circles that touch the parabola 75y2=64(5x-3) at (6/5,8/5) and the x-axis plzzzz explain ...

I thought sir is having busy days so why not we start a thread 4 the calculus I will daily post question on calculus (both integral and differential) So lets take off[1] Q1 If [x] denotes the integral part of x , then the dom ...

This is a fun problem. May i request that only the students attempt this one? If a,b and c are all distinct real numbers, then find values of a,b and c such that \frac{a-b}{1+ab} + \frac{b-c}{1+bc} + \frac{c-a}{1+ca} = 0 ...

find the min value of \left|a+b\omega +c\omega ^{2} \right| where a,b,c are not equal integers and ω≠1 is cube root of unity.. ...

∫ 3+2cosx/(2+3cosx)2 ...

∫([3+2cosx)/(2+3cosx)2]dx ...

let S be the set of 6 -digit numbers a1 a2 a3 a4 a5 a6 (all digits are distinct) where a1≥ a2≥ a3≥ a4≤ a5≤ a6.then n(S) is equal to NOTE :PLEASE IGNORE THE EQUALITY AND CONSIDER ONLY THE INEQUALITY RELATIONS .(i cou ...

Sides a,b,c of a triangle ABC are in AP \cos(\theta_1)=\frac{a}{b+c} , \cos(\theta_2)=\frac{b}{a+c} and \cos(\theta_3)=\frac{c}{a+b} Then \tan^2\left(\frac{\theta_1}{2} \right)+\tan^2\left(\frac{\theta_3}{2} \right) =? ...