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Tamilnadu 11th Standard Tamil மொழி கலை -செய்யுள் - ஒவ்வொரு புல்லையும் Important Questions And Answers Study Material - QB365

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11th Standard Business maths English Medium One Mark important Questions Book back and Creative - 2020

Published on: 20/03/2020

Download Tamil Nadu 11th Standard Business Maths and Statistics question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

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Questions:

Multiple Choice Question

50 x 1 = 50

Probability of an impossible event is _________.

(a)

(b)

(c)

0.2

(d)

0.5

If median = 45 and its coefficient is 0.25, then the mean deviation about median is _________.

(a)

11.25

(b)

180

(c)

0.0056

(d)

Harmonic mean is better than other means if the data are for _________.

(a)

Speed or rates.

(b)

Heights or lengths.

(c)

Binary values like 0 and 1

(d)

Ratios or proportions.

Harmonic mean is the reciprocal of _________.

(a)

Median of the values.

(b)

Geometric mean of the values.

(c)

Arithmetic mean of the reciprocal of the values.

(d)

Quartiles of the values.

The geometric mean of two numbers 8 and 18 shall be _________.

(a)

(b)

(c)

(d)

11.08

The lines of regression intersect at the point ________.

(a)

(X,Y)

(b)

\(\left( \bar { X } ,\bar { Y } \right) \)

(c)

(0,0)

(d)

(σ_x, σ_y)

The person suggested a mathematical method for measuring the magnitude of linear relationship between two variables say X and Y is ________.

(a)

Karl Pearson

(b)

Spearman

(c)

Croxton and Cowden

(d)

Ya Lun Chou

The lines of regression of X on Y estimates ________.

(a)

X for a given value of Y

(b)

Y for a given value of X

(c)

X from Y and Y from X

(d)

none of these

The regression coefficient of Y on X ________.

(a)

b_xy =\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

(b)

b_yx=\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dy^{ 2 }-(\Sigma dy)^{ 2 } } \)

(c)

b_yx =\(\frac { N\Sigma dxdy-(\Sigma dx)(\Sigma dy) }{ N\Sigma dx^{ 2 }-(\Sigma dx)^{ 2 } } \)

(d)

b_xy =\(\frac { N\Sigma xy-(\Sigma x)(\Sigma y) }{ \sqrt { N\Sigma { x }^{ 2 }-(\Sigma x)^{ 2 }\times \sqrt { N\Sigma { y }^{ 2 }-(\Sigma y)^{ 2 } } } } \)

10.

The present value of the perpetual annuity of Rs. 2000 paid monthly at 10 % compound interest is _______.

(a)

Rs. 2,40,000

(b)

Rs. 6,00,000

(c)

Rs. 20,40,000

(d)

Rs. 2,00,400

11.

An annuity in which payments are made at the beginning of each payment period is called _______.

(a)

Annuity due

(b)

An immediate annuity

(c)

perpetual annuity

(d)

none of these

12.

If ‘a’ is the annual payment, ‘n’ is the number of periods and ‘i’ is compound interest for Rs. 1 then future amount of the annuity is _______.

(a)

A = \(\frac{a}{i}(1+i)(1+i)^n-1]\)

(b)

A = \(\frac{a}{i}[(1+i)^n-1]\)

(c)

P = \(\frac{a}{i}\)

(d)

P = \(\frac{a}{i}(1+i)[1-(1+i)^{-n}]\)

13.

If a man received a total dividend of Rs. 25,000 at 10% dividend rate on a stock of face value Rs.100, then the number of shares purchased.

(a)

3500

(b)

4500

(c)

2500

(d)

300

14.

The dividend received on 200 shares of face value Rs.100 at 8% is ________.

(a)

Rs. 1600

(b)

Rs. 1000

(c)

Rs. 1500

(d)

Rs. 800

15.

The variable which influences the values or is used for prediction is called________.

(a)

Dependent variable

(b)

Independent variable

(c)

Explained variable

(d)

Regressed

16.

The demand function is always _______.

(a)

Increasing function

(b)

Decreasing function

(c)

Non-decreasing function

(d)

Undefined function

17.

