Recent questions tagged sec-c

Evaluate the definite integral as limits of sums\[\int\limits_1^4(x^2-x)dx\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral as limits of sums $\displaystyle\int\limits_0^4(x+e^{2x})dx$

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area bounded by the curve $x^2 = 4y$ and the line $x = 4y - 2$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Find the area of the region in the first quadrant enclosed by $x$ - axis, line $x = \sqrt {3}\: y$ and the circle $x^2 + y^2 = 4$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

By using the properties of definite integrals,evaluate the integral\[\int\limits_0^\pi\; log(1+\cos x)\;dx\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Evaluate $ \large \int\limits_0^1e^{2-3x}\;$$dx\;$ as a limit of a sum

asked Dec 2, 2012 by sreemathi.v

1 answer

In a bank,principal increases continuously at the rate of r% per year.Find the value of r if Rs100 doubles itself in 10years. $\quad (log_e2=0.6931)$

asked Nov 30, 2012 by sreemathi.v

1 answer

The volume of spherical balloon being inflated changes at a constant rate.If initially its radius is 3units and after 3seconds it is 6units.Find the radius of balloon after t seconds.

asked Nov 30, 2012 by sreemathi.v

1 answer

In a bank, principal increases continuously at the rate of $5\%$ per year. An amount of $Rs.1000$ is deposited with this bank, how much will it work after $10$ years $(e^{0.5}=1.648)$.

asked Nov 30, 2012 by sreemathi.v

1 answer

In a culture, the bacteria count is $1,00,000.$ The number is increased by $10\%$ in $2$hours.In how many hours will the count reach $2,00,000$ if the rate of growth of bacteria is proportional to the number present?

asked Nov 30, 2012 by sreemathi.v

1 answer

Prove that \[tan^{-1} \frac{1}{5}+ tan^{-1} \frac{1}{7}+tan^{-1}\frac{1}{3}+tan^{-1} \frac{1}{8}= \frac{\pi}{4}\]

asked Nov 29, 2012 by vaishali.a

1 answer

Solve the system of equations: $\large \frac{2}{x}+\frac{3}{y}+\frac{10}{z}=$$4.\quad $ $\large \frac{4}{x}-\frac{6}{y}+\frac{5}{z}$$=1.\quad $ $\large \frac{6}{x}+\frac{9}{y}-\frac{20}{z}$$=2.$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If $A = \begin{bmatrix} 2 &-3 & 5\\ 3& 2 & -4\\ 1& 1& -2 \end{bmatrix}$, $\;$ find $A^{-1}.\;$ Using $ A^{-1}$ solve the system of equations: \[2x-3y+5z=11\] \[3x+2y-4z = -5\] \[x+y-2z = -3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[x-y+2z=7\] \[3x+4y-5z=-5\] \[2x-y+3z=12\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[2x+3y+3z=5\] \[x-2y+z=-4\] \[3x-y-2z=3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[x-y+z=4\] \[2x+y-3z=0\] \[x+y+z=2\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[2x+y+z=1\] \[x-2y-z = \frac{3}{2}\] \[3y-5z=9\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the following Linear Programming Problems graphically: Maximise $Z = 3x + 4y$ . subject to the constraints : $x + y \leq 4, x \geq 0, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Minimise $Z =$ –$3x + 4 y$ subject to $ x + 2y \leq 8, 3x + 2y \leq 12, x \geq 0, y\geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Maximise $Z = 5x + 3y$ subject to $3x + 5y \leq 15, 5x + 2y \leq 10, x \geq 0, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Minimise $Z = 3x + 5y$. such that $ x + 3y \geq 3, x + y \geq 2, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Maximise $Z = 3x + 2y$ subject to $x + 2y \leq 10, 3x + y \leq 15, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Solve the following Linear Programming Problems graphically: Minimise $Z = x + 2y$, subject to $2x + y \geq 3, x + 2y \geq 6, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Show that the minimum of $Z$ occurs at more than two points. Minimise and Maximise $Z = 5x + 10 y$ subject to $x + 2y \leq 120, x + y \geq 60, x – 2y \geq 0, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Show that the minimum of Z occurs at more than two points. Minimise and Maximise $Z = x + 2y$ subject to $ x + 2y \geq 100, 2x – y \leq 0, 2x + y \leq 200; x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Show that the minimum of Z occurs at more than two points. Maximise $z = – x + 2y$, subject to the constraints: $ x \geq 3, x + y \geq 5, x + 2y \geq 6, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

\[ \text{For the matrix A = } \begin{bmatrix} 1&1&1 \\ 1& 2&- 3 \\ 2 &-1& 3 \end{bmatrix} \] \[ \text{Show that } A^{3} - 6A^{2} + 5A + 11I = O. \text{ Hence, find } A^{-1}\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Show that the minimum of Z occurs at more than two points. Maximise $Z = x + y$, subject to$\; x $– $y\leq –1, -x + y \leq 0, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

\[ \text{If A = } \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}, \text{show that } A^{2} -5A +7I = 0. \text{ Hence find } A^{-1}\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

\[ \text{Let A = } \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \text{and B = } \begin{bmatrix} 6 & 8 \\ 7 & 9 \end{bmatrix}. \text{Verify that } (AB^{-1}) = B^{-1}A^{-1}\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 1&-1&2 \\ 3&0&-2 \\ 1&0&3 \\ \end{bmatrix} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Choose the correct answer in the normal to the curve $x^2 = 4y$ passing $(1,2)$ is

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height $h$ and semi vertical angle $\alpha$ is one-third that of the cone and the greatest volume of cylinder is $\large \frac{4}{27}$$\pi h^3 \: tan^2 \: \alpha $

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is $\large\frac{2R}{\sqrt 3}$ . Also find the maximum volume.

asked Nov 28, 2012 by thanvigandhi_1

2 answers

A point on the hypotenuse of a triangle is at distance $a$ and $b$ from the sides of the triangle.Show that the maximum length of the hypotenuse is $ (a^{\large\frac{2}{3}} + $$b^{\large\frac{2}{3}})^{\Large\frac{3}{2}}$

asked Nov 28, 2012 by thanvigandhi_1

1 answer

A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is $2 m$ and volume is $8 m^3$. If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

An urn contains 25 balls of which 10 balls bear a mark 'X' and the remaining 15 bear a mark 'Y'. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability for the following: (i) all will bear 'X' mark. (ii) not more than 2 will bear 'Y' mark. (iii) at least one ball will bear 'Y' mark. (iv) the number of balls with 'X' mark and 'Y' mark will be equal.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that semi-vertical angle of right circular cone of given surface area and maximum volume is $ \sin^{-1} \left(\frac{1}{3}\right)$

asked Nov 27, 2012 by thanvigandhi_1

1 answer

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is $\tan^{-1} \sqrt {2}$.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Show that the right circular cone of least curved surface and given volume has an altitude equal to $\sqrt 2$ time the radius of the base.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is$\large\frac{8}{27}$ of the volume of the sphere.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 1 & 2 & -3 \\ 5 & 0 & 2 \\ 1 & -1 & 1 \end{bmatrix} , B = \begin{bmatrix} 3 & -1 & 2 \\ 4 & 2 & 5 \\ 2 & 0 & 3 \end{bmatrix} \text{ and } C = \begin{bmatrix} 4 & 1 & 2 \\ 0 & 3 & 2 \\ 1 & -3 & 2 \end{bmatrix} $, then compute $( A + B )$ and $( B - C )$. Also verify that $A + ( B - C ) = ( A + B ) - C. $

asked Nov 26, 2012 by pady_1

1 answer

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