Recent questions tagged q1

Write $( fog, \: if \: f : R \rightarrow R)$ are given by $( f(x) = 8x^3)$ and $( g(x)=x^{\large\frac{1}{3}} )$

asked Feb 6, 2013 by thanvigandhi_1

1 answer

If $ f : R \rightarrow R$ is defined by $ f(x)=3x+2$, define $ f[f(x)]. $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

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

Let A = {1,2,3}, B = {4,5,6,7} and let f = {(1,4), (2,5), (3,6)} be a function from A to B. State whether f is one-one or not.

asked Feb 5, 2013 by thanvigandhi_1

1 answer

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

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

Write the value of $ \cos^{-1} \bigg( \cos\large\frac{7\pi}{6} \bigg). $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Write the order and degree of the differential equation.$ \bigg[1+(y')^2\bigg]^{3/2}=y''$

asked Feb 4, 2013 by meena.p

0 answers

Find the area bounded by the curve y = 2 cosx and the x-axis from x = 0 to x =$2\pi$

asked Feb 4, 2013 by meena.p

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If $ f = \{(5,2),(6,3)\} g = \{(2,5),(3,6)\}$ write $ fog$

asked Feb 4, 2013 by thanvigandhi_1

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Write the principal value of $ \cos^{-1} \bigg( -\large\frac{\sqrt 3}{2} \bigg). $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

Using principal value, write the value of $ \cos^{-1} \bigg( \large\frac{1}{2} \bigg)$$ + 2\sin^{-1} \bigg(\large \frac{1}{2} \bigg) $

asked Feb 3, 2013 by thanvigandhi_1

1 answer

If A is square matrix of order 3 such that | adj.A |=81, find | A |.

asked Feb 2, 2013 by thanvigandhi_1

2 answers

Show that the function $ f : R \rightarrow R $ defined by $ f(x)=3x+7$ is one-one.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

choose the correct alternative$ \int \large\frac {\cos \sqrt x}{\sqrt x} dx=$\[(a)\;\sin \sqrt x \qquad (b)\;2\cos \sqrt x\qquad(c)\;2\sin \sqrt x \qquad(d)\;\large\frac{\sqrt \cos x}{x}\]

asked Jan 30, 2013 by meena.p

0 answers

If $ f(x) =\large \frac{4x+3}{6x-4}$$, x \neq \large\frac{2}{3},$ show that 'fof' is an identity function, for all $ x \neq \large\frac{2}{3} .$

asked Jan 30, 2013 by thanvigandhi_1

0 answers

If $ f: R \rightarrow R$ is defined by $ f(x)=x^2-3x+2,$ find $ f [ f(4) ]. $

asked Jan 29, 2013 by thanvigandhi_1

0 answers

The slope of the tangent to the curve represented by $ x=t^2+3t-8\;and\;y=2t^2-2t-5$at the point M(2,-1) is \[(a)\;\frac{7}{6}\qquad(b)\;\frac{2}{3}\qquad(c)\;\frac{3}{2}\qquad(d)\;\frac{6}{7}\]

asked Jan 28, 2013 by meena.p

0 answers

Let * be binary operation on N given by $ ab = 1.c.m.(a,b),a,b \in N.$ Find (23)*6.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

If $ f(x) = \cos \: x \: and \: g(x) = x^3,$ find $ fog \:and \:gof. $

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Write the number of one-one function from the set A = {1, 2, 3} to itself.

asked Jan 25, 2013 by thanvigandhi_1

0 answers

If $ f : R \rightarrow R$ is defined by $ f(x) = x^2-3x+2$ , find $ f (f(x)).$

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Let f be continuous function on [1,3]. If f takes only rational values for all x and f(2) = 10 then find the value of f(1.5)

asked Jan 24, 2013 by meena.p

1 answer

Prove that $f: R → R $ is a bijection given by $f(x) = x^3+3$. Find $f ^{-1} (x)$. Does the truthfulness and honesty may have any relation?

