Recent questions tagged kvquestionbank2012

In a hurdle race a player has to cross 10 hurdles. The probability that will clear each hurdle is 5/6, what is the probability that he will knock down fewer than 2 hurdles.

asked Feb 5, 2013 by meena.p

0 answers

A man fires 4 bullets on a thief. The probability that the thief will be killed by one bullet is 0.6. Find the probability that the thief is still alive.

asked Feb 5, 2013 by meena.p

0 answers

The parameters n and p are 12 and 1/3 for a binomial distribution. Find standard deviation.

asked Feb 5, 2013 by meena.p

0 answers

Given P(A) = 0.3, P(B) = 0.2, Find P(B/A) if A and B are mutually exclusive events.

asked Feb 5, 2013 by meena.p

5 answers

A die is thrown 120 times and getting 1 or 5 is considered success. Find the mean, variance of number of successes.

asked Feb 5, 2013 by meena.p

0 answers

Urn A contain 1 white, 2 black, 3 red balls. Urn B contain 2 white, 1 black, 1 red balls. Urn C contains 4 white, 5 black, 3 red balls. Two balls are drawn from one of the Urn and found to be one white and one red. Find the probabilities that they come from Urns A, B or C.

asked Feb 5, 2013 by meena.p

0 answers

Find the maximum and minimum values of 5x+2y subject to constraints \[-2x-3y\leq-6\]\[x-2y\leq2\]\[6x+4y\leq24\]\[-3x+2y\leq3\]\[x\geq0\;and\;y\geq0\]

asked Feb 5, 2013 by meena.p

0 answers

Determine graphically the minimum value of the objective function.\[z=-50x+20y\] subject to constraints \[2x-y\geq-5\]\[3x+y\geq3\]\[2x-3y\leq12\]\[x\geq0,y\geq0\]

asked Feb 5, 2013 by meena.p

0 answers

Solve the following LPP graphically. Minimize Z = 3x+5y subject to \[-2x+y\leq4\]\[x+y\geq3\]\[x-2y\leq2\]\[x,y\geq0\]

asked Feb 5, 2013 by meena.p

0 answers

Solve the following LPP graphically. Maximize or minimize Z = 3x+5y subject to \[3x-4y\geq-12\]\[2x-y+2\geq0\]\[2x+3y-12\geq0\]\[0\leq x\leq4\]\[y\geq2\]

asked Feb 5, 2013 by meena.p

1 answer

If a young man rides his motorcycle at 25 km/hr, he had to spend Rs.2 per km on petrol. If he rides at a faster speed of 40 km/hr, the petrol cost increases at Rs.5 per km. He has Rs.100 to spend on petrol and wishes to find what is the maximum distance he can travel within one hour. Express this as LPP and solve it graphically.

asked Feb 5, 2013 by meena.p

1 answer

A farmer has a supply of chemical fertilizer of type I which contains 10% nitrogen and 6% phosphoric acid and type II fertilizer which contains 5% nitrogen and 10% phosphoric acid. After testing the soil conditions of a field, it is found that atleast 14 kg of nitrogen and 14 kg of phosphoric acid is required for a good crop. The fertilizer type I costs Rs.2.00 per kg and type II costs Rs.3.00 per kg. How many kilograms of each fertilizer should be used to meet the requirement and the cost be minimum.

asked Feb 5, 2013 by meena.p

0 answers

A firm makes two types of furniture : chairs and tables. The contribution to profit for each product as calculated by the accounting department is Rs.20 per chair and Rs.30 per table. Both products are to be processed on three machines $ M_1,M_2 and M_3.$ The time required in hours by each product and total time available in hours per week on each machine are as follows:

asked Feb 5, 2013 by meena.p

1 answer

An oil company has tow depots A and B with capacities of 7000L and 4000L respectively. The company is to supply oil to three petrol pumps D, E and F whose requirements are 4500L, 3000L and 3500L respectively. The distances (in km) between the depots and the petrol pumps is given in the following table:

asked Feb 5, 2013 by meena.p

0 answers

A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A, while each packet of the same quality of food Q contains 3 units of calcium, 20 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and almost 300 units of cholesterol. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A?

