Eddy current loss is directly proportional to (`f=" frequency " "B_(m)= maximum flux density")(a) `f^(2) and `B_(m)^(2)` (b) `f` and `B_(m)` (c) `f`and `B_(m)^(2)` (d) `f^(2)` and `B_(m)`

If a/b = c/d =e/f = 4, then (m ^(2) a + n^(2) c + p ^(2) e )/( m ^(2) b + n ^(2) d + p ^(2) f )=?

int_(a)^(b-a)f''(x+a)dx equals (a) f(b-a)-f(a) " " (b) f(b)-f(2a) (c) f'(b)-f'(2a) " " (d) f'(b-a)-f'(2a)

If f(x)=x^(3) show that int_(a)^(b)f(x)dx=(b-a)/(6){f(a)+4f((a+b)/(2))+f(b)}

Three particles A, B and C of mass m, m and 2m lie in a straight line as shown. The only force acting on these particles is due to the gravitational attraction towards each other. Let the magnitude of net force on them be F_(A), F_(B) and F_(C ) respectively. Then, F_(A):F_(B):F_(C ) is equal to :

If f(x)=a+b x+c x^2AAa ,b ,c in R and a ,b ,c are distinct, then value of |a b c b c a c a b| is (where omega&omega^2 are complex cube roots of unity) f(1)f(omega)f(omega^2) (b) -f(omega)f(omega^2) -f(1)f(omega)f(omega^2) (d) f(omega)f(omega^2)

f(1)=1 and f(n)=2sum_(r=1)^(n-1)f(r). Then sum_(n=1)^(m)f(n) is equal to (A)3^(m)-1(B)3^(m)(C)3^(m-1) (D)none of these

Two spheres A and B made of same material of masses m and 8m respectively are dropped into a long viscous liquid column. If F_(A) and F_(B) are viscous liquid column. If F_(A) and F_(B) are viscous force on A and B respectively when they attained their terminal velocity find F_(A):F_(B)

If f(x)<0,\ x in (a , b) then at the point C(c ,\ f(c)) on y=f(x) for which F(c) is a maximum, f^(prime)(c) is given by a. f^(prime)(c)=(f(b)-f(a))/(b-1) b. \ f^(prime)(c)=(f(b)-f(a))/(a-b) c. f^(prime)(c)=(2(f(b)-f(a)))/(b-a) d. f^(prime)(c)=0

A B C D E F . If B C=3c m , E F=4c m and a r( A B C)=54 c m^2 , then a r( D E F)= 108 c m^2 (b) 96 c m^2 (c) 48 c m^2 (d) 100 c m^2