U0001f9d1u200d

10.0001+9.9999-8.9995=? (a) 9.0005 (b) 10.9995 (c) 11.0001 (d) 11.0005 (e) None of these

If sum_(n=1)^n u_n =an^2+bn+c, then |(u_1,u_2,u_3),(1,1,1),(7,8,9)|= (A) 0 (B) u_1-u_2+u_3 (C) 1 (D) none of these

The following integral int_(pi/4)^(pi/2)(2cos e cx)^(17)dx is equal to (a)int_0^("log"(1+sqrt(2)))2(e^u+e^(-u))^(16)d u (b)int_0^("log"(1+sqrt(2)))2(e^u+e^(-u))^(17)d u (c)int_0^("log"(1+sqrt(2)))2(e^u-e^(-u))^(17)d u (d)int_0^("log"(1+sqrt(2)))2(e^u-e^(-u))^(16)d u

Prove that d/(dx)|(u_1,v_1,w_1),(u_2,v_2,w_2),(u_3,v_3,w_3)|=|(u_1,v_1,w_1),(u_2,v_2,w_2),(u_4,v_4,w_4)| where u,v,w are functions of x and (du)/(dx)=u_1,(d^2u)/(dx^2)=u_2, etc.

The focal length of a less is given by the formula (1)/(f)=(1)/(u)+(1)/(v) . Make f as the subject of the formula. if u=20cm and v=30, then find f. The following steps are involved in solving the above problem. Arrange them in sequential order. (A) Given (1)/(f)=(1)/(u)+(1)/(v) (B) rArr f=(uv)/(u+v) (C) f=(20xx30)/(20+30)=(600)/(50)=12 cm. (D) rArr (1)/(f)=(v+u)/(uv)

Let a,b,c and d are real numbers in GP. Suppose u,v,w satisfy the system of equations u+2y+3w=6,4u+5y+6w=12 and 6u+9v=4 . Further consider the expressions f(x)=(1/u+1/v+1/w)x^(2)+[(b-c)^(2)+(c-a)^(2)+(x-b)^(2)] x+u+v+w=0 and g(x)=20x^(2)+10(a-d)^(2)x-9=0 (u+v+w) is equal to