General Instructions:
i. All questions are compulsory.
ii. The question paper consists of 29 questions divided into three sections A, B and C. Section A comprises of 10 questions of one mark each, Section B comprises of 12 questions of four marks each, and Section C comprises of 7 questions of six marks each.
iii. All questions in section A are to be answered in one word, one sentence or as per the exact requirements of the question.
iv. There is no overall choice. However, internal choice has been provided in 4 questions of four marks each and 2 questions of six marks each. You have to attempt only one of the alternatives in all such questions.
v. Use of calculators is not permitted.
Question 1
Let * be a binary operation, on the set of all non-zero real numbers, given by for all a, b ∈ R – {0}. Find the value of x, given that 2 * (x * 5) = 10. VIEW SOLUTION
Find the projection of the vector on the vector . VIEW SOLUTION
Question 9
If are two unit vectors such that is also a unit vector, then find the angle between . VIEW SOLUTION
Question 10
Write the vector equation of the plane, passing through the point (a, b, c) and parallel to the plane . VIEW SOLUTION
Question 11
Let A = {1, 2, 3,......, 9} and R be the relation in A × A defined by (a, b) R (c, d) if a + d = b + c for (a, b), (c, d) in A × A. Prove that R is an equivalence relation. Also, obtain the equivalence class [(2, 5)]. VIEW SOLUTION
Find the particular solution of the differential equation given that y = 1 when x = 0. VIEW SOLUTION
Question 19
Solve the following differential equation: VIEW SOLUTION
Question 20
Prove that, for any three vectors
OR
Vectors and are such that .
Find the angle between . VIEW SOLUTION
Question 21
Show that the linesintersect. Also find their point of intersection. VIEW SOLUTION
Question 22
Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls? Give that
(i) the youngest is a girl.
(ii) at least one is a girl. VIEW SOLUTION
Question 23
Two schools P and Q want to award their selected students on the values of discipline, politeness and punctuality. The school P wants to award Rs x each, Rs y each and Rs z each for the three respective values to its 3, 2 and 1 students with a total award money of Rs 1,000. School Q wants to spend Rs 1,500 to award its 4, 1 and 3 students on the respective values (by giving the same award money for the three values as before). If the total amount of awards for one prize on each value is Rs 600, using matrices, find the award money for each value.
Apart from the above three values, suggest one more value for awards. VIEW SOLUTION
Question 24
Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is VIEW SOLUTION
Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x2 + y2 = 32. VIEW SOLUTION
Question 27
Find the distance between the point (7, 2, 4) and the plane determined by the points A(2, 5, −3), B(−2, −3, 5) and C(5, 3, −3).
OR
Find the distance of the point (−1, −5, −10) from the point of intersection of the line and the plane VIEW SOLUTION
Question 28
A dealer in rural area wishes to purchase a number of sewing machines. He has only Rs 5,760 to invest and has space for at most 20 items for storage. An electronic sewing machine cost him Rs 360 and a manually operated sewing machine Rs 240. He can sell an electronic sewing machine at a profit of Rs 22 and a manually operated sewing machine at a profit of Rs 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit? Make it as a LPP and solve it graphically. VIEW SOLUTION
Question 29
A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a spade.
OR
From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution. VIEW SOLUTION
More Board Paper Solutions for Class 12 Science Maths