asked Feb 5, 2013 by meena.p

0 answers

A toy company manufactures two types of doll; a basic version-doll A and a deluxe version doll B. Each doll of type B takes twice as long as to produce as one of type A, and the company would have time to make a maximum of 2000 per day if it produces only the basic version. The supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 600 per day available. If company makes profit of Rs.3 and Rs.5 per doll, respectively, on doll A and B; how many each should be produced per day in order to maximize profit.

asked Feb 5, 2013 by meena.p

0 answers

A variable plane is at constant distance p from the origin and meet the axes in A, B & C. Show that the locus of the centroid of the tetrahedron $\bigtriangleup ABC\;is\; \Large\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{16}{p^2}$

asked Feb 5, 2013 by meena.p

1 answer

A variable plane which remains at a constant distance 3p from the origin cuts the co-ordinate axes at A, B & C. Show that the locus of the centroid of the $ \bigtriangleup ABC\;is\; \Large\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=\frac{1}{p^2}$

asked Feb 5, 2013 by meena.p

1 answer

A line makes angles $\alpha,\beta,\gamma\;and\;\delta$ with the four diagonals of a cube. Prove that $ \cos ^2 \alpha+\cos ^2\beta+\cos ^2 \gamma+\cos ^2 \delta=\Large\frac{4}{3}$

asked Feb 5, 2013 by meena.p

0 answers

Find the distance of the point (2,3,4) from the line $\Large\frac{x+3}{3}=\frac{y-2}{6}=\frac{z}{2}$ measured parallel to the plane 3x+2y+2z+5 = 0

asked Feb 5, 2013 by meena.p

0 answers

Find the distance of the point (1,-2,3) from the plane x-y+z = 5 measured parallel to the line $ \Large\frac{x+1}{2}=\frac{y+3}{2}=\frac{z+1}{-6}$

asked Feb 5, 2013 by meena.p

0 answers

Find the reflection of the point (1,2,-1) in the plane 3x-5y+4z = 5

asked Feb 5, 2013 by meena.p

0 answers

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

asked Feb 5, 2013 by meena.p

0 answers

Find the vector equation of the plane through the intersection of the planes $ \bar{r}. (2\bar{j}+6\bar{j})+12=0$ & $ \bar{r}.(3\bar{i}-\bar{j}+4\bar{k})=0$ which are at a unit distance from the origin.

asked Feb 5, 2013 by meena.p

0 answers

Find the shortest distance between two lines whose vector equations are $ \overrightarrow{r}=(1-t)i+(t-2) \bar{j}+(3-2t) \bar{k} $ and $ \overrightarrow{r}=(s+1) \bar {i}+(2s-1)\bar {j}-(2s+1) \bar {k}$

asked Feb 5, 2013 by meena.p

0 answers

Find the values of P so that the lines $ \Large\frac{1-x}{3}=\frac{7y-14}{2p}=\frac{z-3}{2}$ and $ \Large\frac{7-7x}{3p}=\frac{y-5}{1}=\frac{6-z}{5}$ are at right angles.

asked Feb 5, 2013 by meena.p

1 answer

The foot of the perpendicular drawn from the origin to the plane is (2,5,7). FInd the equation of the plane.

asked Feb 5, 2013 by meena.p

0 answers

Find the perpendicular distance of point (2,3,4) from the line $ \Large\frac{4-x}{2}=\frac{y}{6}=\frac{1-z}{3}$

asked Feb 5, 2013 by meena.p

0 answers

Find the equation of the plane through the points (-1,1,1) and (1,-1,1) perpendicular to the plane x+2y+2z = 5

asked Feb 5, 2013 by meena.p

1 answer

Find the length and co-ordinates of the foot of perpendicular from point (1,1,2) to the plane 2x-2y+4z+5 = 0

asked Feb 5, 2013 by meena.p

0 answers

Find the foot of the perpendicular drawn from the point A(1,0,3) to the join of the points B(4,7,1) and C(3,5,3)

asked Feb 5, 2013 by meena.p

1 answer

Find the equation of the plane passing through the points (1,-1,2) and (2,-2,2) and perpendicular to the plane 6x-2y+2z = 9.

