The price of an item x increases by ₹10 every year and an item y decreases by ₹15 every year. If in 2018, the price of x is ₹50 and y is ₹90, then which item will costlier in the year 2020?

A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find: (i) the production in the 1st yea (ii) the production in the 10th year (iii) the total production in first 7 years Solution :

A factory has two machines X and Y .X produces 70% and Y produces 30% of the items of which items produced by X have 5% defective items and items produced by Y have 8% defective. An item is drawn at random for the product and is found to be defective. Find the probability that it was produced by Machine Y.

The price of a product is related to the number of units available (supply) by the equation Px+3P-16x=234 , where P is the price of the product per unit in Rupees (Rs) and x is the number of units. Find the rate at which the price is changing with respect to time when 90 units are available an the supply is increasing at a rate of units/week .

The supply equation is given p(x+2) = 4x + 90 , where p is the price/unit in rupees and x is the no. of units find the rate at which the price is changing with respect to time when 39 units are available and the supply is increasing at the rate of 5 units/week.

The length x of a rectangle is decreasing at the rate of 3 cm/minute and the width y is increasing at the rate of 2cm/minute. When x =10cm and y = 6cm, find the rates of change of (a) the perimeter and (b) the area of the rectangle.

A square loop of side 12 cm with its sides parallel to X and Y axes is moved with a velocity of 8cms^(-1) in the possitive x-direction in an environment containing a magnetic field in the positive z- direction. The field is neither uniform in space nor constant in time. It has a gradient of 10^(-3)Tcm^(-1) along the negative x-direction (that is it increases by 10^(-3)T as one moves in the negative x-direction), and it is decreasing in time at the rate of 10^(-3)Ts^(-1) . Determine the direction and magnitude of the induced current in the loop of its resistance is 4.50mOmega .

Three candidates X, Y, and Z are going to play in a chess competition to win FIDE (World Chess Federation) cup this year. X is thrice as likely to win as Y and Y is twice as likely as to win Z. Find the respective probability of X, Y and Z to win the cup