Recently Active Mathematics Questions

Calculate the product for n≥2 *Image* ...

f(x)=\int_{0}^{\pi}\sin (x-t)\sin (2t-a)\ dt with respect to x... ...

Find the area of the region bounded by the curves y = logex, y = sin4Ï€x and x = 0. ...

Show that the curve (x/a)2n + (y/b)2n=2 touches the straight line x/a+y/b=2 at (a,b) no matter what the value of n be. ...

22. There are n triangles of positive area that have one vertex A(0,0) and the other two vertices whose coordinares are drawn independently with replacement from the set {0,1,2,3,4} e.g. (1,2), (0,1), (2,2) etc. Find the valu ...

(y3-2x2y)dx + (2xy2 - x3)dy =0, then the value of xy√(y2-x2) is 1. y2 +x 2. xy2 3. any constant 4. none of these ...

Use the substitution y2=a-x to reduce the equation y3 dy/dx +x+y2=0 to homogeneous form and hence solve it. ...

*Image* ...

Δ= 1+x (1+x)a (1+x)bc 1+x (1+x)b (1+x)ca 1+x (1+x)c (1+x)ab find coeff. of x and x2. ...

Find the value(s) of the parameter 'a' (a>0) for each of which the area of the figure bounded by the straight line, y = a2-ax/1+a4 and the parabola y = x2+2ax+3a2/1+a4 is the greatest. ...

EX 2 1 ) Find the no. of ways in which 3 distinct no.s can be selected from the set { 3 , 32,......,3101} so that they form a GP. 2 ) Find the no. of ways in which 12 identical coins can be distributed in 6 diff purses , if n ...

Find the no of solutions of |x2 - 6|x| +8|= 1/4 |sin|x|| 1) 4 2) 6 3) 8 4) 10 ...

find the differential equation of the following y=c1sin2x+c2cos2x+c3 ...

Prove that every circle passing through the points z_{0} and 1/z 0 intersects the circle |z|=1 at right angles ...

Does any body know whats rotation theorem ,locus of a complex nos . if you can explain me in detail its fine or if you have any link or you have any material can you send me at karanmehtaforu@yahoo.com Thanks in advance ...

Find the curve y = f(x) where f(x)≥0, f(0)= 0, bounding a curfilinear trapezoid with the base {0,x] whose area is proportional to (n+1)th power of f(x). It is known that f(1) = 1. ...

Sagnik just posted this one on my chatbox... Prove that (a,b, c +ve) a2+1/b+c + b2+1/a+c + c2+1/a+b ≥3 RMO: 2006 Hint: Nesbitts? ...

A point P moves inside the triangle formed by A (0,0) , B(1,1/ 3 ) and C(2,0) such that min { PA,PB,PC} =1 then the area bounded by the curve traced by P is a. 3 3 +3pi/2 b. 3 3 -3pi/2 c. 3 -pi/2 d. 3 +pi/2 NOTE→Please give ...

(x^2+x-2)^3+(2x^2-x-1)^3=27(x^2-1)^3 Source: RMO 2002 ...

Just saw this problem in some Coaching Institute material. If cos A + cos B + cos C = sin A + sin B + sin C = 0, prove that cos (A-B) + cos (B-C) + cos (C-A) = -3/2 ...

Can neone pls explain how n{1+(n-1)+ (n-1)(n-2)/1.2 +...........+1} =n.2n-1 ? AND nx{1+(n-1)x+ (n-1)(n-2)/1.2 x2+........+xn-1} =nx(1+x)n-1 ? Pleaaaaaaaase do explain this... ...

Evaluate the following:- 1) *Image* 2) *Image* ...

Let x1,x2,x3...xn be roots of equation xn+xn-1+.....+x+1=0 Compute the expression \frac{1}{x_1 -1}+\frac{1}{x_2 -1}+\frac{1}{x_3 -1}...+\frac{1}{x_n -1} Hence prove that \sum_{r=1}^{n}{cot \frac {r\pi}{n+1}} ...

Let P(x) be a polynomial with integral coefficients. Prove that we can never have P(a) = b and P(b) = c and P(c) = a where a,b and c are integers. ( bhatt sir , please stay away) ...

Ques) Find / Evaluate *Image* ...

find the Domain and Range(of course give explanation) these are also last yrs question 1)f(x)=limn->∞cos(n! 2Πx) 2)g(x)=limn->∞cosn( 2Πx) 3)h(x)=limn->∞{cos(nx) + 2}1/n ...

Prove the following (a2<1) a) \int _{0} ^ { \pi } ln(1-2a \cos \theta +a^2) d \theta=\begin{Bmatrix} 0 & a<1\\ 2\pi lna & a>1 \end{Bmatrix} b) \int _{0} ^ { \pi } ln(1-2a \cos \theta +a^2)\cos n \theta d \theta= - \f ...

A man begins running along a circular track at 10 km/hr . There is a source of light at the centre of the circle and a wall which is tangential to the point from which the man begins running. Find the speed of the man's shado ...

Find the product of these numbers... (1-\frac{1}{2^2})(1-\frac{1}{3^2})(1-\frac{1}{5^2})(1-\frac{1}{7^2})(1-\frac{1}{11^2})... till infinity... Given that \frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+ ...

errr....just got confused...which one of these is correct?? sin(a) + sin(a+d) + sin(a+2d) + sin(a+3d) + ...... + sin(a+nd) = \frac{sin\left(\frac{2a+nd}{2}\right)sin\left(\frac{nd}{2} \right)}{sin\left(\frac{d}{2} \right)} OR ...