If u = 4x² + 4xy + y² + 32 + 16 , then \(\frac { \partial ^{ 2 }u }{ \partial y\partial x } \) is equal to ________.

(a)

8x + 4y + 4

(b)

(c)

2y + 32

(d)

18.

Profit P(x) is maximum when ________.

(a)

MR = MC

(b)

MR = 0

(c)

MC = AC

(d)

TR = AC

19.

Relationship among MR, AR and η_d is ______.

(a)

\({ n }_{ d }=\frac { AR }{ AR-MR } \)

(b)

η_d = AR - MR

(c)

MR = AR = η_d

(d)

\(AR=\frac { MR }{ {ηd } } \)

20.

If the demand function is said to be inelastic, then _______.

(a)

|η_d| > 1

(b)

|η_d| = 1

(c)

|η_d| < 1

(d)

|η_d| = 0

21.

Given an L.P.P maximize Z = 2x₁ + 3x₂ subject to the constrains x₁ + x₂ ≤ 1, 5x₁ + 5x₂≥ 0 and x₁ ≥ 0, x₂ ≥ 0 using graphical method, we observe ______.

(a)

No feasible solution

(b)

unique optimum solution

(c)

multiple optimum solution

(d)

none of these

22.

The objective of network analysis is to ________.

(a)

Minimize total project cost

(b)

Minimize total project duration

(c)

Minimize production delays, interruption and conflicts

(d)

All the above

23.

Which of the following is not correct?

(a)

Objective that we aim to maximize or minimize

(b)

Constraints that we need to specify

(c)

Decision variables that we need to determine

(d)

Decision variables are to be unrestricted

24.

The minimum value of the objective function Z = x + 3y subject to the constraints 2x + y ≤ 20, x + 2y ≤ 20, x > 0 and y > 0 is ______.

(a)

(b)

(c)

(d)

25.

A solution which maximizes or minimizes the given LPP is called ______.

(a)

a solution

(b)

a feasible solution

(c)

an optimal solution

(d)

none of these

26.

If the function f(x) is continuous at x = a if \(\lim _{ x\rightarrow a }{ f\left( x \right) } \) is equal to ________.

(a)

f(-a)

(b)

f\((\frac{1}{a})\)

(c)

2f(a)

(d)

f(a)

27.

For what value of x, f(x) = \(\frac{x+2}{x-1}\) is not continuous?

(a)

-2

(b)

(c)

(d)

-1

28.

If f(x) = x² and g(x) = 2x + 1 then (fg)(0) is ________.

(a)

(b)

(c)

(d)

29.

The graph of f(x) = e^x is identical to that of ________.

(a)

f(x) = a^x, a > 1

(b)

f(x) = a^x, a < 1

(c)

f(x) = a^x, 0 < a < 1

(d)

y = ax +b, a \(\ne\) 0

30.

If f(x) = \(\frac{1-x}{1+x}\) then f(-x) is equal to _______.

(a)

-f(x)

(b)

\(\frac{1}{f(x)}\)

(c)

\(-\frac{1}{f(x)}\)

(d)

f(x)

31.

\(\sec^{-1}\frac{2}{3}+cosec^{-1}\frac{2}{3}=\) ______.

(a)

\(\frac{-\pi}{2}\)

(b)

\(\frac{\pi}{2}\)

(c)

\(\pi\)

(d)

\(-\pi\)

32.

If sin A + cos A = 1, then sin 2A is equal to _______.

(a)

(b)

(c)

(d)

\(\frac{1}{2}\)

33.

The value of sin 15^o cos 15^o is ______.

(a)

(b)

\(\frac{1}{2}\)

(c)

\(\frac{\sqrt3}{2}\)

(d)

\(\frac{1}{4}\)

34.

The value of \(\sin(-420^o)\) is _______.

(a)

\(\frac{\sqrt3}{2}\)

(b)

\(-\frac{\sqrt3}{2}\)

(c)

\(\frac{1}{2}\)

(d)

\(\frac{-1}{2}\)

35.

The value of \(\sin15^o\) is ______.

(a)

\(\frac{\sqrt{3}+1}{2\sqrt{2}}\)

(b)

\(\frac{\sqrt{3}-1}{2\sqrt{2}}\)

(c)

\(\frac{\sqrt3}{\sqrt2}\)

(d)

\(\frac{\sqrt3}{2\sqrt2}\)

36.

