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Recent questions tagged sec-b

Show that equation of the tangent to the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$ at \( (x_0,y_0) \) is $\large\frac{xx_0}{a^2}+\frac{yy_0}{b^2}$$=1 $

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int \large\frac{5x+3}{\sqrt{x^2+4x+16}}$$dx.$

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Evaluate : $\int \large\frac{x^2tan^{-1}x}{1+x^2}$$dx $

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Prove that an angle in a semi-circle is a right angle (using vector only).

asked Jan 31, 2013 by thanvigandhi_1

1 answer

Find p, when the scalar projection of \( \overrightarrow a = p\hat i + \hat j + 4\hat k \: on \: \overrightarrow b = 2\hat i + 6\hat j + 3\hat k\) is 4 units.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Show that the plane through (1, 1, 1), (1, -1, 1) and (-7, 3, 5) is perpendicular to XZ-plane.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

A card from the pack of 52 cards is lost from the remaining cards of the pack, two cards are drawn and are found to be both diamonds. (i) Find the probability of lost card being a diamond.(ii)While playing in the ground you found a purse containing rupees and some documents,what will you do?

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Find the equation of a curve passing through the point (0,2) given that the sum of the coordinate of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Find the particular solution of the following differential equation satisfying the given condition : $ \bigg[ x\: sin^2 \bigg(\large\frac{y}{x} \bigg)$$ - y \bigg] dx+x\: dy=0; y(1)=\large\frac{\pi}{4} $

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Find the differential equation of all the circles in first quadrant which touch the coordinate axes.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

Show that the function \( f : Z \rightarrow Z \) defined by \( f(x)=x^2\) is neither one-one nor onto.

asked Jan 30, 2013 by thanvigandhi_1

1 answer

Let L be the set of all lines in a plane and R be thr relation in L defined as \( \{(L_1, L_2):L_1\) is perpendicular to \( L_2 \}. \) Show that R is symmetric but neither reflexive nor transitive.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Prove that $ 2\tan^{-1}\large\frac{1}{2}$$+ \tan^{-1}\large\frac{1}{7}$$= \tan^{-1}\large\frac{31}{17} $

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Using properties of determinants, prove that $ \begin{bmatrix} 2ab & a^2 & b^2 \\ a^2 & b^2 & 2ab \\ b^2 & 2ab & a^2 \end{bmatrix} = -(a^3+b^3)^2$

asked Jan 30, 2013 by thanvigandhi_1

1 answer

Using elementary transformation, find the inverse of the matrix $\begin{bmatrix} 3 & 10 \\ 2 & 7 \end{bmatrix} $

asked Jan 30, 2013 by thanvigandhi_1

1 answer

Show that the function $ f(x) = \left\{ \begin{array}{l l}\large\frac{x}{|x|+2x^2}, & \quad { x \neq 0} \\ \lambda, & \quad { x = 0} \end{array} \right. $ remains discontinuous at x = 0 regardless of the choice of \( \lambda \).

asked Jan 30, 2013 by thanvigandhi_1

0 answers

If $ y = \large\frac{2}{\sqrt{a^2-b^2}}$$ \tan^{-1} \bigg( \sqrt{\frac{a-b}{a+b}} \tan\large\frac{x}{2} \bigg). $ prove that \( \large\frac{dy}{dx} =\large \frac{1}{(a+bcos \: x)}. \)

asked Jan 30, 2013 by thanvigandhi_1

0 answers

If \( x^py^q=(x+y)^{p+q}\), prove that \( \large\frac{dy}{dx}=\frac{y}{x} \).

asked Jan 30, 2013 by thanvigandhi_1

0 answers

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

asked Jan 30, 2013 by thanvigandhi_1

0 answers

The surface area of a spherical bubble of water increasing at the rate of \( 2 \: cm^2/sec.\) Find the rate at which the volume of the water bubble is increasing at that instant when its radius is 6 cm.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_1^4 \large\frac{\sqrt x \: dx}{\sqrt{5-x}+\sqrt x}$

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\Large\frac{\pi}{2}} \log \sin\: x\: dx $

asked Jan 30, 2013 by thanvigandhi_1

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Find the equation of the line which is perpendicular from the point (3,-1,1) to the line \( \large\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}\) Also find the foot of perpendicular and the length of the perpendicular.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Using vector, prove that in any triangle \( ABC, a=b\cos C + c \cos B.\)

asked Jan 30, 2013 by thanvigandhi_1

0 answers

The items produced by a company contain 100% defective items. Show that probability of getting 2 defective items in a sample space is \( \large\frac{28 \times 9^6}{10^8} \).

asked Jan 30, 2013 by thanvigandhi_1

0 answers

A problem in mathematics is given to three students A, B and C whose probabilities of solving are \( \frac{1}{3},\frac{2}{7}\) and \( \frac{3}{8}\) respectively. If all the three try to solve the problem simultaneously, find the probability that exactly one of them, solve the problem.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Show that the function \( f ; R \rightarrow R\) given by \( f(x)=7x-11\) is a bijection.

