#### Term 1 Model Question Paper

12th Standard EM

Reg.No. :
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Time : 02:00:00 Hrs
Total Marks : 60
7 x 1 = 7
1. The rank of m×n matrix whose elements are unity is

(a)

0

(b)

1

(c)

m

(d)

n

2. The system of linear equations x+y+z=2,2x+y−z=3,3x+2y+k =4 has unique solution, if k is not equal to

(a)

4

(b)

0

(c)

-4

(d)

1

3. $\frac { { 2x }^{ 3 } }{ 4+{ x }^{ 4 } }$dx is

(a)

$log\left| 4+{ x }^{ 4 } \right| +c$

(b)

$\frac { 1 }{ 2 } log\left| 4+{ x }^{ 4 } \right| +c$

(c)

$\frac { 1 }{4 } log\left| 4+{ x }^{ 4 } \right| +c$

(d)

$log\left| \frac { { 2x }^{ 3 } }{ { 4+x }^{ 4 } } \right| +c$

4. $\int _{ 0 }^{ \frac { \pi }{ 3 } }{ tanx } dx$ is

(a)

log 2

(b)

0

(c)

log$\sqrt { 2 }$

(d)

2 log 2

5. If the marginal revenue MR = 35 + 7x − 3x2, then the average revenue AR is

(a)

35x + $\frac { 7{ x }^{ 2 } }{ 2 } -{ x }^{ 3 }$

(b)

35x - $\frac { 7{ x }^{ 2 } }{ 2 } -{ x }^{ 2 }$

(c)

35 +$\frac { 7{ x }^{ 2 } }{ 2 } +{ x }^{ 2 }$

(d)

35 + 7x + x2

6. The particular integral of the differential equation is $\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -8\frac { dy }{ dx }$+16y = 2e4x

(a)

$\frac { { x }^{ 2 }{ e }^{ 4x } }{ 2! }$

(b)

$\frac { { e }^{ 4x } }{ 2! }$

(c)

x2e4x

(d)

xe4x

7. E f (x)=

(a)

f(x− h)

(b)

f (x)

(c)

f(x+ h)

(d)

f(x+ 2h)

8. 4 x 1 = 4
9. If A is a square matrix of order n, then |Adj A|=______

()

|A|n-1

10. If A is a square matrix such that A2 = I, then A-1=_______

()

A

11. The system of linear equations x + y + Z = 2, 2x + Y - z = 3, 3x + 2y + kz = 4 has a unique solution if k is_______

()

Not equal to 0

12. A set of values of the variable x1,x2,...xn satisfying all the equations simultaneously is called__________ of the system

()

Solution

13. 5 x 1 = 5
14. $\Gamma (n)\quad$

15. (1)

(n - 1) $\Gamma$
(n - 1), n > 1

16. R

17. (2)

ഽR'(x)dx+k

18. R(x)

19. (3)

Family of lines

20. y= mx

21. (4)

Total revenue

22. E (Δf(x))

23. (5)

Δ . E. f(x)

7 x 2 = 14
24. Find the rank of the following matrices.
$\left( \begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix} \right)$

25. If f(x) = x + b, f (1)= 5 and f (2) = 13, then find f (x)

26. Evaluate the following using properties of definite integrals:
$\int _{ 0 }^{ 1 }{ log\left( \frac { 1 }{ x } -1 \right) dx }$

27. Calculate the producer’s surplus at x = 5 for the supply function p = 7 + x.

28. Find the order and degree of the following differential equations.
${ \left( \frac { dy }{ dx } \right) }^{ 3 }+y=x-\frac { dx }{ dy }$

29. From the following table obtain a polynomial of degree y in x

 x 1 2 3 4 5 y 1 -1 1 -1 1
30. Define critical value.

31. 5 x 3 = 15
32. Find the rank of the matrix $\begin{pmatrix} 1 & 5 \\ 3 & 9 \end{pmatrix}$

33. Evaluate ഽ$\frac { dx }{ x^{ 2 }-3x+2 }$

34. Solve : (D2−4D−1)y = e−3x

35. From the following table find the missing value

 x 2 3 4 5 6 f(x) 45 49.2 54.1 - 67.4
36. Assume the mean height of children to be 69.25 cm with a variance of 10.8 cm. How many children in a school of 1,200 would you expect to be over 74 cm tall?

37. 3 x 5 = 15
38. Solve by Cramer’s rule x+y+z=4,2x−y+3z=1,3x+2y−z = 1

39. Evaluate
$\int _{ 0 }^{ \infty }{ { e }^{ -2x }{ x }^{ 5 }dx }$

40. The normal lines to a given curve at each point(x,y) on the curve pass through the point (1,0). The curve passes through the point (1,2). Formulate the differential equation representing the problem and hence find the equation of the curve.