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School/+2

Maths Class - XII 2000(CBSE)
You are on Set no 2 Question 1 to 30

 

Q2) Find a matrix X such that A + 2B + X = 0, where        

A =  2  -1
 3   5
B = -1   1
 0   2 

Q4) Calculate Spearman's rank correlation from the following Data:

x 1 2 3 4 5 6
y 2 3 1 6 5 4

Q7) Evaluate

  1+ Cot x    dx
x + log Sin x

Q9) If the distance s is given by s = at2 + bt + c, where t is the time and a, b, c are constants prove that 4a(s - c) = v2 - b2, where v denotes the velocity

Q10) Evaluate

  {(1 - Cos 3x)/x2}

Q11)
Find the regression coefficients and hence the coefficient of correlation from the following regression lines:
x - 2y + 4 = 0 ; 3x - 2y + 3 = 0

Q19) Using matrices solve the following system of equation for x, y and z:
            x + y + z = 5
            2x + y - z = 2
            2x - y + z = 2

(Students are expected to solve either part B or part C )

Part B

Q25) Find the centre and radius of the sphere:
2x2 + 2y2 + 2z2 + 2x - 4y + 2z + 1 = 0.

Q27) Solve the differential equation:
dx/dy = (x + y - 3)/(x + y + 3)

Q28) Find so that the four points with positive vector + 2 + 3 ,  3 - + 2,  -2 + + and 6 - 4 + 2 are coplanar.

Part C

Q23) The cost function of a firm is given by
C = 2x2 + x + 10
find (i) the average cost (ii) the marginal cost , when x = 2.

Q27) A began a business unit with Rs. 70,000. After 2 month B joined with a certain capital. At the end of the year, the profit were divided in the ratio of 5 : 2. Find how much money was invested by B.

Q28) Eight percent of the bolts produced in a certain factory turn out to be defective. Find the probability using poisson distribution, that in a sample of 25 bolts chosen at random, (i) Exactly 3 (ii) more than 3 bolts, will be defective (Take e-2 = 0.135).


 
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