The value of x if \(\begin{vmatrix} 0 & 1 & 0 \\ x & 2 & x \\ 1 & 3 & x \end{vmatrix}=0\) is

1. 0, -1

2. 0, 1

3. -1, 1

4. -1, -1

Relationship among MR, AR and ηd is

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

2. n₄ =  AR - MR

3. MR = AR = n₄

4. \(AR=\frac { MR }{ { n }_{ 4 } } \)

The constant term in the expansion of \({ \left( x+\frac { 2 }{ x } \right) }^{ 6 }\)

1. 156

2. 165

3. 162

4. 160

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

1. 8x + 4y + 4

2. 4

3. 2y + 32

4. 0

The value of \(\sin15^o\) is

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

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

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

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

(1, - 2) is the centre of the circle x² + y² + ax + by - 4 = 0 , then its radius

1. 3

2. 2

3. 4

4. 1

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

1. A = \(\frac{a}{i}(1+i)(1+i)^n-1]\)

2. A = \(\frac{a}{i}[(1+i)^n-1]\)

3. P = \(\frac{a}{i}\)

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

\(\sin\left(\cos^{-1}\frac{3}{5}\right)\) is

1. \(\frac{3}{5}\)

2. \(\frac{5}{3}\)

3. \(\frac{4}{5}\)

4. \(\frac{5}{4}\)

The value of n, when nP₂ = 20 is

1. 3

2. 6

3. 5

4. 4

The value of \(\begin{vmatrix} 2x+y & x & y \\ 2y+z & y & z \\ 2z+x & z & x \end{vmatrix}\) is

1. xyz

2. x+y+z

3. 2x+2y+2z

4. 0

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

1. Annuity due

2. An immediate annuity

3. perpetual annuity

4. none of these

If y = log x then y₂ =

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

2. \(-\frac{1}{x^2}\)

3. \(-\frac{2}{x^2}\)

4. e²

The inventor of input-output analysis is

1. Sir Francis Galton

2. Fisher

3. Prof. Wassily W. Leontief

4. Arthur Caylay

The value of \(\frac{2\tan30^o}{1+tan^230}\) is

1. \(\frac12\)

2. \(\frac{1}{\sqrt3}\)

3. \(\frac{\sqrt{3}}{2}\)

4. \(\sqrt3\)

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

1. 1

2. 3

3. 4

4. 2

adj (AB) is equal to

1. adj A adj B

2. adj A^T adj B^T

3. adj B adj A

4. adj B^T adj A^T

Which of the following is positional measure?

 

1. Range

2. Mode

3. Mean deviation

4. Percentiles

The first quartile is also known as

 

1. median.

2. lower quartile.

3. mode.

4. third decile

In constructing the network which one of the following statement is false?

1. Each activity is represented by one and only one arrow. (i.e) only one activity can connect any two nodes

2. Two activities can be identified by the same head and tail events

3. Nodes are numbered to identify an activity uniquely. Tail node (starting point) should be lower than the head node (end point) of an activity

4. Arrows should not cross each other

Which of the following matrix has no inverse

1. \(\begin{pmatrix} -1 & 1 \\ 1 &-4 \end{pmatrix}\)

2. \(\begin{pmatrix} 2 & -1 \\ -4 &2 \end{pmatrix}\)

3. \(\begin{pmatrix} cos\ a & sin\ a \\ -sin\ a & cos\ a \end{pmatrix}\)

4. \(\begin{pmatrix} sin\ a & cos\ a \\ -cos\ a & sin\ a \end{pmatrix}\)

\(\tan\left(\frac{\pi}{4}-x\right)\) is

1. \(\left(\frac{1+\tan x}{1-\tan x}\right)\)

2. \(\left(\frac{1-\tan x}{1+\tan x}\right)\)

3. 1-tan x

4. 1+tan x

For the cost function C =\(\frac { 1 }{ 25 } { e }^{ 25 }\), the marginal cost is 

1. \(\frac { 1 }{ 25 } \)

