HSC Science (Computer Science) इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

Solve the following LPP:

Minimize z = 4x + 2y

Subject to 3x + y ≥ 27, x + y ≥ 21, x + 2y ≥ 30, x ≥ 0, y ≥ 0

A carpenter makes chairs and tables. Profits are ₹ 140 per chair and ₹ 210 per table. Both products are processed on three machines: Assembling, Finishing and Polishing. The time required for each product in hours and availability of each machine is given by the following table:

Formulate the above problem as LPP. Solve it graphically

A company produces mixers and food processors. Profit on selling one mixer and one food processor is Rs 2,000 and Rs 3,000 respectively. Both the products are processed through three machines A, B, C. The time required in hours for each product and total time available in hours per week on each machine arc as follows:

How many mixers and food processors should be produced in order to maximize the profit?

A chemical company produces a chemical containing three basic elements A, B, C, so that it has at least 16 litres of A, 24 litres of B and 18 litres of C. This chemical is made by mixing two compounds I and II. Each unit of compound I has 4 litres of A, 12 litres of B and 2 litres of C. Each unit of compound II has 2 litres of A, 2 litres of B and 6 litres of C. The cost per unit of compound I is ₹ 800 and that of compound II is ₹ 640. Formulate the problems as LPP and solve it to minimize the cost.

A firm manufactures two products A and B on which profit earned per unit are ₹ 3 and ₹ 4 respectively. Each product is processed on two machines M₁ and M₂. The product A requires one minute of processing time on M₁ and two minutes of processing time on M₂, B requires one minute of processing time on M₁ and one minute of processing time on M₂. Machine M₁ is available for use for 450 minutes while M₂ is available for 600 minutes during any working day. Find the number of units of products A and B to be manufactured to get the maximum profit.

A firm manufacturing two types of electrical items A and B, can make a profit of ₹ 20 per unit of A and ₹ 30 per unit of B. Both A and B make use of two essential components a motor and a transformer. Each unit of A requires 3 motors and 2 transformers and each units of B requires 2 motors and 4 transformers. The total supply of components per month is restricted to 210 motors and 300 transformers. How many units of A and B should be manufactured per month to maximize profit? How much is the maximum profit?

A spherical soap bubble is expanding so that its radius is increasing at the rate of 0.02 cm/sec. At what rate is the surface area is increasing, when its radius is 5 cm?

The volume of a sphere increases at the rate of 20 cm³/sec. Find the rate of change of its surface area, when its radius is 5 cm

A man of height 2 metres walks at a uniform speed of 6 km/hr away from a lamp post of 6 metres high. Find the rate at which the length of the shadow is increasing.

A man of height 1.5 meters walks towards a lamp post of height 4.5 meters, at the rate of `(3/4)` meter/sec. Find the rate at which (i) his shadow is shortening (ii) the tip of shadow is moving.

A ladder 10 metres long is leaning against a vertical wall. If the bottom of the ladder is pulled horizontally away from the wall at the rate of 1.2 metres per second, find how fast the top of the ladder is sliding down the wall, when the bottom is 6 metres away from the wall.

Choose the correct option from the given alternatives :

A ladder 5 m in length is resting against vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of `(1.5 "m")/sec`. The length of the higher point of ladder when the foot of the ladder is 4.0 m away from the wall decreases at the rate of

Solve the following:

A water tank in the farm of an inverted cone is being emptied at the rate of 2 cubic feet per second. The height of the cone is 8 feet and the radius is 4 feet. Find the rate of change of the water level when the depth is 6 feet.

Solve the following : Find all points on the ellipse 9x² + 16y² = 400, at which the y-coordinate is decreasing and the coordinate is increasing at the same rate.

Solve the following : The position of a particle is given by the function s (t) = 2t² + 3t – 4. Find the time t = c in the interval 0 ≤ t ≤ 4 when the instantaneous velocity of the particle equal to its average velocity in this interval.

Integrate the following w.r.t. x : x³ + x2 – x + 1

Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`

Integrate the following w.r.t. x:

`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`

Integrate the following w.r.t. x:

`2x^3 - 5x + 3/x + 4/x^5`

Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`