[21.e^(2r)s_(ih)..],[C],[qquad C]

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) , then sumsum_(0lerltslen)(r+s)C_(r)C_(s) is equal to :

If the circle S_(1)=0,S_(2)=0i.e,g_(1),f_(1),c_(1) and g_(2),f_(2),c_(2) touch each other than prove that [2g_(1)g_(2)+2f_(1)f_(2)-[c_(1)+c_(2))]^(2)=4r^(2)r_(1)^(2), where r_(1),r_(2) are the radia of the two circles.

For the consecutive unimolecular-type first-order reaction A overset(k_(1))rarr R overset(k_(2))rarr S , the concentration of component R, C_( R) at any time t is given by - C_(R ) = C_(OA)K_(1)[e^(-k_(1)t)/((k_(2)-k_(1))) +e^(-k_(2)t)/((k_(1)-k_(2)))] if C_(A) = C_(AO), C_(R ) = C_(RO) = 0 at t = 0 The time at which the maximum concentration of R occurs is -

The solution set of the ineuality (c o s e c^(- 1)x)^2-2c o s e c^(- 1)xgeqpi/6(c o s e c^(- 1)x-2) is (-oo,a] uu [b,oo) , then (a+b) equals

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+…..+C_(n)x^(n) , then the value of sumsum_(0lerltslen)(r*s)C_(r)C_(s) is :

Write the order of the differential equation associated with the primitive y=C_1+C_2e^x+C_3e^(-2x)+C_4,\ w h e r e\ C_1, C_2, C _3,\ C_4 are arbitrary constants.

If C_(0),C_(1),C_(2),.........,C_(n) denote the binomial coefficients in the expansion of (1+1)^(n), then sum_(0<=r

Find the principal values of " (1) c o s e c"^(-1)(2) and "c o s e c"^(-1)(-2/(sqrt(3)))

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) , then the value of sumsum_(0lerltslen)(r+s)(C_(r)+C_(s)+C_(r)C_(s)) is :

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+….+C_(n)x^(n) , then the value of sumsum_(0lerltslen)(r+s)(C_(r)+C_(s)) is :