2. \(\frac { 1 }{ 5 } { e }^{ 5x }\)

3. \(\frac { 1 }{ 125 } { e }^{ 5x }\)

4. 25e^5x

In the context of network, which of the following is not correct

1. A network is a graphical representation

2. A project network cannot have multiple initial and final nodes

3. An arrow diagram is essentially a closed network

4. An arrow representing an activity may not have a length and shape

The lines of regression intersect at the point

1. (X,Y)

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

3. (0,0)

4. (σ_x, σ_y)

The Income on 7 % stock at 80 is

1. 9%

2. 8.75%

3. 8%

4. 7%

The degree measure of \(\frac{\pi}{8}\) is

1. 20^o60^'

2. 22^o30^'

3. 20^o60^'

4. 20^o30^'

The co-factor of -7 in the determinant \(\begin{vmatrix} 2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7 \end{vmatrix}\) is

1. -18

2. 18

3. -7

4. 7

A man purchases a stock of Rs 20,000 of face value 100 at a premium of 20%, then investment is

1. Rs 20,000

2. Rs 25,000

3. Rs 24,000

4. Rs 30,000

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

1. 1600

2. 1000

3. 1500

4. 800

\(\left(\frac{\cos x}{cosec x}\right)-\sqrt{1-\sin^2x}\sqrt{1-\cos^2x}\) is

1. cos²x-sin²x

2. sin²x-cos²x

3. 1

4. 0

If R = 5000 units / year, C₁ = 20 paise , C₃ = Rs 20 then EOQ is 

1. 5000

2. 100

3. 1000

4. 200

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

1. No feasible solution

2. unique optimum solution

3. multiple optimum solution

4. none of these

Median is same as

 

1. Q₁

2. Q₂

3. Q₃

4. D₂

The term containing x³ in the expansion of (x - 2y)⁷ is

1. 3^rd

2. 4^th

3. 5^th

4. 6^th

If m₁ and m₂ are the slopes of the pair of lines given by ax²+ 2hxy + by² = 0, then the value of m₁ + m₂ is

1. 2h/b

2. -2h/b

3. 2h/a

4. -2h/a

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

1. -f(x)

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

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

4. f(x)

If the values of two variables move in opposite direction then the correlation is said to be

1. Negative

2. Positive

3. Perfect positive

4. No correlation

The value of sec A sin(270^o+A) is

1. -1

2. cos² A

3. sec² A

4. 1

The number of ways to arrange the letters of the word "CHEESE" is

1. 120

2. 240

3. 720

4. 6

The value of the determinant \({\begin{vmatrix} a & 0 & 0 \\ 0 & b& 0 \\ 0 & 0 & c \end{vmatrix}}^{2}\)is

1. abc

2. 0

3. a²b²c²

4. -abc

The number of parallelograms that can be formed from the set of four parallel lines intersecting another set of three parallel lines is

1. 18

2. 12

3. 9

4. 6

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

1. 81

2. 16

3. 8\(\sqrt{2}\)

4. 27\(\sqrt{3}\)

f(x) = - 5 , for all \(x\epsilon R\), is a

1. an identity function

2. modulus function

3. exponential function

4. constant function

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

1. 1

2. 0

3. -1

4. -xyz

Probability that at least one of the events A, B occur is

 

1. \(P(A\cup B)\)

2. \(P(A\cap B)\)

3. P(A/B)

4. P\((A\cup B)\)

If \(\begin{vmatrix} 4 & 3 \\ 3 & 1 \end{vmatrix}=-5\) then value of \(\begin{vmatrix} 20 & 15 \\ 15 & 5 \end{vmatrix}\) is

1. -5

2. -125

3. -25

4. 0

The locus of the point P which moves such that P is at equidistance from their coordinate axes is

1. \(y={1\over x}\)

2. y=-x

3. y=x

4. \(y=-{1\over x}\)

ax² + 4xy + 2y² = 0 represents a pair of parallel lines then 'a' is

1. 2

2. -2

3. 4

4. -4

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

1. f(-a)

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

3. 2f(a)

4. f(a)

Which of the following function is neither even nor odd?