asked Jan 24, 2013 by shanthinig

0 answers

Find the equation of the plane through point (2, 0, -1) and perpendicular to the line joining the two points (1, 2, 3) and (3, -1, 6)

asked Jan 24, 2013 by thanvigandhi_1

1 answer

If a+b+c=0 anb $ \begin{vmatrix} a-x & a & b \\ c & b-x & a \\ b & a & c-x \end{vmatrix}$ then prove that either x=0 or $x= \pm\sqrt{\frac{3}{2}(a^2+b^2+c^2)}$

asked Jan 24, 2013 by meena.p

0 answers

Prove that $f: \text{R} \rightarrow \text{R}$ is a bijection given by $f(x) = x^3 + 3$. Find $f^{-1}(x)$. Does the truthfulness and honesty may have any relation?

asked Jan 24, 2013 by pady_1

0 answers

Find the value of $\cos\bigg\{\cos^{-1}\bigg(\frac{-\sqrt {3}}{2}\bigg)+\frac{\pi}{6}\bigg\}$

asked Jan 23, 2013 by meena.p

1 answer

Write the following functions in the simplest form $\cos^{-1} (2x^2-1), 0 \leq x \leq 1.$

asked Jan 23, 2013 by thanvigandhi_1

0 answers

If $f(x)=\frac{x-1}{x+1},(x \neq 1,-1),$ show that $fof^{-1}$ is an identity function.

asked Jan 22, 2013 by meena.p

0 answers

Find the principal value of $ \sec^{-1}(2). $

asked Jan 22, 2013 by thanvigandhi_1

0 answers

Give an example of relation which is reflexive but neither symmetric nor transitive.

asked Jan 21, 2013 by thanvigandhi_1

1 answer

Find the solution of $\Large \frac{dy}{dx}\normalsize =2^{y-x}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the unit vector in the direction of sum of vectors $\overrightarrow{a}=2\hat i+\hat j+\hat k\;and\;\overrightarrow{b}=2\hat j-\hat k$

asked Jan 16, 2013 by sreemathi.v

1 answer

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 area of the region bounded by the curves $y^2=9x,y=3x.$

asked Jan 15, 2013 by sreemathi.v

1 answer

Find x if $ tan^{-1} 4 + cot^{-1}x =\large \frac{\pi}{2} $

asked Jan 15, 2013 by thanvigandhi_1

1 answer

Verify the following$ \int\frac{2x-1}{2x+1}dx=x-log \mid (2x+3)^2\mid+C$

asked Jan 14, 2013 by sreemathi.v

1 answer

Show that the matrix $ A = \begin{bmatrix} 0 & 1 & -1 \\ -1 & 0 & 1 \\ 1 & -1 & 0 \end{bmatrix} $ is a skew - symmetric matrix.

asked Jan 11, 2013 by thanvigandhi_1

1 answer

A spherical ball of salt is dissolving in water in such a manner that the rate of decrease of the surface.Prove that the radius is decreasing at a constant rate.

asked Jan 10, 2013 by sreemathi.v

1 answer

Relation R is the set N of natural numbers defined as R = (x, y): y=x+5 and x < y}.

asked Jan 10, 2013 by thanvigandhi_1

0 answers

Relation R in the set A = { 1, 2, 3, 4, 5, 6} defined as R = (x, y):y is divided by x}.

asked Jan 10, 2013 by thanvigandhi_1

0 answers

If $ f(x) = x+7 \: and \: g(x) = x-7, x\: \in \: R, $ find (fog) (7).

asked Jan 9, 2013 by thanvigandhi_1

0 answers

For a loaded die,the probabilities of outcomes are given as under P(1)=P(2)=0.2,P(3)=P(5)=P(6)=0.1 and P(4)=0.3.The die is thrown two times.Let A and B be the events,'same number each time',and 'a total score is 10 or more',respectively.Determine whether or not A and B are independent.

asked Jan 8, 2013 by sreemathi.v

1 answer

Let * be a operation on N given by ab=H.C.F, (a, b), a,b $ \in $ N. Write the value of 224.

asked Jan 8, 2013 by thanvigandhi_1

0 answers

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

Let * be a binary operation defined by ab = 2a+b-3, find 34.

asked Jan 6, 2013 by thanvigandhi_1

0 answers

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} -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

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

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