Author: shivamlohiya

SECTION-A

Question numbers 1 to 6 carry 1 mark each.

3.If P(2, 3, 4) is the foot the of the perpendicular from the origin to a plane, then write the vector equation of this plane.

6.Write the differential equation representing the curve y² = 4ax, where a is an arbitrary constant.

SECTION – B

Question numbers 7 to 19 carry 4 marks each.
7.To raise money for an orphanage, students of three schools A, B and C organized an exhibition in their locality, where they sold paper bags, scrap-books and pastel sheets made by them using recycled paper, at the rate of Rs 20, Rs 15 and Rs 5 per unit respectively. School A sold 25 paper-bags, 12 scrap-books and 34 pastel sheets. School B sold 22 paper-bags, 15 scrapbooks and 28 pastel-sheets while school C sold 26 paper-bags, 18 scrap-books and 36 pastel sheets. Using matrices, find the total amount raised by each school.By such exhibition, which values are inculcated in the students ?

12.Consider the experiment of tossing a coin. If the coin shows tail, toss it again but if it shows head, then throw a die. Find the conditional probability of the event that ‘the die shows a number greater than 3’ given that ‘there is at least one head’.
Or
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90% ?

16.If x = sin t, y = sin kt, show that,

SECTION – C

Question numbers 20 to 26 carry 6 marks each.

21.Compute, using integration, the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7

24.40% students of a college reside in hostel and the remaining reside outside. At the end of year, 50% of the hostellers got A grade while from outside students, only 30% got A grade in the examination. At the end of the year, a student of the college was chosen at random and was found to get A grade. What is the probability that the selected student was a hosteller ? What value is shown here ?

25.A merchant plans to sell two types of personal computer : a desktop model and a portable model that will cost Rs 25,000 and Rs 40,000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get a maximum profit, if the does not want to invest more than 70 lakh and if his profit on the desktop model is Rs 4,500 and that on portable is Rs 5,000.

26.A jet of enemy is flying along the curve y = x² + 2 and a soldier is placed at the point (3, 2). Find the minimum distance between the soldier and the jet.

ANSWERS

SECTION-A

Question numbers lto6 carry 1 mark each.

Ans.

Ans. 5 sq.units

3.If P(2, 3, 4) is the foot the of perpendicular from the origin to a plane, then write the vector equation of this plane.
Ans.

Ans.-14

Ans.m+n=4

6.Write the differential equation representing the curve y² = 4ax, where a is an arbitrary constant.
Ans.

SECTION – B

Question numbers 7 to 19 carry 4 marks each.
7.To raise money for an orphanage, students of three schools A, B and C organized an exhibition in their locality, where they sold paper bags, scrap-books and pastel sheets made by them using recycled paper, at the rate of Rs 20, Rs 15 and Rs 5 per unit respectively. School A sold 25 paper-bags, 12 scrap-books and 34 pastel sheets. School B sold 22 paper-bags, 15 scrapbooks and 28 pastel-sheets while school C sold 26 paper-bags, 18 scrap-books and 36 pastel sheets. Using matrices, find the total amount raised by each school.By such exhibition, which values are inculcated in the students ?
Ans.

Values:i) Helping the Orphans ii)Use of recycled paper

Ans.

Ans.

Ans.

Ans.

12.Consider the experiment of tossing a coin. If the coin shows tail, toss it again but if it shows head, then throw a die. Find the conditional probability of the event that ‘the die shows a number greater than 3’ given that ‘there is at least one head’.
Or
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90% ?
Ans.

Ans.

Ans.

Ans.

16.If x = sin t, y = sin kt, show that,

Ans.

Ans.

Ans.

Ans.

SECTION – C

Question numbers 20 to 26 carry 6 marks each.

Ans.

21.Compute, using integration, the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7
Ans.

Ans.

Ans.

24.40% students of a college reside in hostel and the remaining reside outside. At the end of year, 50% of the hostellers got A grade while from outside students, only 30% got A grade in the examination. At the end of the year, a student of the college was chosen at random and was found to get A grade. What is the probability that the selected student was a hosteller ? What value is shown here ?
Ans.

25.A merchant plans to sell two types of personal computer : a desktop model and a portable model that will cost Rs 25,000 and Rs 40,000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get a maximum profit, if the does not want to invest more than 70 lakh and if his profit on the desktop model is Rs 4,500 and that on portable is Rs 5,000.
Ans.

26.A jet of enemy is flying along the curve y = x² + 2 and a soldier is placed at the point (3, 2). Find the minimum distance between the soldier and the jet.
Ans.

SECTION — A

Question numbers 1 to 6 carry 1 mark each

SECTION — B

Question numbers 11 to 22 carry 4 marks each







18.An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.

SECTION — C

Question numbers 23 to 29 carry 6 marks each.
23.A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B re­quires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of Rs 80 on each piece of type A and Rs 120 on each piece of type B. How many pieces of type A and type B should be manufac­tured per week to get a maximum profit ? Make it as an LPP and solve graphically. What is the maximum profit per week ?

24.There are three coins. One is a two-headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tails 40% of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin ?
OR
Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of the random variable X, and hence find the mean of the distribution.

26.Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award Rs x each, Rs y each and Rs z each for the three respective values to 3,2 and 1 students respectively with a total award money of Rs 1,600. School B wants to spend Rs 2,300 to award its 4,1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is Rs 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.

27.Using integration, find the area of the region bounded by the triangle whose vertices are (-1,2), (1,5) and (3,4).