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#### All Imparten Questions Test

12th Standard EM

Reg.No. :
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Time : 01:00:00 Hrs
Total Marks : 40
40 x 1 = 40
1. For the system of equations x+2y+3z=1, 2x+y+3z=25x+5y+9z =4

(a)

there is only one solution

(b)

there exists infinitely many solutions

(c)

there is no solution

(d)

None of these

2. Cramer’s rule is applicable only to get an unique solution when

(a)

${ \triangle }_{ z }\neq 0$

(b)

${ \triangle }_{ x }\neq 0$

(c)

${ \triangle }_\neq 0$

(d)

${ \triangle }_{ y }\neq 0$

3. For what value of k, the matrix $A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right)$ has no inverse?

(a)

$\cfrac { 3 }{ 10 }$

(b)

$\cfrac { 10 }{ 3 }$

(c)

3

(d)

10

4. If A, B are two n x n non-singular matrices, then

(a)

AB is non-singular

(b)

AB is singular

(c)

(AB)-I = A-1 B-1

(d)

(AB)-1I does not exit

5. $\int _{ 0 }^{ 1 }{ \sqrt { { x }^{ 4 }({ 1-x) }^{ 2 } } } dx$ is

(a)

$\frac{1}{12}$

(b)

$\frac{-7}{12}$

(c)

$\frac{7}{12}$

(d)

$\frac{-1}{12}$

6. $\Gamma (1)$ is

(a)

0

(b)

1

(c)

n

(d)

n!

7. If $\int { \frac { { 2 }^{ \frac { 1 }{ x } } }{ { x }^{ 2 } } } dx=k{ 2 }^{ \frac { 1 }{ x } }$ +c, then k is

(a)

$-\frac { 1 }{ { log }_{ e }2 }$

(b)

- loge2

(c)

-1

(d)

$\frac { 1 }{ 2 }$

8. $\int _{ 1 }^{ 4 }{ f\left( x \right) } dx,$ where f(x) =  $\begin{cases} 7x+3\quad if\quad 1\le x\le 3 \\ 8x\quad if\quad 3\le x\le 4 \end{cases}$ is _____________.

(a)

58

(b)

60

(c)

62

(d)

52

9. Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

(a)

$\frac{30}{3}$ sq.units

(b)

$\frac{31}{3}$sq.units

(c)

$\frac{32}{3}$ sq.units

(d)

$\frac{15}{2}$ sq.units

10. When x0 = 2 and P0 = 12 the producer’s surplus for the supply function Ps = 2x2 + 4 is

(a)

$\frac{31}{5}$units

(b)

$\frac{31}{2}$ units

(c)

$\frac{32}{3}$ units

(d)

$\frac{30}{7}$ units

11. The area of the region bounded by the line y = 3x + 2, the X-axis and the ordinates x = - 1 and x = 1is_________ sq. units.

(a)

$\frac{13}{3}$

(b)

13

(c)

$\frac{26}{3}$

(d)

$\frac{3}{13}$

12. The value of $\int _{ -3 }^{ 2 }{ |x+1| } dx$ is______.

(a)

4

(b)

$\frac{1}{4}$

(c)

8

(d)

2

13. The integrating factor of the differential equation $\frac{dx}{dy}+Px=Q$

(a)

eഽPdx

(b)

eഽPdx

(c)

ഽPdy

(d)

eഽPdy

14. The complementary function of $\frac { { d }^{ 3 }y }{ d{ x }^{ 3 } } -\frac { dy }{ dx }$ = 0 is

(a)

A + Bex

(b)

(A + B)ex

(c)

(Ax + B)ex

(d)

Aex + B

15. The integrating factor of (1+x2)$\frac { dy }{ dx }$+xy = (1+x2)3 is

(a)

$\sqrt { 1+{ x }^{ 2 } }$

(b)

log(1+x2)

(c)

etan-1x

(d)

log(tan-1x)

16. The integrating factor of $\frac { dy }{ dx } +\frac { 2y }{ x }$=x3 is

(a)

2 log x

(b)

${ e }^{ { x }^{ 2 } }$

(c)

3log(x2)

(d)

x2

17. E ≡

(a)

1 + Δ

(b)

1 - Δ

(c)

1 + ∇

(d)

1 - ∇

18. For the given points (x0, y0) and (x1,y1) the Lagrange’s formula is

(a)

$y(x)=\frac { x-{ x }_{ 1 } }{ { x }_{ 0 }-{ x }_{ 1 } } { y }_{ 0 }+\frac { x-{ x }_{ 0 } }{ { x }_{ 1 }-{ x }_{ 0 } } { y }_{ 1 }$

(b)

