`(10!)=(2)^p.(3)^q.(5)^r.(7)^8` then

If 10! =2^(p).3^(q).5^(r).7^(s) , then -

Let (1+x)^10= sum_(r=0)^(10)c_(r) x^(r), and (1+x)^(7)= sum_(r=o)^(7)d_(r)x^(r). If P= sum_(r=0)^5c_(2r) and Q= sum_(r=o)^(3) d_(2r+1) , then (p)/(Q) is equl to

Simply (a^(p)/a^(q))^(p+q-r).(a^(q)/a^(r ))^(q+r-p).(a^(r )/a^(p))^(r+p-q)

Let (1+x)^10=sum_(r=0)^(10)c_rx^r and (1+x)^7=sum_(r=0)^7d_rx^r . If P=sum_(r=0)^5c_(2r) and Q=sum_(r=0)^3d_(2r+1) , then P/Q is equal to

Let alpha,beta be the roots of the equation x^(2)-px+r=0 and alpha//2,2beta be the roots of the equation x^(2)-qx+r=0 , then the value of r is (1) (2)/(9)(p-q)(2q-p) (2) (2)/(9)(q-p)(2p-q) (3) (2)/(9)(q-2p)(2q-p) (4) (2)/(9)(2p-q)(2q-p)

"If " a_(1) ,a_(2), a_(3)….." are in A.P, then find the value of the following determinant:" |{:(a_(p)+a_(p+m) +a_(p+2m),,2a_(p)+3a_(p+m)+4a_(p+2m),,4a_(p)+9a_(p+m)+16a_(p+2m)),(a_(p)+a_(q+m)+a_(q+2m),,2a_(q)+3a_(q+m) +4a_(q+2m),,4a_(q)+9a_(q+m)+16a_(q+2m)),(a_(r)+a_(r+m)+a_(r+2m),,2a_(r)+3a_(r+m)+4a_(r+2m),,4a_(r) +9a_(r+m)+16a_(r+2m)):}|

State with reason wheher following functins have inverse (i) f : {1,2,3,4} to {10} with f = {(1,10), (2,10), (3,10) ,(4,10)} (ii) g: {5,6,7,8} to {1,2,3,4} with g = {(5,4) , (6,3), (7,4), (8,2)} (iii) h : {2,3,4,5} to {7,9,11,13} with h = {(2,7), (3,9) , (4, 11), (5,13)}

Let P be (5, 3) and a point R on y=x and Q on the x-axis be such that P Q+Q R+R P is minimum. Then the coordinates of Q are ((17)/4,0) (b) (17 ,0) ((17)/2,0) (d) none of these

Let p , q , r in R^(+) and 27pqr ge (p+q+r)^(3) and 3p+4q+5r=12 . Then the value of 8p+4q-7r=