Recent questions tagged easy

In a LPP,the objective function is always ______________.

asked Jan 8, 2013 by sreemathi.v

1 answer

In a LPP,the linear inequalities or restrictions on the variables are called _____________.

asked Jan 8, 2013 by sreemathi.v

1 answer

Corner points of the feasible region determined by the system of linear constraints are $(0,3),(1,1)$ and $(3,0).$

asked Jan 8, 2013 by sreemathi.v

1 answer

Corner points of the feasible region for an LPP are (0,2)(3,0),(6,0),(6,8) and (0,5).Let $F=4x+6y$ be the objective function,Maximum of F - Minimum of F =

asked Jan 8, 2013 by sreemathi.v

1 answer

Corner points of the feasible region for an LPP are $(0,2)(3,0),(6,0),(6,8) and (0,5)$.

asked Jan 8, 2013 by sreemathi.v

1 answer

The corner points of the feasible region determined by the system of linear constraints are $(0,0),(0,40),(20,40),(60,20),(60,0)$.The objective function is $Z=4x+3y.$ Compare the quantity in column A and column B: <br>$\begin{array}{1 1}column\; A & column\; B\\maximum\;of \;z &325\end{array}$

asked Jan 8, 2013 by sreemathi.v

1 answer

Find the value of x if $ \begin{bmatrix} 3x+y & -y \\ 2y-x & 3 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ -5 & 3 \end{bmatrix} $

asked Jan 8, 2013 by thanvigandhi_1

1 answer

A man rides his motorcycle at the speed of 50km/hour.He has to speed Rs 2 per km on petrol.If he rides it at at a faster speed of 80km/hour,the petrol cost increases to Rs 3 per km.He has at most Rs120 to spend on petrol and one hour's time.He wishes to find the maximum distance that he can travel.Express this problem as a linear programming problem.

asked Jan 7, 2013 by sreemathi.v

1 answer

A company manufactures two types of sweaters :type A sweaters type B.It costs Rs 360 to make a type A sweater and Rs 120 to make a type B sweater.The company can make at most 300 sweaters and spend at most Rs72,000 a day.The number of sweaters of type B cannot exceed the number of sweaters of type A by more than 100.The company makes a profit of Rs 200 for each sweater of type A and Rs 120 for every sweater of type B.Formulate this problem at a LPP to maximise the profit to the company.

asked Jan 7, 2013 by sreemathi.v

1 answer

A company manufactures two types of screws A and B.All the screws have to pass through a threading machine and a slotting machine.A box of type A screws requires 2 minutes on the threading machine and 3minutes on the slotting machine.A box of type B screws requires 8 minutes of threading on the threading machine and 2 minutes on the slotting machine.In a week,each machine is available for 60 hours.On selling these screws,the company gets a profit of Rs100 per box on type A screws and Rs170 per box on type B screws.

asked Jan 7, 2013 by sreemathi.v

1 answer

A manufacture of electronic circuits has a stock of 200 resistors,120 transistors and 150 capacitors and is required to produce two types of circuits A and B .Type A requires 20 resistors,10 transistors and 10 capacitors .Type B requires 10 resistors,20 transistors and 30 capacitors.If the profit on type A circuit is Rs 50 and that an type B circuit is Rs 60,formulate this problem as a LPP so that the manufacturer can maximize his profit.

asked Jan 7, 2013 by sreemathi.v

1 answer

Minimise $Z=13x-15y$ subject to the constraints: $x+y\leq 7,2x-3y+6\geq 0,x\geq 0,y\geq 0$.

asked Jan 7, 2013 by sreemathi.v

1 answer

Maximise the function $Z=11x+7y$,subject to the constraints : $x\leq 3,y\leq 2,x\geq 0,y\geq 0.$

asked Jan 7, 2013 by sreemathi.v

1 answer

Maximise $Z=3x+4y$,subject to the constraints: $x+y\leq 1,x\geq 0,y\geq 0$.

asked Jan 7, 2013 by sreemathi.v

1 answer

Determine the maximum value of $z=11x+7y$ subject to the constraints: $2x+y\leq 6,x\leq 2,y\geq 0.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: If the foot of perpendicular drawn from the origin to a plane is (5,-3,-2), then the equation of plane is $\overrightarrow{r}.(5\hat i-3\hat j-2\hat k)=38.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The equation of aline,which is parallel to $2\hat i\;-\hat j\;+\hat 3k$ and which passes through the point (5,-2,4) is $\Large \frac{x-5}{2}\;=\frac{y-2}{-1}\;=\frac{z-4}{3}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The line $\overrightarrow{r}=(2\hat i-3\hat j-\hat k)+\lambda(\hat i-2\hat j-2\hat k)$ lies in the plane $\overrightarrow{r}.(3\hat i-\hat j-\hat k)-2=0$

asked Jan 7, 2013 by sreemathi.v

0 answers

True or False: The intercepts made by the plane $2x-3y+5z+4=0$ on the co-ordinate axis are $-2,\large\frac{4}{3},\frac{-4}{5}.$

asked Jan 7, 2013 by sreemathi.v

1 answer

True or False: The unit vector normal to the plane $x+2y+3z-6=0$ is $\large \frac{1}{\sqrt {14}}\hat i+\frac{2}{\sqrt {14}}\hat j+\frac{3}{\sqrt {14}}\hat k.$

asked Jan 6, 2013 by sreemathi.v

1 answer

The cartesian equation of the plane $\overrightarrow{r}.(\hat i\;+\hat j-\hat k)\;=2$ is ____________.