$y(x)=\frac { { x }_{ 1 }-{ x }_{ 0 } }{ { x }_{ 0 }-{ x }_{ 1 } } { y }_{ 0 }+\frac { { x }_{ 1 }-{ x }_{ 0 } }{ { x }_{ 1 }-{ x }_{ 0 } } { y }_{ 1 }$

(c)

$y(x)=\frac { x-{ x }_{ 1 } }{ { x }_{ 0 }-{ x }_{ 1 } } { y }_{ 1 }+\frac { x-{ x }_{ 0 } }{ { x }_{ 1 }-{ x }_{ 0 } } { y }_{ 0 }$

(d)

$y(x)=\frac { { x }_{ 1 }-{ x } }{ { x }_{ 0 }-{ x }_{ 1 } } { y }_{ 1 }+\frac { x-{ x }_{ 0 } }{ { x }_{ 1 }-{ x }_{ 0 } } { y }_{ 0 }$

19. E [f(x0)] is

(a)

f(xo + h)

(b)

f(xo - h)

(c)

f(xo) + h

(d)

f(xo) - h

20. Newton's backward interpolation formula is used when the value of y is required at the __________ of the table.

(a)

beginning

(b)

end

(c)

left

(d)

right

21. A variable that can assume any possible value between two points is called

(a)

discrete random variable

(b)

continuous random variable

(c)

discrete sample space

(d)

random variable

22. If p(x)=$\frac{1}{10}$, c=10, then E(X) is

(a)

zero

(b)

$\frac{6}{8}$

(c)

1

(d)

-1

23. Variance of the random variable. X is 4, Its mean is 2. Then E(X2) is

(a)

2

(b)

4

(c)

6

(d)

8

24. μ2=20, μ12 =276 for a discrete random variable. X. Then the mean of the random variable. X is

(a)

16

(b)

5

(c)

2

(d)

1

25.  In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is

(a)

0.0613

(b)

0.613

(c)

0.00613

(d)

0.3913

26. Monthly expenditure on their credit cards, by credit card holders from a certain bank, follows a normal distribution with a mean of  Rs.1,295.00 and a standard deviation of Rs.750.00. What proportion of credit card holders spend more than Rs.1,500.00 on their credit cards per month?

(a)

0.487

(b)

0.392

(c)

0.500

(d)

0.791

27. The area under the standard normal curve between Z=-∞ and z=∞ is

(a)

0

(b)

0.5

(c)

1

(d)

0.75

28. In a poison distribution, mean is 16, then standard deviation is

(a)

4

(b)

128

(c)

256

(d)

20

29. A ________ may be finite or infinite according as the number of observations or items in it is finite or infinite.

(a)

Population

(b)

census

(c)

parameter

(d)

none of these

30. In ___________ the heterogeneous groups are divided into homogeneous groups.

(a)

Non-probability sample

(b)

a simple random sample

(c)

a stratified random sample

(d)

systematic random sample

31. If 55 is the mean mark obtained by a sample of 5 students randomly drawn from a class of 100 students is considered to the means marks of the entire class. This single value 55 is a

(a)

estimation

(b)

estimate

(c)

point estimate

(d)

estimator

32. If α is the level of significance. then the confidence Co-efficient is

(a)

α

(b)

1

(c)

1-α

(d)

1+α

33. A typical control charts consists of

(a)

CL, UCL

(b)

CL, LCL

(c)

CL, LCL, UCL

(d)

UCL, LCL

34. Most commonly used index numbers are _________ index number

(a)

diffusion

(b)

price

(c)

value

(d)

none ofthese

35. The normal equations of fitting a straight line y = ax+ b are 10a + 5b = 15 and 30a + 10b = 43. The slope of the line of best fit is _____

(a)

1.2

(b)

1.3

(c)

13

(d)

12

36. The normal -equations in fitting a line y = ax + b, by the method of least squares over n points are 4 = 4a + b and Σxy = 120a + 24b. Then n = _____

(a)

30

(b)

5

(c)

6

(d)

4

37. The transportation problem is said to be unbalanced if _________

(a)

Total supply ≠ Total demand

(b)

Total supply = Total demand

(c)

m = n

(d)

m+n–1

38. North-West Corner refers to ________

(a)

top left corner

(b)

top right corner

(c)

bottom right corner

(d)

bottom left corner

39. A set of non-negative values that satisfies the constants in a transportation problem is a

(a)

Basic feasible solution

(b)

Feasible solution

(c)

Optimal solution

(d)

Non degenerate basic feasible solution

40. To assign different jobs to the different machines to minimize the overall cost is

(a)

transportation problem

(b)

assignment problem

(c)

minimax principle

(d)

maximin principle