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Recent questions tagged 2012

Show that the line $ \large\frac{x}{a}+\frac{y}{b}$$=1$ touches the curve \(y=be^{\large\frac{-x}{a}}\) at the point where it crosses the y - axis.

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{2x+1}{\sqrt {x^2+4x+3}}$$dx$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{xe^x}{(x+1)^2}$$dx.$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Solve the differential equation $ 2xy+y^2-2x^2\large\frac{dy}{dx}$$=0 : y(1)=2.$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Solve the differential equation $ (y+x)\large\frac{dy}{dx}$$=y-x. $

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Let \( \overrightarrow a = 2\hat i + \hat k, \overrightarrow b = \hat i + \hat j + \hat k\) and \( \overrightarrow c = 4\hat i - 3\hat j + 7\hat k\) be three vectors. Find a vector \( \overrightarrow r \) which satisfies \( \overrightarrow r\) x \( \overrightarrow b = \overrightarrow c \) x \( \overrightarrow b\) and \( \overrightarrow r. \overrightarrow a =0.\)

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Find the shortest distance between the lines $\large\frac{x-3}{1} = \frac{y-5}{-2} = \frac{z-7}{1}$$ \: and \: \large\frac{x+1}{7} = \frac{y+1}{-6} = \frac{z+1}{1}. $

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Assume that each child born is equally likely to be a boy or girl. If a family has two children, what is the conditional probability that both are girls given that (a) the eldest is a girl (b) at least one is a girl (c) pre-natal * determination is a crime. What will you do if you come to know that some of your known is indulging in pre-natal * determination?

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Using matrices, solve the following : $2x+y-3z=13; x+y-z=6 ;2x-y+4z = -12$

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Using elementary transformation, find the inverse of the following matrix \( \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \end{bmatrix} \)

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Show that the semi-vertical angle of rightcircular of given surface area and maximum volume is \( \sin^{-1} \bigg( \large\frac{1}{3} \bigg).\)

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Find the area of circle \( x^2+y^2=16\) which is exterior of the parabola \( y^2=6x\).

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int\large \frac{x^2+x+1}{(x^2+1)(x+2)}$$dx.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^3 (x^2+2x)dx $ as limit of a sum.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

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

asked Jan 16, 2013 by thanvigandhi_1

0 answers

A housewife wishes to mix up two kind of foods X and Y in such a way that mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of 1 kg of food X and 1 kg of food Y are as given in the table : If 1 kg of food X costs Rs. 6 and 1 kg of food Y costs Rs. 10, find the least cost of the mixture which will produce the desired diet.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Probability of solving a mathematical problem by A, B and C respectively are $\large\frac{1}{3}, \frac{1}{2}$$ \: and \: \frac{1}{4} $. If they try to solve the problem independently, find the probability that : (i) the problem is solved (ii) exactly one of them solve the problem (iii) exactly two of them solve the problem (iv) what do you think that problem solving attitude from books helpful in real life also?

asked Jan 16, 2013 by thanvigandhi_1

0 answers

If \( f(x)=x^2-1, g(x)=2x+5\), then find (fog)(x).

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Find the value of \( \cos^{-1} \bigg( \frac{1}{2} \bigg) + 2 \sin^{-1} \bigg(\large \frac{1}{2} \bigg) \)

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Evaluate [ 1 2 1 ] \( \begin{bmatrix} 2 \\ 4 \\ 2 \end{bmatrix}\)

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Show that elements on the main diagonal of a skew-symmetric matrix are all zero.

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Let \( \begin{bmatrix} 3 & y \\ x & 1 \end{bmatrix} = \begin{bmatrix} 3 & 2 \\ 4 & 1 \end{bmatrix} \). Find the possible values of x and y, if x, y \( \in \) N.

asked Jan 16, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \sqrt{\tan x} (1+\tan^2x)dx.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{\sin^2x}{1+\cos x}$$dx.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

If \( \overrightarrow a. \hat i = \overrightarrow a. (\hat i + \hat j ) = \overrightarrow a.(\hat i + \hat j + \hat k )=1.\)then find \( \overrightarrow a\).

asked Jan 16, 2013 by thanvigandhi_1

0 answers

If \( | \overrightarrow a\) x \( \overrightarrow b | = 4, | \overrightarrow a. \overrightarrow b |=2\) then find \(| \overrightarrow a |^2 | \overrightarrow b |^2\).

