Recent questions tagged modelpaper

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

Evaluate : $ \int \large\frac{\cos x\: dx}{(2+\sin x)(3+4\sin x) } $

asked Feb 6, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_{\large\frac{\pi}{6}}^{\large\frac{\pi}{3}} \large\frac{dx}{1+\sqrt{tan\:x}} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

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

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Find the area of triangle having the points as A(1,1,1), B(1,2,3) and C(2,3,1) as its vertices.

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Two cards are drawn from a well - shuffled pack of 52 cards without replacement. What is the probability that one is a red queen and the other is a king of black colour.

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Obtain the inverse of the following matrix, using elementary operations $ A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

A given quantity of metal is to be cast into a solid half cicular cylinder (i.e., with rectangular base and semicircular ends). Show that in order that the total surface area may be minimum, the ratio of the length of the cylinder to the diameter of its circular ends is $ \pi : ( \pi + 2). $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Find all the local maximum values and local minimum values of the function $ f(x)=\sin 2x-x, -\large\frac{\pi}{2} < x < \large\frac{\pi}{2} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

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