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Show that $ \sin^{-1}\large\frac{12}{13}$$+\cos^{-1}\large\frac{4}{5}$$+\tan^{-1}\large\frac{63}{16} $$= \pi $

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Solve for x : $ \sin \bigg(\sin^{-1} \large\frac{1}{5}$$+\cos^{-1}x \bigg) = 1 $.

asked Jan 29, 2013 by thanvigandhi_1

0 answers

The total monthly earnings of a worker in a factory is given by \( I=p+qx+ry\), where X denotes the number of points of honesty and Y denotes the number of points of punctuality. Data for three months are as follows : (a) represent the above data by linear equations and write its matrix form. (b) Is it possible to solve the system of equations so obtained using matrices?

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Show that the function 'f' given by \( f(x)=|x|+|x+1|, x \in R\) is continuous both at \( x=0 \: and \: x=1.\)

asked Jan 29, 2013 by thanvigandhi_1

0 answers

If $ y=x\log \bigg( \large\frac{x}{a+bx} \bigg)$, find $\large\frac{d^2y}{dx^2} $.

asked Jan 29, 2013 by thanvigandhi_1

0 answers

If \( y = e^{\Large m\tan^{-1}x}\), prove that $ (1+x^2)\large\frac{d^2y}{dx^2}$$+(2x-m)\large\frac{dy}{dx}=0.$

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Find the points on the curve \( y = 5x^2-2x^3\) at which the tangent is parallel to the line \( y-4x=5.\)

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Find the intervals in which the following function is (a) increasing (b) decreasing $ f(x)=2x^3-9x^2+12x+30 $

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Obtain the differential equation by eliminating 'a' and 'b' from the equation \( y=e^x(a\cos \: x+b\sin \: x). \)

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Solve the differential equation : $ (x^3+y^3)dy-x^2ydx=0.$

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int\large\frac{\log x}{(1+\log x)^2}$$dx.$

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Evaluate : $ \int \large\frac{5x-2}{1+2x+3x^2}$$dx.$

asked Jan 29, 2013 by thanvigandhi_1

0 answers

If \( \overrightarrow a,\overrightarrow b \: and \overrightarrow c \)are three mutually perpendicular vectors of equal magnitude, prove that the angle which \( (\overrightarrow a+\overrightarrow b+\overrightarrow c)\) makes with any of the vectors \( \overrightarrow a, \overrightarrow b \: or \overrightarrow c\) is \( \cos^{-1}\large\frac{1}{\sqrt3}.\)

asked Jan 29, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane passing thriugh a point (3, -3, 1) and normal to the line joining the points (3, 4,-1) and (2, -1, 5).

asked Jan 29, 2013 by thanvigandhi_1

0 answers

To test the quality of electric bulbs produced in a factory, two bulbs are randomly selected from a large sample without replacement. If either bulb is defective, the entire lot is rejected. Suppose a sample of 200 bulbs contains 5 defective bulbs. Find the probability that the sample will be rejected.

asked Jan 29, 2013 by thanvigandhi_1

1 answer

Express the vector $\overset \rightharpoonup {a} = 5\hat{i} - 2\hat{j} + 5\hat{k}$ as sum of two vectors such that one is parallel to the vector $\overset \rightharpoonup {b} = 3\hat{i} + \hat{k}$ and the other is perpendicular to $\overset \rightharpoonup {b}$

asked Jan 28, 2013 by fingeazy

0 answers

If the vectors $a\hat{i} + a\hat{j} + c\hat{k}$. $\hat{i} + \hat{k}$ and $c\hat{i} + c\hat{j} + b\hat{k}$ be coplanar, show that $c^2$ = ab

asked Jan 28, 2013 by fingeazy

0 answers

A car, traveling with a uniform acceleration, has a velocity of 18 km/hour at a certain time and 54 km/hour after covering a distance of 500m. How much further will it travel to attain a velocity of 72 km/hour?

asked Jan 28, 2013 by fingeazy

0 answers

A body falls freely from the top of a tower; It covers $\large\frac{5}{9}$th second. Find the height of the tower and the total by the body to fall down. of the whole distance in the last

asked Jan 28, 2013 by fingeazy

0 answers

A cricket ball is project with a velocity of 29.4 m/sec. Find (a) The greatest range on the horizontal plane; and (b) The angle of projection to give a range of 44.10 m.

asked Jan 28, 2013 by fingeazy

0 answers

Find the co-ordinates of the foot of the perpendicular drawn from the point A(1,8,4,) to the line joining the points B(0,-1,3) and C(2,-3,-1).

asked Jan 28, 2013 by fingeazy

0 answers

$\overset \rightharpoonup {P}$ and $\overset \rightharpoonup {Q}$ are two unlike parallel forces. When the magnitude of $\overset \rightharpoonup {P}$ is doubled, it is found that the line of action of $\overset \rightharpoonup {Q}$ is midway between the lines of action of the new and the original resultants, find the ratio of P and Q.

asked Jan 28, 2013 by fingeazy

0 answers

Let A = set of workers in a publication house. Let a R b, if and only if a and b tell lie; \( a,b \in A \) (i) Is R symmetric relation? (ii) Is this relation an equivalence relation?

asked Jan 28, 2013 by thanvigandhi_1

0 answers

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