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Find the cartesian equation of the line through (5, 2, -4) and which is parallel to the vector \( 3\hat i + 2\hat j - 8\hat k\)

asked Jan 16, 2013 by thanvigandhi_1

0 answers

'' is a binary operation defined on Q. Find which of the following binary oprations are associative and which are commutative : $(i) ab=a-b\: for \: a,b \in Q (ii) a*b = \large\frac{ab}{4}$$\: for \: a,b \in Q.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Show that the relation in the set \( A = { x : x \in W, o \leq x \leq 12} \) given by R = {(a, b) : a-b is a multiple of 4} is an equivalence relation.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Prove that : $ \cos^{-1}\large \frac{4}{5}+\tan^{-1}\large\frac{3}{5}$$=\tan^{-1}\large\frac{27}{11} $

asked Jan 16, 2013 by thanvigandhi_1

1 answer

(i) There are 2 men, 3 women and 3 children in family Y. The daily requirement of calories and protiens for men, women and children are 2000, 1800 and 1200 ; 50 g , 40 g and 35 g respectively. Represent the above information by matrices. Using matrix multiplication , calculate the total requirement of calories and protiens for each of the two families. (ii) Explain the importance of balance diet.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

If \( y = tan^{-1}x,\) prove that $ (1+x^2)\large\frac{d^2y}{dx^2}$$+2x\large\frac{dy}{dx}$$=0.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

If \( x^{\large p}.y^{\large q} = (x+y)^{\large p+q}, \) prove that \( \large\frac{dy}{dx}=\large\frac{y}{x}.\)

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Examine for continuity the function f' defined by $ f(x) = \left\{ \begin{array}{l l} \large\frac{e^{\large \frac{1}{x}} - 1}{e^{\large\frac{1}{x}} + 1}, & \quad { x \neq 0}\\ 0, & \quad \text{ $x$ = 0} \end{array}. \right. \: at\: x = 0.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Compute the area of the bounded by the line $x+2y=2,y-x=1$ and $2x+y=7.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Discuss the applicability of Roll's theorem for the function \( f(x) = x^{\large\frac{1}{3}} \) on [-1, 1].

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Using differentials, find the approximate value of \( \sqrt {0.037}\).

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\large\frac{\pi}{2}} \large\frac{x \sin x}{1+\sin x}$$dx $

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\Large\frac{\pi}{4}} \log(1+tan \: x) dx.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Solve the differential equation $ (x^2-1)\large\frac{dy}{dx}$$+2(x+2) y = 2(x+1). $

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Solve the differential equation : $ 2x^2 \large\frac{dy}{dx}$$-2xy+y^2 = 0, \: y(e) = e.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

If \( \overrightarrow a = 4\hat i + 2\hat j - \hat k \: and \: \overrightarrow b = 5\hat i + 2\hat j - 3\hat k\), find the angle between \( \overrightarrow a + \overrightarrow b \: and \: \overrightarrow a - \overrightarrow b\).

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Show that the line : $ \large\frac{x-5}{4}=\large\frac{y-7}{4}=\frac{z+3}{-5}$$ \: and \: \large\frac{x+8}{7}=\frac{y-4}{1}=\frac{z-5}{3} $ intersect each other.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

A box contains 2 gold and 3 silver coins. A box is choosen at random and a coin is drawn from it. If the selected coin is a gold coin, find the probability that it was drawn from the second box. A student should not carry ornaments and other precious things to school. why?

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove the following : \( \begin{bmatrix} (b+c)^2 & ab & ca \\ ab & (a+c)^2 & bc \\ ac & bc & (a+b)^2 \end{bmatrix} = 2abc (a+b+c)^3.\)

asked Jan 16, 2013 by thanvigandhi_1

0 answers

A square piece of tin of side 24 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that volume of the box is maximum?

asked Jan 15, 2013 by thanvigandhi_1

1 answer

An open box with a square base is to be made out of given quantity of sheet of area \( a^2\). Show that maximum volume of the box is \( \large\frac{a^3}{6\sqrt 3}. \)

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{x^4}{x^4-1}$$ dx $

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \: \sqrt {\large\frac{1-\sqrt x}{1+\sqrt x}}dx. $

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Find the area enclosed by the parabolas \( y^2=9x \: and \: x^2=9y\)

asked Jan 15, 2013 by thanvigandhi_1

0 answers

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