CBSE Class 12 Applied Mathematics — Short Answer Questions

(a) (i) Apply addition modulo to positive integers 17 and 13 for modulo 30. (ii) Find subtraction modulo 8 for numbers 11 and 3. OR (b) Three pipes A, B and C can together fill a tank in 8 hours. After working at it together for 2 hours, B is closed and A and C fill the remaining part in 9 hours. Determine the time in which pipe B alone can fill the tank.

Using Cramer's rule, show that the following system of linear equations is consistent and hence solve it : $2x - 3y + 5z = 11$ $3x + 2y - 4z = -5$ $x + y - 2z = -3$

(a) Find the intervals in $\mathbb{R}$ for which the function $f(x) = x^4 - 2x^2$ is increasing or decreasing. OR (b) Find : $\int \frac{2x + 1}{\sqrt{18 - 4x - x^2}} dx$

A company XYZ Ltd. has issued a bond having a face value of Rs 10,000 paying annual dividend at 8.5% p.a. The bond will be redeemed at par at the end of 10 years. Find the purchase value of this bond, if the investor wishes a yield rate of 8%. [Given : $(1.08)^{-10} = 0.46319349$]

A soap manufacturing company was distributing a particular brand of a soap through a large number of retail shops. Before a heavy advertisement campaign, the mean sales per week per shop was 140 dozen. After the campaign, a sample of 26 shops was taken and mean sales was found to be 147 dozen with standard deviation 16. Can you consider the advertisement campaign effective ? [Given $t_{25}(0.05) = 2.06$]

Solve the following Linear Programming Problem (LPP) graphically : Maximize $z = 3x + 5y$ subject to the constraints : $x + 2y \le 2000$ $x + y \le 1500$ $y \le 600$ $x \ge 0, y \ge 0$