The double ordinate passing through the focus is _______.

(a)

focal chord

(b)

latus rectum

(c)

directrix

(d)

axis

37.

The centre of the circle x² + y - 2x + 2y - 9 = 0 is _______.

(a)

(1,1)

(b)

(-1,-1)

(c)

(-1,1)

(d)

(1, -1)

38.

The length of the tangent from (4,5) to the circle x² + y² = 16 is _______.

(a)

(b)

(c)

(d)

39.

The x-intercept of the straight line 3x + 2y - 1 = 0 is _______.

(a)

(b)

(c)

1/3

(d)

1/2

40.

If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is _______.

(a)

(-1, 1)

(b)

(1,1)

(c)

(1, -1 )

(d)

(-1, -1)

41.

The total number of 9 digit number which have all different digit is ________.

(a)

10!

(b)

(c)

9\(\times\)9!

(d)

10\(\times\)10!

42.

If \(\frac { kx }{ (x+4)(2x-1) } =\frac { 4 }{ x+4 } +\frac { 1 }{ 2x-1 } \) then k is equal to _______.

(a)

(b)

(c)

(d)

43.

The last term in the expansion of (3 +\(\sqrt{2}\) )⁸ is ________

(a)

(b)

(c)

8\(\sqrt{2}\)

(d)

27\(\sqrt{3}\)

44.

If nP_r = 720 (nC_r), then r is equal to ______.

(a)

(b)

(c)

(d)

45.

If nC₃ = nC₂, then the value of nC₄ is _______.

(a)

(b)

(c)

(d)

46.

If any three rows or columns of a determinant are identical then the value of the determinant is ________.

(a)

(b)

(c)

(d)

47.

If \(\begin{vmatrix} x & 2 \\ 8 &5 \end{vmatrix}=0\) then the value of x is ________.

(a)

\({{-5}\over{6}}\)

(b)

\({{5}\over{6}}\)

(c)

\({{-16}\over{5}}\)

(d)

\({{16}\over{5}}\)

48.

The value of \(\begin{vmatrix} x & x^2 & -yz & 1 \\ y & y^2 & -zx & 1 \\ z & z^2 & -xy &1 \end{vmatrix}\) is ________.

(a)

(b)

(c)

-1

(d)

-xyz

49.

The number of Hawkins-Simon conditions for the viability of an input - output analysis is ________.

(a)

(b)

(c)

(d)

50.

If A is square matrix of order 3, then |kA| is________.

(a)

k|A|

(b)

-k|A|

(c)

k³|A|

(d)

-k³|A|

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Answers Key:

Multiple Choice Question

50 x 1 = 50

(b)
0

Mean deviation about median = co-eficient of mean deviation about median x Median
= 0.25 x 45
= 11.25

(a)
Speed or rates.

GM = \(\sqrt{8 \times 18} = \sqrt{144} = 12\)

(b)
\(\left( \bar { X } ,\bar { Y } \right) \)

(a)
Karl Pearson

(a)
X for a given value of Y

10.

\(P =\frac{\frac{a}{i}}{k} \)
\(=\frac{\frac{2000}{0.1}}{12}=2,40,000\)

11.

(a)
Annuity due

12.

(b)
A = \(\frac{a}{i}[(1+i)^n-1]\)

13.

\(25,000=\frac{x\times 100\times10}{100}\Rightarrow x=2500\)

14.

Investment = 200 x 100 x \(\frac{8}{100}\)= Rs. 1600

15.

(b)
Independent variable

16.

(b)
Decreasing function

17.

\(\frac{\partial u}{\partial x} =8 x+4 y+4 \)
\(\frac{\partial^2 u}{\partial y \partial x} =4 \)

18.

(a)
MR = MC

19.

(a)
\({ n }_{ d }=\frac { AR }{ AR-MR } \)

20.

(a)
|η_d| > 1

21.

Since there is no common area between the lines x₁ + x₂ ≤ 1 and 5x₁ + 5x₂≥ 0

22.

(b)
Minimize total project duration

23.

