Recent questions tagged sec-b

Prove that $\large \frac{9\pi}{8}-\frac{9}{4}$$\sin^{-1}\large\frac{1}{3}=\large\frac{9}{4}$$\sin^{-1}\large\frac{2\sqrt2}{3} $

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Express $ \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix} $ as the sum of a symmetic and skew-symmetric matrix.

asked Jan 28, 2013 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 3 & 2 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 5 \end{bmatrix},$ show that $ A^2-7A+10I=0.$ Hence , find $ A^{-1} $

asked Jan 28, 2013 by thanvigandhi_1

1 answer

For what value of k, is the following continuous at x = 0? $ f(x) = \left\{ \begin{array}{l l}\large\frac{\sqrt{1+x}-\sqrt{1-x}}{sin^{-1}x}, & \quad { x \neq 0}\\ k, & \quad { x = 0} \\ \end{array}. \right.$

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Differentiate $ \sin(x^x)+(\sin x)^x,$ with respect to x.

asked Jan 28, 2013 by thanvigandhi_1

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Find the equations of tangent and normal to curve $ y=x-\sin x\cos x$ at $ x=\large\frac{\pi}{2}.$

asked Jan 28, 2013 by thanvigandhi_1

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

asked Jan 28, 2013 by thanvigandhi_1

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Evaluate : $\int_{-1}^{\Large\frac{3}{2}} |x\sin\: \pi\:$$x|dx$

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Show that $ x\cos \: \bigg(\large\frac{y}{x} \bigg) \large\frac{dy}{dx}=$$y\cos \bigg(\large \frac{y}{x} \bigg) +x$ is homogeneous and solve it.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

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

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Solve the differential equation: $\large \frac{dy}{dx}=\frac{y}{x}$$+\log x$

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Let $ \overrightarrow a = \hat i + \hat j,\overrightarrow b = \hat i - \hat j \: and \: \overrightarrow c = \hat i + 2\hat j + 3\hat k,$ if $ n $ is unit vector such that $ \overrightarrow a.\overrightarrow n=0 \: and \: \overrightarrow b.\overrightarrow n=0,$ then show that $ \overrightarrow c.\overrightarrow n=3.$

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Show that the points with position vectors are given by $ 2\hat i - \hat j + \hat k, \hat i - 3\hat j - 5\hat k$ and $ 3\hat i - 4\hat j - 4\hat k$ from a right-angled triangle.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Find the equation of plane through the points (2,2,1), (9,3,6) and perpendicular to the plane $ 2x+6y+6z=9.$

asked Jan 28, 2013 by thanvigandhi_1

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In a village of 50 people, 20 people have their fast on 2nd october. Two persons are selected at random out of them. Write the probability distribution for selected persond who are on fast. Also, find the mean of the distribution.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Show that the R defined on the set A of all triangles as $R = \{(T_1, T_2): T_1$ is similar to $T_2 \}$ is an equivalence relation. Consider three right-angled triangles $ T_1$ with sides 3, 4, 5, $ T_2$ with sides 5, 12, 13 and $ T_3$ with sides 6, 8, 10. Which triangles among $ T_1, T_2 and T_3$ are related?

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Solve for x : $ \tan^{-1}(x+1)+\tan^{-1}(x-1)=\tan^{-1}\large\frac{8}{31} $

asked Jan 27, 2013 by thanvigandhi_1

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If $ \cos^{-1}\large\frac{x}{a}$$+\cos^{-1}\large\frac{y}{b}= \alpha $, prove that $\large \frac{x^2}{a^2}-\frac{2xy}{ab}$$\cos \alpha+\large\frac{y^2}{b^2}$$=\sin^2\alpha. $

asked Jan 27, 2013 by thanvigandhi_1

1 answer

(i)A sum of rupees ten thousand is put into three investments at the rate of 10%, 12% and 15% p.a. The combined income of first and second investment is Rs. 620 more of the income of third investment. If the combined income is Rs. 2420, then find the investment in each using matrices.(ii)"One can buy many things with very little savings".Explain the importance of savings in student's life.

asked Jan 27, 2013 by thanvigandhi_1

0 answers

If $ f(x) = \left\{ \begin{array}{l l}x^2, & \quad if\; { x \leq 1}\\ ax+b, & \quad if\; { x > 1} \\ \end{array}. \right.$ is differentiable at x = 1. Find the value of a and b.

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Verify Lagrange's mean value theorem for the following function : $ f(x) = \sin \: x - \sin\: 2x \: in \: [0, \pi ] $

asked Jan 27, 2013 by thanvigandhi_1

1 answer

If $ x\sqrt{1+y} +y\sqrt{1+x}=0, \: find \:\large \frac{dy}{dx} $

asked Jan 27, 2013 by thanvigandhi_1

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If $ y\sqrt{1-x^2}+x\sqrt{1-y^2}=1,$ prove that $ \large\frac{dy}{dx}=-\sqrt{\frac{1-y^2}{1-x^2}} $

asked Jan 27, 2013 by thanvigandhi_1

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Prove that : $\int_{-a}^a \sqrt{\large\frac{a-x}{a+x}}dx=a\pi$

asked Jan 27, 2013 by thanvigandhi_1

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Show that the curve $ 4x=y^2\: and \: 4xy=k$ cut at right angles, if $ k^2=512$

asked Jan 27, 2013 by thanvigandhi_1

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Solve the following differential equation : $ \large\frac{dy}{dx}$$+2y=xe^{4x} $

asked Jan 27, 2013 by thanvigandhi_1

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Find the differential equation of all circles which pass through origin and whose centre lies on y - axis.

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Solve the differential equation $ (x+y)dy+(x-y)dx=0$

asked Jan 27, 2013 by thanvigandhi_1

1 answer

Find a vector of magnitude 15 which is perpendicular to both the vectors $ 4\hat i - \hat j + 8\hat k $ and $ - \hat j + \hat k$

asked Jan 27, 2013 by thanvigandhi_1

0 answers

Find the equation of the line through A(5,-3,2) and through the intersection $\large \frac{x-2}{1} = \frac{y-3}{5} = \frac{z-4}{4}$ and $ \large\frac{x-4}{3} = \frac{y-2}{4} = \frac{z+3}{-3} $

asked Jan 27, 2013 by thanvigandhi_1

0 answers