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12TH STANDARD MATHS COME BOOK

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+2 maths come book created one mark questions & key answers (English Medium). Posted by Dr. K. Thirumurugan | Oct 2, | STATE BOARD (12th) | 1 |. Download Tamil Nadu plus two maths PTA COME BOOK English Medium. 12th Maths come book free download tamil Medium. Plus two. 12th maths come book download plus two maths come book for 12th tamil medium 12th std maths come book english medium free download here 12th maths. Author: DEBI MCELHANNON Language: English, Spanish, Hindi Country: Iceland Genre: Science & Research Pages: 190 Published (Last): 30.05.2015 ISBN: 401-6-78275-163-1 ePub File Size: 21.47 MB PDF File Size: 9.26 MB Distribution: Free* [*Regsitration Required] Downloads: 44457 Uploaded by: SHARILYN Example 5. How fast is the distance between the ships changing at 4. Both are headed for the intersection of the two roads. A ladder 10m long rests against a vertical wall. At what rate are the cars approaching each other when car A is 0.

Find the angle between the curves Example 5.

How fast is the height of the pile increasing when the pile is 10 ft high? Prove that the slope at Q is four times the slope at P.

The material for the top and bottom of the box is to cost Rs. The top and bottom margins of a poster are each 6 cms and the side margins are each 4cms. Show that the volume of the largest right circular cone that can be inscribed in a sphere of radius a is 3 8 27 volume of the sphere.

He could row his boat directly across the river to point R and then run to Q. Find the area of the largest rectangle that can be inscribed in a semi circle of radius r. A farmer has feet of fencing and want to fence of a rectangular field that borders a straight river. If the cost of the materials is to be the least. A man is at a point P on a bank of a straight river. He needs no fence along the river. What ar the dimensions of the field that has the largest area? A closed cuboid box with a square base is to have a volume of c.

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If the area of the printed material on the poster is fixed at cms2. Find the intervals of concavity and the points of inflection of the following functions: Find the length of the curve Example 7. How many grams of the first substance was there initially? Example 8. The urine is monitored continuously using a catheter. At the end of one hour. A bank pays interest by continuous compounding. He records the first temperature at Assume normal temperature of a human body to be The number of bacteria in a yeast culture grows at a rate which is proportional to the number present.

A drug is excreted in a patients urine. Solve the following differential equations: After 2 hours he finds the temperature to be Show that the number of bacteria at the end of five hours will be 3 5 times of the population at initial time. Solve the following: If the population of a colony of yeast bacteria triples in 1 hour. In a certain chemical reaction the rate of conversion of a substance at time t is proportional to the quantity of the substance still untransformed at that instant. For a postmortem report. Calculate the percentage increase in such an account over one year.

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Show that G. Example 9. Find its temperature after a further interval of 5 minutes. Prove that the set of four functions f 1. The rate at which the population of a city increases at any time is proportional to the population at that time. The sum of Rs. When its mass is 10 mgm. Radium disappears at a rate proportional to the amount present.

How long will it take for the mass to be reduced from 10 mgm to 5 mgm. If there were 1. In how many years will the amount be twice the original principal? Show that the nth roots of unity form an abelian group of finite order with usual multiplication. Example The total life time in year of 5 year old dog of a certain breed is a Random Variable whose distribution function is given by.

An urn contains 4 white and 3 red balls. Find the probability distribution of number of red balls in three draws one by one from the urn. If X is normally distributed with mean 6 and standard deviation 5 find. The number of accidents in a year involving taxi drivers in a city follows a Poisson distribution with mean equal to 3. The mean score of students for an examination is 34 and S. Find c. Assuming the weights are normally distributed.

Obtain k. The air pressure in a randomly selected tyre put on a certain model new car is normally distributed with mean value 31 psi and standard deviation 0. Solve the following non-homogeneous system of linear equations by determinant method: Find the rank of the following matrices: Examine the consistency of the following system of equations.

Find the adjoint of the matrix Example 1. If it is consistent then solve the same. Solve by matrix inversion method Example 1. Solve the following system of linear equations by determinant method. It is enough to prove any three vectors formed by these four points are coplanar. Find the work done by the forces. Prove by vector method that the parallelogram on the same base and between the same parallels are equal in area. Prove that twice the area of a parallelogram is equal to the area of another parallelogram formed by taking as its adjacent sides the diagonals of the former parallelogram.

Prove by vector methods. Diagonals of a rhombus are at right angles. Find the equation of the plane. Angle in a semi-circle is a right angle. Find the equation of the plane through the point whose p. Justify your answer.

Find also the centre and radius of the sphere. Prove by vector method. Obtain the vector and Cartesian equation of the sphere whose centre is 1.

If the position vectors of three points A. Also find the equation in Cartesian form. C of a triangle ABC. For any three vectors a.

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Find the distance from the point 1. Find the vector and Cartesian equations of the straight line passing through the points Show that the points 3. The foot of perpendicular drawn from the origin to the plane is 4. Prove that in triangle ABC with usual notations. Let i a. Find the distance between the parallel planes Example 2. Plot the points and use midpoint formula.

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Find the vector and Cartesian equation of the sphere whose centre is 1. Find the point of intersection of the line passing through the two points 1. Example 3. Find all the values of the following: Prove that the points representing the complex numbers vertices of a rectangle.

Find the modulus and argument of the following complex numbers: If n is a positive integer. If the mirror is 25cm deep. Find the equatin of the hyperbola if focus: Find the equations of the tangent and normal to the parabolas. The headlight of a motor vehicle is a parabolic reflector of diameter 12cm and depth 4cm. Find the position of bulb on the axis of the reflector for effective functioning of the headlight.

Find the equation of the ellipse with focus Find the equation of the ellipse whose centre is 1.

Find the equation of the rectangular hyperbola which has its centre at 2. Find the equation of the ellipse whose major axis is along x-axis. Find the equation of the ellipse given that the centre is 4. Find its equation and asymptotes. A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 9mts.

Find the equation of the ellipse if the major axis is parallel to y-axis. If the distance across diameter the top of the mirror is cm. Find the equation of the ellipse whose foci are 1. Find the equation of the ellipse whose one of the foci is 2. Find the equations of the asymptotes of the following rectangular hyperbolas.

Find the equations of directrices.

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Find the equation of the hyperbola whose transverse axis is along x-axis. The centre is 0. Find the equation of a point which moves so that the sum of its distances from Find how close the earth gets to sun and the greatest possible distance between the earth and the sun. Find the equation of the ellipse whose foci are 2. Find the equation of the hyperbola whose centre is 2. The orbit of the earth around the sun is elliptical in shape with sun at a focus.

Find the equation of the ellipse whose vertices are The semi major axis is of length Find the equation of the hyperbola whose centre is 1. Find the equation of the hyperbola whose transverse axis is parallel to x-axis.

Find the angle between the asymptotes of the hyperbola Example 4. Show that the tangent to a rectangular hyperbola terminated by its asymptotes is bisected at the point of contact. Also find the points of contact. Find the equations of the two tangents that can be drawn from the point 5.

Find the equation of the locus of all points such that the differences of their distances from 4. Determine the equation of the 9 hyperbola if its eccentricity is 2. Find the angle between the asymptotes to the hyperbola Example 4.

Points A and B are 10km apart and it is determined from the sound of an explosion heard at those points at different times that the location of the explosion is 6km closer to A than B. 