#### Model 1 Mark Book Back Questions (New Syllabus) 2020

12th Standard

Reg.No. :
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Time : 00:25:00 Hrs
Total Marks : 25

Part A

25 x 1 = 25
1. If the rank of the matrix  $\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right)$  is 2. Then $\lambda$ is

(a)

1

(b)

2

(c)

3

(d)

only real number

2. If $\frac { { a }_{ 1 } }{ x } +\frac { { b }_{ 1 } }{ y } ={ c }_{ 1 },\frac { { a }_{ 2 } }{ x } +\frac { { b }_{ 2 } }{ y } ={ c }_{ 2 },$ ${ \triangle }_{ 1= }\begin{vmatrix} { a }_{ 1 } & { b }_{ 1 } \\ { a }_{ 2 } & { b }_{ 2 } \end{vmatrix}, \ { \triangle }_{ 2 }=\begin{vmatrix} { b }_{ 1 } & { c }_{ 1 } \\ { b }_{ 2 } & { c }_{ 2 } \end{vmatrix}{ \triangle }_{ 3 }=\begin{vmatrix} { c }_{ 1 } & { a }_{ 1 } \\ { c }_{ 2 } & a_{ 2 } \end{vmatrix}$ then (x, y) is

(a)

$\left( \frac { { \triangle }_{ 2 } }{ { \triangle }_{ 1 } } ,\frac { { \triangle }_{ 3 } }{ { \triangle }_{ 1 } } \right)$

(b)

$\left( \frac { { \triangle }_{ 3 } }{ { \triangle }_{ 1 } }, \frac { { \triangle }_{ 2 } }{ { \triangle }_{ 1 } } \right)$

(c)

$\left( \frac { { \triangle }_{ 1 } }{ { \triangle }_{ 2 } } ,\frac { { \triangle }_{ 1 } }{ { \triangle }_{ 3 } } \right)$

(d)

$\left( \frac { { -\triangle }_{ 1 } }{ { \triangle }_{ 2 } }, \frac { {- \triangle }_{ 1 } }{ { \triangle }_{ 3 } } \right)$

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. If f (x) is a continuous function and a < c < b, then $\int_{a}^{c} f(x) d x+\int_{c}^{b} f(x) d x$ is

(a)

$\int_{a}^{b} f(x) d x-\int_{a}^{c} f(x) d x$

(b)

$\int_{a}^{c} f(x) d x-\int_{a}^{b} f(x) d x$

(c)

$\int_{a}^{b} f(x) d x$

(d)

0

5. $\int _{ 0 }^{ \infty }{ { x }^{ 4 }{ e }^{ -x } }$dx is

(a)

12

(b)

4

(c)

4!

(d)

64

6. The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is

(a)

9x2 + 54x

(b)

9x2 − 54x

(c)

54x - $\frac { { 9x }^{ 2 } }{ 2 }$

(d)

54x - $\frac { { 9x }^{ 2 } }{ 2 }$ + k

7. The producer’s surplus when the supply function for a commodity is P = 3 + x and x0 = 3 is

(a)

$\frac{5}{2}$

(b)

$\frac{9}{2}$

(c)

$\frac{3}{2}$

(d)

$\frac{7}{2}$

8. The area bounded by the parabola y2 = 4x bounded by its latus rectum is

(a)

$\frac { 16 }{ 3 }$ sq.units

(b)

$\frac { 8 }{ 3 }$ sq.units

(c)

$\frac { 72 }{ 3 }$ sq.units

(d)

$\frac { 1 }{ 3 }$ sq.units

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

(a)

eഽPdx

(b)

$\int P d x$

(c)

ഽPdy

(d)

eഽPdy

10. The solution of the differential equation $\frac { dy }{ dx }$ + Py = Q where P and Q are the function of x is

(a)

$y=\int Q e^{\int P d x} d x+c$

(b)

$y=\int Q e^{-\int P d x} d x+c$

(c)

$y e^{\int P d x}=\int Q e^{\int P d x} d x+c$

(d)

$y e^{\int P d x}=\int Q e^{-\int P d x} d x+C$

11. Which of the following is the homogeneous differential equation?

(a)

(3x−5)dx = (4y−1)dy

(b)

xy dx−(x3+y3)dy = 0

(c)

y2dx+(x− xy  − y2)dy = 0

(d)

(x2+y)dx = (y2+x)dy

12. E f (x)=

(a)

f(x− h)

(b)

f (x)

(c)

f(x+ h)

(d)

f(x+ 2h)

13. Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are $0 \cdot 29,0 \cdot 40,0\cdot35$. Profit per unit is $0\cdot50$ paisa then expected profits for three days are

(a)

21, 19, 22

(b)

21.5, 19.5, 22.5

(c)

0.29, 0.40, 0.35

(d)

3.045, 3.8, 3.85

14. A probability density function may be represented by:

(a)

table

(b)

graph

(c)

mathematical equation

(d)

both (b) and (c)

15. A variable which can assume finite or countably infinite number of values is known as

(a)

continuous

(b)

discrete

(c)

qualitative

(d)

none of them

16. The height of persons in a country is a random variable of the type

(a)

discrete random variable

(b)

continuous random variable

(c)

both (a) and (b)

(d)

neither (a) nor (b)

17. The parameters of the normal distribution $f(x)=\left(\frac{1}{\sqrt{72 \pi}}\right)$$\frac{e^{-(x-10)^{2}}}{72}$ –∞ <  x  <

(a)

(10,6)

(b)

(10,36)

(c)

(6,10)

(d)

(36,10)

18. The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of  Rs.180,000 and a standard deviation of Rs. 10,000. What is the probability that a randomly selected newly qualified CA will earn between Rs. 165,000 and Rs. 175,000 per annum?

(a)

0.819

(b)

0.242

(c)

0.286

(d)

0.533

19. Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be:

(a)

1.00

(b)

-1.00

(c)

0.00

(d)

-0.41

20. Errors in sampling are of

(a)

Two types

(b)

three types

(c)

four types

(d)

five types

21. The components of a time series which is attached to short term fluctuation is

(a)

Secular trend

(b)

Seasonal variations

(c)

Cyclic variation

(d)

Irregular variation

22. Which of the following Index number satisfy the time reversal test?

(a)

Laspeyre’s Index number

(b)

Paasche’s Index number

(c)

Fisher Index number

(d)

All of them

23. The LCL for R chart is given by

(a)

${ D }_{ 2 }\bar { R }$

(b)

${ D }_{ 2 }\overset { = }{ R }$

(c)

${ D }_{ 3 }\overset { = }{ R }$

(d)

${ D }_{ 3 }\bar { R }$

24. In a degenerate solution number of allocations is

(a)

equal to m+n–1

(b)

not equal to m+n–1

(c)

less than m+n–1

(d)

greather than m+n–1

25. A type of decision –making environment is

(a)

certainty

(b)

uncertainty

(c)

risk

(d)

all of the above