Recent questions tagged 2012

A manufacturer produces two types of steel trunks. He has two machines A and B. The first type of trunk requires 5 hours on machine A and 3 hours on machine B. The second type requires 3 hours on machine A and 2 hours on machine B.Machines A and B can work at most for 24 hours and 15 hours per day, respecively. He earns a profit of Rs. 30 and RS. 25 per trunk on the first type and second type, respecively. How many trunk of each type must be made each day to make the maximum profit?

asked Feb 8, 2013 by thanvigandhi_1

1 answer

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

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find the area of the region $ {(x,y):x^2+y^2 \leq 1 \leq x + y}.$

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Solve for x : $ \begin{bmatrix} 1 - x & 1 \end{bmatrix} \begin{bmatrix} 2 & -1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ 3 \end{bmatrix} = 0 $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Write the principal value of $ cot^{-1} \{ cot \bigg( -\frac{\pi}{4} \bigg) \} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

If $ tan^{-1}x+tan^{-1}y=\frac{\pi}{4} $, then write the value of $ x+y+xy$.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \begin{vmatrix} x^2-x+1 & x-1 \\ x+1 & x+1 \end{vmatrix} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Differentiate $ cos(sin\: x)$ with respect to x.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the value of x if $ \begin{bmatrix} 2 & 4 \\ 5 & 1 \end{bmatrix} = \begin{bmatrix} 2x & 4 \\ 6 & x \end{bmatrix} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Determine the order and degree of following differential equation $ \bigg(\large \frac{ds}{dt} \bigg)^4 +$$ 3s\bigg(\large \frac{d^2s}{dt^2} \bigg) $$= 0 $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the projection of $ \overrightarrow a = 2\hat i - \hat j + \hat k\: on \: \overrightarrow b = \hat i - 2\hat j + \hat k. $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Write the perpendicular distance of the plane $ \overrightarrow r.(2\hat i - \hat j + 2\hat k)=12$ from the origin.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

If $ | \overrightarrow a | = 2, | \overrightarrow b | = 7 \: and \: \overrightarrow a $ x $ \overrightarrow b=3\hat i + 2\hat j + 6\hat k$, find the angle between $ \overrightarrow a \: and \: \overrightarrow b.$

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find $ \frac{dy}{dx} $, if $ y=tan^{-1} \bigg( \frac{3x-x^3}{1-3x^2} \bigg), \frac{1}{\sqrt 3} < x < \frac{1}{3} $

asked Feb 7, 2013 by thanvigandhi_1

0 answers

Find the values of x which satisfy the equation \[ sin^{-1}x+sin^{-1}(1-x)=cos^{-1}x.\]

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Prove that $ 2sin^{-1}\frac{3}{5}-tan^{-1}\frac{17}{31}=\frac{\pi}{4} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find $\large \frac{dy}{dx}$ if $ x=\large\frac{1+\log\:t}{t^2}$$,y= \large\frac{3+2log\: t}{t} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Using properties of determinants prove that \[ \begin{vmatrix} -bc & b^2+bc & c^2+bc \\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{vmatrix}= (ab+bc+ca)^3 \]

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : \[ \int \frac{(x-4)e^x}{(x-2)^3} dx \]

asked Feb 7, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int\large\frac{dx}{2\sin^2x+5\cos^2x} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find $ \int_2^8 \large\frac{\sqrt{10-x}}{\sqrt x+\sqrt{10-x}}$$dx $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the area of the parallelogram whose diagnols are represented by the vectors $ \overrightarrow d_1 = 3\hat i +\hat j -2\hat k\: and \: \overrightarrow d_2 = \hat i -3\hat j +4\hat k.$

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are kings.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Bag I contains 3 black and 2 white balls. Bag II contains 2 black and 4 white balls. A bag and a ball is selected at random. Determine the probability of selecting a black ball.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : \[ \frac{sin\: 2x}{a^2sin^2x+b^2cos^2x}dx\]

asked Feb 7, 2013 by thanvigandhi_1

0 answers

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 Feb 7, 2013 by thanvigandhi_1