asked Feb 5, 2013 by meena.p

1 answer

Find the image of the point (1,2,3) in the plane x+2y+4z = 38.

asked Feb 5, 2013 by meena.p

0 answers

Show that the lines $ \Large\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $ \Large\frac{x-4}{5}=\frac{y-1}{2}=2$ intersect. Also find the point of intersection.

asked Feb 5, 2013 by meena.p

0 answers

Find the equation of the plane passing through the point (1,1,1) and perpendicular to each of the plane x+2y+3z = 7 and 2x-3y+4z = 0

asked Feb 5, 2013 by meena.p

0 answers

Find the value of k for which the lines $\Large\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$ and $\Large \frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are co-planar.

asked Feb 5, 2013 by meena.p

0 answers

Find the equation of the plane passing through the point (1,6,3) and perpendicular to the plane 2x+3y-z = 7

asked Feb 5, 2013 by meena.p

1 answer

Find the value of k for which the two lines $ \large\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\; and \;\frac{x-3}{1}=\frac{y-k}{2}=z$ intersect at a point?

asked Feb 5, 2013 by meena.p

0 answers

What are the conditions that the planes $ a_1x+b_1y+c_1z=d_1\;and\; a_2x+b_2y+c_2z=d_2 $ are (i) parallel (ii) perpendicular to each other?

asked Feb 5, 2013 by meena.p

0 answers

Find the equation of the plane passing through the point (1,4,-2) and parallel to the plane -2x+y-3z=7

asked Feb 5, 2013 by meena.p

0 answers

Show that the line $ \bar{r}=(2\bar{i}-2\bar{j}+3\bar{k})+\lambda(\bar{i}-\bar{j}+4\bar{k})$ is parallel to the plane.$\bar{r}.(\bar{i}+5\bar{j}+\bar{k})=5$

asked Feb 5, 2013 by meena.p

0 answers

If a, b & c are the lengths of the sides of a triangle, using vector method, show that its area is $\sqrt {s(s-a)(s-b)(s-c)}$ where $2s=a+b+c$

asked Feb 5, 2013 by meena.p

1 answer

If D, E & F are the mid-points of the sides of a triangle ABC, prove by vector method that area of \[\bigtriangleup DEF=\frac{1}{4}(area\;of\;\bigtriangleup ABC).\]

asked Feb 5, 2013 by meena.p

0 answers

If a, b & c are the lengths of the sides opposite respectively to the angles A, B & C of a $\bigtriangleup ABC,$ using vector method show that \[a)\cos A=\frac{b^2+c^2-a^2}{2bc} \qquad b)\;a=b\cos C+c \cos B.\]

asked Feb 5, 2013 by meena.p

0 answers

Prove by vector method, that the parallelogram on the same base and between the same parallels are equal in area.

asked Feb 5, 2013 by meena.p

0 answers

Using vector method, show that the diagonals of a Rhombus bisect each other at right angles.

asked Feb 5, 2013 by meena.p

1 answer

Using vector method, prove that if two medians of a triangle are equal, then it is an isosceles.

asked Feb 5, 2013 by meena.p

1 answer

Using vector method, prove that if the diagonals of a parallelogram are equal in length, then it is a rectangle.

asked Feb 5, 2013 by meena.p

1 answer

Prove that the perpendicular bisectors of a triangle are concurrent.

asked Feb 5, 2013 by meena.p

1 answer

Prove that the altitudes of a triangle are concurrent.

asked Feb 5, 2013 by meena.p

1 answer

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