(d)
Decision variables are to be unrestricted

24.

2x	+	y	=	20	x	+	y	=	20
x		0		10	x		0		20
y		20		0	y		20		0

Corner points	Z = x + 3y
(0, 0)	0
(0, 20)	60
(10, 0)	10

25.

26.

(d)
f(a)

27.

(b)
1

28.

(fg) (x) = 2x³ + x² = fg (0) = 0

29.

(a)
f(x) = a^x, a > 1

30.

\(f(x) = \)\(\frac{1-x}{1+x} = \frac {1} {f(x)}\)

31.

(b)
\(\frac{\pi}{2}\)

32.

\((\sin A+\cos A)^2=1\)
\(\sin ^2 \mathrm{~A}+\cos ^2 \mathrm{~A}+2 \sin \mathrm{A} \cos \mathrm{A}=1\)
\(1+\sin 2 \mathrm{~A}=1 \Rightarrow \sin 2 \mathrm{~A}=0\)

33.

\(\frac{1}{2}\left(2 \sin 15^{\circ} \cos 15^{\circ}\right) =\frac{1}{2} \sin 2\left(15^{\circ}\right)=\frac{1}{2} \sin 30^{\circ} =\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}\)

34.

\(\sin \left(-420^{\circ}\right) =-\sin 420^{\circ}=-\sin (360+60) =-\sin 60^{\circ}=\frac{-\sqrt{3}}{2} \)

35.

\(\sin15^o = \sin(45^o - 30^o) = \sin45^o \cos 30^o - \cos 45^o \sin 30^o\)
\(= \frac{\sqrt{3}}{2\sqrt{2}} - \frac{1}{2\sqrt{2}}\)

36.

(b)
latus rectum

37.

C(- g, -f)

38.

\(\sqrt{4^2+5^2-16}=\sqrt{5^2}=5\)

39.

On x axis y = 0
\(3 x=1 \Rightarrow x=\frac{1}{3}\)

40.

41.

The ninth digit cannot be filled with zero
Ninth place can be filled in 9 ways
Eighth place can be filled in 9 ways
Seventh place can be filled in 8 ways and so on No. of ways
= 9 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2
= 9 x 9!

42.

Equality coefficient of x in the numerator
kx = 4 (2n) + 1 (x)
kx = 9x

43.

\((\sqrt{2})^8=2^4=16\)

44.

\(n P_r =720(\mathrm{nCr}) \)
\(\frac{n !}{(n-r) !} =720\left(\frac{n !}{r !(n-r) !}\right) \)
\(r ! =720 \)
\(r ! =6 ! \)
r = 6

45.

x + y = n
3 + 2 = 5 = n
nC₄ = 5C₄ = 5C₁ = 5

46.

(a)
0

47.

5x - 16 = 0
5x = 16
\(x=\frac{16}{5}\)

48.

\(\left|\begin{array}{ccc} x & x^2 & 1 \\ y & y^2 & 1 \\ z & z^2 & 1 \end{array}\right|+\left|\begin{array}{ccc} x & -y z & 1 \\ y & -z x & 1 \\ z & -x y & 1 \end{array}\right|\)
Multiply R₁, R₂, R₃, of second determinant by x, y, z respectively
\(\left|\begin{array}{ccc} x & x^2 & 1 \\ y & y^2 & 1 \\ z & z^2 & 1 \end{array}\right|-\frac{1}{x y z}\left|\begin{array}{ccc} x^2 & x y z & x \\ y^2 & x y z & y \\ z^2 & x y z & z \end{array}\right|\)
\(=\left|\begin{array}{lll} x & x^2 & 1 \\ y & y^2 & 1 \\ z & z^2 & 1 \end{array}\right|-\frac{x y z}{x y z}\left|\begin{array}{ccc} x^2 & 1 & x \\ y^2 & 1 & y \\ z^2 & 1 & z \end{array}\right|\)
\(=\left|\begin{array}{lll} x & x^2 & 1 \\ y & y^2 & 1 \\ z & z^2 & 1 \end{array}\right|-\left|\begin{array}{lll} x & x^2 & 1 \\ y & y^2 & 1 \\ z & z^2 & 1 \end{array}\right|=0\)

49.