0 answers

Obtain the inverse of the following matrix using elementary operation $A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the area of a minor segment of the circle $ x^2+y^2=a^2$ cut off by the line $ x=\large \frac{a}{2}.$

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Solve the differential equation $ y.e^{\large\frac{x}{y}} dx=(x.e^{\large\frac{x}{y}}+y^2)dy ; y \neq 0$

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the image of the point (1,6,3) in the line $ \large\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

A manufacturing company makes two types of television sets, one is black and white and other is coloured. The company has resources to make at most 300 sets a weak. It takes Rs. 1800 to make a black and white set and Rs. 2700 to make a coloured set. The company can spend not more than Rs. 648000 a weak to make television sets. It makes a profit of Rs. 510 per black and white set and Rs. 675 per coloured set, how many sets of each type should be produced so that the company has maximum profit? Formulate this as LPP given that the objective is to maximise the profit.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

20% of the bulbs produced by a machine are defective. Find the probability distribution of the number of defective bulbs in a sample of 4 bulbs chosen at random.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

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

asked Feb 7, 2013 by thanvigandhi_1

1 answer

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

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Construct a 2 x 2 matrix $ A = [ a_{ij} ]$, whose elements are given by $ a_{ij} $ is $ \large\frac{( \hat i + \hat j )^2}{2} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the value of x from the following : $\begin{bmatrix} 2x-y & 5 \\ 3 & y \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 3 & -2 \end{bmatrix} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 1 & 2 \\ 4 & 2 \end{bmatrix} $ then show that | 2A | = 4| A |

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int \large\frac{1+cot x}{x+\log \sin x}$$ dx $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Evaluate : $ \int_1^2 \bigg( \large\frac{1}{x} - \frac{1}{x^2} \bigg) $$e^x \: dx$

asked Feb 7, 2013 by thanvigandhi_1

1 answer

For two non zero vectors $ \overrightarrow a \: and \: \overrightarrow b$ write when $ |\overrightarrow a+\overrightarrow b | = | \overrightarrow a | + | \overrightarrow b | $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the value of p for which $ p(\hat i + \hat j + \hat k) $ is a unit vector.

asked Feb 7, 2013 by thanvigandhi_1

0 answers

The cartesian equation of a line is $ \large\frac{x+3}{2} = \large\frac{y-5}{4}=\large\frac{z+6}{2} $ Find vector equation of line.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Prove that $ \tan^{-1} \large\frac{63}{16}=\sin^{-1}\bigg( \large\frac{5}{13} \bigg) + \cos^{-1} \bigg( \large\frac{3}{5} \bigg). $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Show that the relation R in the set $ A = \{ x/x \in W, 0 \leq x \leq 12 \} $ given by $ R = \{ (a,b):(a-b)$ is a multiple of 4 } is an equivalence relation. Also find the set of all element related to 2.

asked Feb 7, 2013 by thanvigandhi_1

0 answers

Examine which of the following is a binary operation.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

If a,b and c are real number and $ \begin{vmatrix} b+c & c+a & a+b \\ c+a & a+b & b+c \\ a+b & b+c & c+a \end{vmatrix} $Show that either $a+b+c=0 \: or \: a=b=c$

asked Feb 7, 2013 by thanvigandhi_1

0 answers

Express the following matrix as the sum of a symmetric (B) and skew symmetric matrix (C) $\begin{bmatrix} 3 & -2 & -4 \\ 3 & -2 & -5 \\ -1 & 1 & 2 \end{bmatrix} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Differentiate the following function w.r.t.$ x$ $(x)^{\Large\cos x}+(\sin x)^{\Large\tan \: x} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Show that the function $ f(x) = |x+2 | $ is continuous at every $ x \in R$ but fails to be differentiable at x = -2.

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Find the equation of tangent lines to the curve $ y=4x^3-3x+5$ which are perpendicular to the line $ 9y+x+3=0$

asked Feb 6, 2013 by thanvigandhi_1

1 answer

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