Board Paper of Class 12-Commerce 2007 Maths Delhi(SET 1) - Solutions

Find the projection of , where

Find the value of λ which makes the vectors coplanar, where

A particle starting with initial velocity of 30 m/sec, moves with a uniform acceleration of 9 m/sec²Find:

(a) the velocity of the particle after 6 seconds

(b) how far will it go in 9 seconds.

(c) its velocity when it has travelled 150 m.

(a) Find the resultant of two velocities 4 m/sec and 6 m/sec inclined to one another at an angle of 120°.

(b) A ball projected with a velocity of 28 m/sec has a horizontal range 40 m. Find the two possible angles of projection.

A body of weight 70 N is suspended by two strings of lengths 27 cm and 36 cm, fastened to two points in the same horizontal line 45 cm apart and is in equilibrium. Find the tensions in the strings.

The resultant of two unlike parallel forces of 18 N and 10 N act along a line at a distance of 12 cm from the line of action of the smaller force. Find the distance between the lines of action of two forces.

Find the equation of the plane which is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and which contains the line of intersection of the planes x + 2y + 3z − 4 = 0 and 2x + y − z + 5 = 0.

Find the equation of the sphere passing through the points (3, 0, 0), (0, −1, 0), (0, 0, −2) and having the centre on the plane 3x +2y + 4z = 1.

Find the face value of a bill, discounted at 6% per annum 146 days before the due date, if the banker’s gain is Rs. 36.

Out of current syllabus

A bill for Rs. 7650 was drawn on 8^th March, 2005 at 7 months. It was discounted on 18^th May, 2005 and the holder of the bill received Rs. 7497. What rate of interest did the banker charge?

Out of current syllabus

There are two bags I and II. Bag I contains 2 white and 3 red balls and Bag II contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag II.

Find mean μ, variance σ² for the following probability distribution:

Or

Find the binomial distribution for which the mean is 4 and variance 3.

A, B, C entered into a partnership investing Rs. 12000, Rs. 16000 and Rs. 20000 respectively. A as working partner gets 10% of the annual profit for the same. After 5 months, B invested Rs. 2000 more while C withdrew Rs. 2000 after 8 months from the start of the business. Find the share of each in an annual profit of Rs. 97000.

Out of current syllabus

Find present value of an annuity due of Rs. 700 per annum payable at the beginning of each year for 2 years allowing interest 6% per annum, compounded annually. [Take (1.06)⁻¹ = 0.943]

Out of current syllabus

The total cost C(x), associated with the production and making x units of an item is given by

C(x) = 0.005 x³ − 0.02 x² + 30 x + 5000

Find (i) the average cost function (ii) the average cost of output of 10 units (iii) the marginal cost function (iv) the marginal cost when 3 units are produced.

Out of current syllabus

If a young man rides his motorcycle at 25 km/hour, he has to spend Rs. 2 per km on petrol. If he rides at a faster speed of 40 km/hour, the petrol cost increases at Rs. 5 per km. He has Rs. 100 to spend on petrol and wishes to find the maximum distance he can travel within one hour. Express this as an LPP and solve it graphically.