Mathematics – Important Question Bank for Kerala Board (+ 2) HSE (HSC) Board Exam 2017 

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Maths Commerce 

1.There are two identical boxes .Box I contains 2 red and 3 white balls while box II contains 1 red and 4 white balls .A person chooses a box at random and take out a ball,

(i) Find the probability that the ball drawn is red.

(ii) If the ball drawn is white , what is the probability that it is drawn from box II

2. Consider the curve y=x3 -3x+2,

 (i) Find a point on the curve whose x –coordinate is 3.

 (ii)Find the slopes of the tangent and normal at this point.

(iii)Write the equations of the tangent and the normal at this point.

3. A random variable X has the following probability distribution

(i)Find the value of k. (ii) Find P(1<X<4)

(iii) Find the mean of the random variable X

4. Consider the following linear programming problem.

Maximize Z=3x+2y, Subject to: x+2y≤10, 3x=y≤15, x,y≥0

(i)Draw the graph of the straight lines x+2y=10,3x +y=15 on the same plane

(ii)Solve the given linear programming problem graphically.

5. Consider the curves y ²=x    and    x²=y

 (i)Find the points of intersection of these two curves.

 (ii)Find the area of the region enclosed by the given two curves.

6. A company manufactures two products A and B on which the profits earned per unit are Rs 30/-and Rs 40/-respectively. Each product is processed on two machines M₁ and M₂ .One unit of product A requires 1 hour of processing time on M₁and 2 hours on M₂ while one unit of product B requires 1 hour each on M₁ and M₂.  Machines M₁ and M₂ are available at most 10 hours and 12 hours respectively during a working day .The company wants to know how many units of each product A and B should produce to maximize the profit. To formulate a linear programming problem,

(i)Write the objective function. (ii)Write all the constraints

7. Two cards are drawn simultaneously from a well shuffled deck of 52 cards

Let X denotes the number of aces.

(i)Find the probability distribution of X

(ii)Find the mean and variance of X

8. A catering agency has two kitchens to prepare food at two places A and B. From these places ‘Mid-day Meal’ is to be supplied to three different schools situated at P, Q, R. The monthly requirements of the schools are respectively 40, 40 and 50 food packets. A packet contains lunch for 1000 students. Preparing capacity of kitchens A and B are 60 and 70 packets per month respectively. The transportation cost per packet from the kitchens to schools is given below:

How many packets from each kitchen should be transported to school so that the cost of transportation is minimum? Also find the minimum cost.

9. Solve the Liner programming problem graphically

Maximize

Z = 5x + 3y Subject to

3x + 5y ≤ 15

5 x + 2y ≥ 10, x ≥ 0, y ≥ 0

10. Consider the function y = x ³

(i)Find the slope of the tangent to the given curve at the point (1,1)

(ii)Find the equation of normal to the curve at (1,1)

11. Check Whether the function f(x) = x 2 is bijective or not

12. Find the equation of line joining (1,2) and (3,6)

13. Solve by using matrix method the system of equations

2x + 5y = 1

3x + 2y = 7

14. If y = sin – ¹x; show that (1-x ²) y₂ – xy₁ =0

15. A man is known to speak truth 3 out of 4 times. He throws a die and reports that it s a six. Find the probability that it is actually a six.

Maths Science

1.Solve the given linear programming problem graphically.

Minimize Z=6x+3y, Subject to: 4x+y≥80, x+y≥115, 3x+y≤ 150 x,y≥0

2. Let A and B be independent events with P (A) =0.3 and P(B) =0.4

Find (i) P (AᴖB) (ii) P(AUB) (iii) P(A/B)

3. (i) A bag contains 4 red and 4 black balls .Another bag contains 2red and 6 black balls. One of the bag is selected at random and a ball is drawn. If the ball drawn is red, find the probability that the ball drawn is from the first bag.

(ii) There are 5% defective items in large bulk of items. Using binomial distribution find the probability that a sample of 10 items will include not more than one defective item.

4. . Find the equation of the plane passing through the intersection of the planes x+y+4z+5=0 and 2x-y+3z+6=0 and containing the point (1,0,0)

5. Consider the following system of equations x+2y+5z =10, x-y-z = -2 , 2x+3y-z = -11

 (i) Express this system of equations in the form Ax=B.

 (ii) Prove that A is non singular.

(iii) Find the values of x, y and z satisfying the above system of equations.

(i) Using differentials, find the approximate value of (8)^1/4 upto 3 decimal places

(ii) Find two positive numbers x and y such that their sum is 35 and product x²y⁵ is maximum.

6. Using integration find the area of the region bounded by the triangle whose vertices are (1,0),(2,2 and (3,1)

7. One kind of cake requires 200g of flour and 25g of fat and another kind of cake requires 100 g of flour and 50 g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuring that there is no shortage of the other ingredients that there is no shortage of the other ingredients used is making the cakes.

8. A stone is dropped into a quite lake and waves move in a circle at the speed of 5cm/s. at the instant when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing ?

9. Given that the two numbers appearing on throwing two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’

10. Three fair coins are tossed and X be the number of heads turning up. Write the probability distribution of X

11. On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

12. Let a pair of dice be thrown and the random variable X be the sum of the numbers that appear on the two dice .Find

 (a) The probability distribution of X

 (b) Expectation of X

(c) Variance of X

13. The two adjacent sides of a parallelogram are 2i-4j+5k and i-2j 3k.

 (a) Find the unit vector parallel to its diagonal

 (b) Find the area of the parallelogram

14.  (a) Find the equation of the plane through the point of intersection of the planes x+y+z-1 = 0 and 2x+3y+4z = 5 which is perpendicular to the plane x-y+ z = 0

(b) Find the vector and cartesian equations of the line that passes through origin and (5,-2,3)

15. A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of Calcium, 4 units of Iron, 6 units of Cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of Calcium, 20 units of Iron, 4 units of Cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of Calcium, atleast 460 units of Iron and at most 300 units of Cholesterol. Formulate this problem as a linear programming problem to find how many packets of each food should be used to minimize the amount of vitamin A in the diet? What is the minimum amount of vitamin A?