Current passing through resistance R , `I=(dQ)/(dt)=a-2bt` Now , I will be zero when `a-2bt=0" or, " t=(a)/(2b)` `therefore ` Total heat produced in R `= int_(0)^(t)=I^(2)Rdt=int_(0)^((2)/(2b))(a-2bt)^(2)Rdt` `=int_(0)^((a)/(2b))(a^(2)R+4b^(2)Rt^(2)-4abRt)dt` `=[a^(2)Rt+(4b^(2))/(3)Rt^(3)-(4abR)/(2)t^(2)]_(0)^((a)/(2b))=(a^(3)b)/(6b)`
Let , a , b ,c ,d , p ,q ,r be positive real number such that a ,b , c are in G.P and a^(p)=b^(q)=c^(r) Then-
If (p+q)t h term of a G.P. is a and its (p-q)t h term is b where a ,b in R^+ , then its pth term is (a). sqrt((a^3)/b) (b). sqrt((b^3)/a) (c). sqrt(a b) (d). none of these
Show that **: R xx R to R given by (a,b) to a + 4b ^(2) is a binary operation.
For a general chemical change 2A =3B to products, the rates with respect to A Is r_1 and r_2 are related as
Prove that r_(1) r_(2) + r_(2) r_(3) + r_(3) r_(1) = (1)/(4) (a + b + c)^(2)
The exradii r_1,r_2 and r_3 of /_\A B C are in H.P. Show that its sides a , b a n d c are in AdotPdot
The largest area of the trapezium inscribed in a semi-circle or radius R , if the lower base is on the diameter, is (a) (3sqrt(3))/4R^2 (b) (sqrt(3))/2R^2 (3sqrt(3))/8R^2 (d) R^2
Check whether the realtion R defined in the set {1,2,3,4,5,6} as R = {(a,b) : b =a +1} is reflexive, symmetric or transitive.
CHHAYA PUBLICATION-ELECTRIC ENERGY AND POWER-EXAMINATION ARCHIVE (NEET)