1. f(x) = x³ + 5

2. f(x) = x⁵

3. f(x) = x¹⁰

4. f(x) = x²

The minimum value of the function f(x)= Ixl is

1. 0

2. -1

3. +1

4. \(-\infty \)

The Inverse of matrix of\(\begin{pmatrix} 3 & 1 \\ 5 & 2\end{pmatrix}\) is

1. \(\begin{pmatrix} 2 & -1 \\-5 & 3 \end{pmatrix}\)

2. \(\begin{pmatrix} -2 & 5 \\1 & -3 \end{pmatrix}\)

3. \(\begin{pmatrix} 3 & -1 \\-5 & -3 \end{pmatrix}\)

4. \(\begin{pmatrix} -3 & 5 \\1 & -2 \end{pmatrix}\)

In the equation of the circle x² +y² = 16 then y-intercept is (are)

1. 4

2. 16

3. ±4

4. ±16

The brokerage paid by a person on this sale of 400 shares of face value Rs.100 at 1% brokerage

1. Rs 600

2. Rs 500

3. Rs 200

4. Rs 400

In critical path analysis, the word CPM mean

1. Critical path method

2. Crash project management

3. Critical project management

4. Critical path management

The number of diagonals in a polygon of n sides is equal to

1. nC₂

2. nC₂ - 2

3. nC₂ - n

4. nC₂ - 1

The value of 1-2sin²45^o is

1. 1

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

3. \(\frac14\)

4. 0

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

1. 3

2. 2

3. 1/3

4. 1/2

Example of contingent annuity is

1. Life insurance premium

2. An endowment fund to give scholarships to a student

3. Personal loan from a bank

4. All the above

The equation of directrix of the parabola y² = - x is

1. 4x+ 1 =0

2. 4x - 1 = 0

3. x - 4=0

4. x + 4 = 0

The objective of network analysis is to

1. Minimize total project cost

2. Minimize total project duration

3. Minimize production delays, interruption and conflicts

4. All the above

The mean of the values 11,12,13,14 and 15 is

 

1. 15

2. 11

3. 12.5

4. 13

The number of ways selecting 4 players out of 5 is

1. 4!

2. 20

3. 25

4. 5

Correlation co-efficient lies between

1. 0 to ∞

2. -1 to +1

3. -1 to 0

4. -1 to ∞

13 guests have participated in a dinner. The number of handshakes happened in the dinner is

1. 715

2. 78

3. 286

4. 13

When one regression coefficient is negative, the other would be

1. Negative

2. Positive

3. Zero

4. None of them

The middle term in the expansion of \({ \left( x+\frac { 1 }{ x } \right) }^{ 10 }\)

1. 10C₄\(\left( \frac { 1 }{ x } \right) \)

2. 10C₅

3. 10C₆

4. 10C₇x⁴

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

1. 4

2. 5

3. 6

4. 7

The range of f(x) = |x|, for all \(x\epsilon R\), is

1. (0, \(\infty \))

2. (0, \(\infty \))

3. (-\(\infty \), \(\infty \))

4. (1, \(\infty \))

The inverse matrix of \(\begin{pmatrix} \frac { 1 }{ 5 } & \frac { 5 }{ 25 } \\ \frac { 2 }{ 5 } & \frac { 1 }{ 2 } \end{pmatrix}\) is

1. \({{7}\over{30}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { 5 }{ 12 } \\ \frac { 2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)

2. \({{7}\over{30}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { -5 }{ 12 } \\ \frac { -2 }{ 5 } & \frac { 1 }{ 5 } \end{pmatrix}\)

3. \({{30}\over{7}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { 5 }{ 12 } \\ \frac { 2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)

4. \({{30}\over{7}}\begin{pmatrix} \frac { 1 }{ 2 } & \frac { -5 }{ 12 } \\ \frac { -2 }{ 5 } & \frac { 4 }{ 5 } \end{pmatrix}\)