asked Jan 6, 2013 by sreemathi.v

1 answer

The vector equation of the line through the points $(3,4,-7)$ and $(1,-1,6)$ is ______________.

asked Jan 6, 2013 by sreemathi.v

1 answer

Find the transpose of each of the following matrices : $ (i)\begin{bmatrix} 5 \\ \frac{1}{2} \\ -2 \end{bmatrix} $.

asked Jan 6, 2013 by thanvigandhi_1

1 answer

The vector equation of the line $\Large \frac{x-5}{3}\;\frac{y-4}{7}\;\frac{z-6}{2}$ is _______________.

asked Jan 4, 2013 by sreemathi.v

1 answer

The direction cosines of the vector $(2\hat i+2\hat j-\hat k)$ are ___________.

asked Jan 4, 2013 by sreemathi.v

1 answer

A plane passes through the points $(2,0,0) (0,3,0)$ and $(0,0,4)$.The equation of plane is__________.

asked Jan 4, 2013 by sreemathi.v

1 answer

The locus represented by $xy+yz=0$ is

asked Jan 4, 2013 by sreemathi.v

1 answer

The reflection of the point $(\alpha,\beta,\gamma)$ in the xy-plane is

asked Jan 4, 2013 by sreemathi.v

1 answer

The sine of the angle between the straight line $\large \frac{x\;-2}{3}=\frac{y\;-3}{4}=\frac{z\;-4}{5}\;$ and the plane $2x-2y+z=5$ is

asked Jan 4, 2013 by sreemathi.v

1 answer

The distance of the plane $\overrightarrow{r}.\bigg(\frac{2}{7}\hat i+\frac{3}{7}\hat j-\frac{6}{7}\hat k\bigg)$=1 from the origin is

asked Jan 4, 2013 by sreemathi.v

1 answer

If the directions cosines of a line are $k,k,k$ then

asked Jan 4, 2013 by sreemathi.v

1 answer

Find the value of a, b, c and d from the equation : $ \begin{bmatrix} a-b & 2a+c \\ 2a-b & 3c+d \end{bmatrix} = \begin{bmatrix} -1 & 5 \\ 0 & 13 \end{bmatrix} $

asked Jan 4, 2013 by thanvigandhi_1

1 answer

Compute the following : $ \begin{bmatrix} cos^2x & sin^2x \\ sin^2x & cos^2x \end{bmatrix} + \begin{bmatrix} sin^2x & cos^2x \\ cos^2x & sin^2x \end{bmatrix} $

asked Jan 4, 2013 by thanvigandhi_1

1 answer

Find the equations of the line passing through the point $(3,0,1)$ and parallel to the planes $x+2y=0$ and $3y-z=0.$

asked Jan 3, 2013 by sreemathi.v

1 answer

Two systems of rectangular axis have the same origin.If a plane cuts them at distances a,b,c and a',b',c',respectively,from the origin,prove that\[\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=\frac{1}{{a'}^2}+\frac{1}{{b'}^2}+\frac{1}{{c'}^2}\]

asked Jan 3, 2013 by sreemathi.v

1 answer

Compute the following : $ \begin{bmatrix} -1 & 4 & -6 \\ 8 & 5 & 16 \\ 2 & 8 & 5 \end{bmatrix} + \begin{bmatrix} 12 & 7 & 6 \\ 8 & 0 & 5 \\ 3 & 2 & 4 \end{bmatrix} $

asked Jan 3, 2013 by thanvigandhi_1

1 answer

If $ A' = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix} $ and $ B = \begin{bmatrix} -1 & 0 \\ 1 & 2 \end{bmatrix} $ then find $( A + 2B)'.$

asked Jan 3, 2013 by thanvigandhi_1

1 answer

O is the origin and A is (a,b,c).Find the direction cosines of the line OA and the equation of plane through A at right angle to OA.

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equation of the plane through the points (2,1,0),(3,-2,-2) and (3,1,7).

asked Jan 3, 2013 by sreemathi.v

1 answer

If the line drawn from the point $(-2,-1,-3)$ meets a plane at right angle at the point $(1,-3,3)$ find the equation of the plane.

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the equation of a plane which is at a distance $3\sqrt 3$ units from origin and the normal to which is equally inclined to coordinate axis.

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the angle between the lines $r=(3\hat i+2\hat j+6\hat k) +\lambda(2\hat i+\hat j+2\hat k) \;and\; r=(2\hat i-5\hat k)+\mu(6\hat i+3\hat j+2\hat k)$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the vector equation of the line which is parallel to the vector $3\hat i+2\hat j+6\hat k$ and which passes through the point $(1,-2,3).$

asked Jan 3, 2013 by sreemathi.v

1 answer

Find the position vector of a point A in space such that $\overrightarrow{OA}$ is inclined at $60^{\circ}$ to OX and at $45^{\circ}$ to OY and $\mid \overrightarrow{OA}\mid$=10 units.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: If f.g is continuous at $x=a$,then f and g are separately continuous at $x=a.$

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: The composition of two continuous functions is a continuous function.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: If f is continuous on its domain D ,then | f | is also continuous on D.

asked Jan 3, 2013 by sreemathi.v

1 answer

True or False: Rolle's theorem is applicable for the function $f(x)=|x-1|$ in [0,2].

asked Jan 3, 2013 by sreemathi.v

1 answer

If $f(x)=\mid \cos x-\sin x\mid,then\;f'(\frac{\pi}{3})$=__________.

asked Jan 3, 2013 by sreemathi.v

1 answer

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