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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 |
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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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