`(9v+1)+(3v+1)`

Evaluate : 1/3 int ( 1 + 2v ) / ( v^2 + v + 1 )dv

Find a rational number between (i) (3)/(8) and (2)/(5) (ii) 1.3 and 1.4 (iii) - 1 and (1)/(2) (iv) -(3)/(4) and -(2)/(5) (v) (1)/(9) and (2)/(9)

Give the magnitude and polarity of the following voltages in the circuit of figure: i. V_1 ii. V_2 iii. V_3 iv. V_(3-2) v. V_(1-2) V_(1-3)

Give the magnitude and polarity of the following voltages in the circuit of figure: i. V_1 ii. V_2 iii. V_3 iv. V_(3-2) v. V_(1-2) V_(1-3)

Find 3 -dimensional vectors vec v_ (1), vec v_ (2), vec v_ (3) satisfying vec v_ (1) * vec v_ (1) = 4, vec v_ (1) * vec v_ (2) = - 2, vec v_ (1) * vec v_ (3) = 6, vec v_ (2) * vec v_ (2) = 2, vec v_ (2) * vec v_ (3) = - 5, vec v_ (3) * vec v_ (3)

In the circuit shown in figure reading of voltmeter is V_(1) when only S_(1) is closed, reading of voltmeter is V_(2) when only S_(2) is closed and reading of voltmeter is V_(3) when both S_(1) and S_(2) are closed. Then 1) V_(3) gt V_(2) gt V_(1) 2) V_(2) gt V_(1) gt V_(3) 3) V_(3) gt V_(1) gt V_(2) 4) V_(1) gt V_(2) gt V_(3)

A car moves with speed v_(1) upto (t)/(3) time and then with speed v_(2) upto next (2t)/(3) time. Path is straight line.What is the average speed of car? " (A) (2v_(1)v_(2))/(v_(1)+v_(2)) (B) (v_(1)+v_(2))/(2) (C) (2v_(1)+v_(2))/(3) (D) (v_(1)+2v_(2))/(3)