Recent questions tagged sec-b

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

asked Feb 8, 2013 by thanvigandhi_1

1 answer

If $ \overrightarrow a = \hat i + \hat j + \hat k \: and \: \overrightarrow b = \hat j - \hat k$, then find a vector $ \overrightarrow c$ such that $ \overrightarrow a $ x $ \overrightarrow c = \overrightarrow b\: and \: \overrightarrow a.\overrightarrow c = 3 $

asked Feb 8, 2013 by thanvigandhi_1

1 answer

In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is $ \frac{5}{6} $, What is the probability that he will knock down fewer than 2 hurdles.

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Find the vector equation of the line passing through (1,2,3) and perpendicular to the plane $ \overrightarrow r.(\hat i + 2\hat j - 5\hat k)+9=0$

asked Feb 8, 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

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