#### First Mid Term Model Questions

12th Standard EM

Reg.No. :
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Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. The rank of m×n matrix whose elements are unity is

(a)

0

(b)

1

(c)

m

(d)

n

2. If the number of variables in a non- homogeneous system AX = B is n, then the system possesses a unique solution only when

(a)

$\rho (A)=\rho (A,B)>n$

(b)

$\rho (A)=\rho (A,B)<n$

(c)

$\rho (A)=\rho (A,B)=n$

(d)

none of these

3. $\sqrt { { e }^{ x } }$ dx is

(a)

$\sqrt { { e }^{ x } } +c$

(b)

$2\sqrt { { e }^{ x } }$ + c

(c)

$\frac12\sqrt { { e }^{ x } } +c$

(d)

$\frac { 1 }{ 2\sqrt { { e }^{ x } } } +c$

4. The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

(a)

40

(b)

$\frac{41}{2}$

(c)

$\frac{40}{3}$

(d)

$\frac{41}{5}$

5. If MR = 15 - 8x, then the revenue function is

(a)

15x-4x2+k

(b)

$\frac{15}{x}-8$

(c)

-8

(d)

15x-8

6. 5 x 1 = 5
7. If $\rho (A,B)\neq \rho (A)$ then the system is

8. (1)

inconsistent

9. $\int _{ 0 }^{ 1 }{ { e }^{ -t } } dt\quad$

10. (2)

2x+5ex+k

11. Cost function

12. (3)

ഽmc dx+k

13. ഽ(2+5ex)dx

14. (4)

$\int _{ 0 }^{ N }{ { Pe }^{ rt }dt }$

15. Amount of annuity after N payments

16. (5)

proper definite integer

5 x 2 = 10
17. Solve the following system of equations by rank method
x+y+z=9,2x+5y+7z=52,2x−y−z =0

18. Find the rank of the matrix A =$\left( \begin{matrix} 1 & -3 \\ 9 & 1 \end{matrix}\begin{matrix} 4 & 7 \\ 2 & 0 \end{matrix} \right)$

19. Integrate the following with respect to x.
$\frac { { x }^{ 3 } }{ x+2 }$

20. Evaluate $\int { \frac { 2+3cosx }{ { sin }^{ 2 }x } } dx$

21. Find the revenue function and the demand function if the marginal revenue for x units is MR= 10 + 3x − x2.

22. 5 x 3 = 15
23. Find the rank of the matrix $\left( \begin{matrix} 0 & -1 & 5 \\ 2 & 4 & -6 \\ 1 & 1 & 5 \end{matrix} \right)$

24. Solve: 2x + 3y = 5, 6x + 5y= 11

25. Evaluate ഽ$\frac { dx }{ { 4x }^{ 2 }-1 }$

26. Using integration find the area of the region bounded between the line x = 4 and the parabola y2 = 16x.

27. Determine the cost of producing 3000 units of commodity if the marginal cost in rupees per unit is C'(x)=$\frac{x}{3000}+2.50$

28. 3 x 5 = 15
29. Solve by Cramer’s rule x+y+z=4,2x−y+3z=1,3x+2y−z = 1

30. The marginal revenue function (in thousand of rupees ) of a commodity is 10 + e−0.05x Where x is the number of units sold. Find the total revenue from the sale of 100 units (e−5 = 0.0067)

31. Find the area of the region bounded by the parabola y2 = 4x and the line 2x - Y = 4.