Recent questions tagged q10

If the equation of the line AB is $ \large\frac{x-3}{1} = \frac{y+2}{-2} = \frac{z-5}{4} ,$ find the direction ratios of a line parallel to AB.

asked Jan 22, 2013 by thanvigandhi_1

0 answers

Find the general solution of $(x+2y^3)\Large \frac{dy}{dx}\normalsize =y \;dx$

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the direction cosine of the line joining the points (-2, 4, -5) and (1,2,3).

asked Jan 17, 2013 by thanvigandhi_1

0 answers

If $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0,$show that $\overrightarrow{a} \times \overrightarrow{b}=\overrightarrow{b} \times \overrightarrow{c} =\overrightarrow{c} \times \overrightarrow{a}$.Interpret the result geometrically?

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the cartesian equation of the line through (5, 2, -4) and which is parallel to the vector $ 3\hat i + 2\hat j - 8\hat k$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Using integration,find the area of the region bounded by the line $2y=5x+7,x$-axis and the lines $x=2$ and $x=8.$

asked Jan 16, 2013 by sreemathi.v

1 answer

Find the distance of (3, -2, 1) from the plane $ 2x-y+2z+3=0$.

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Evaluate the following $\displaystyle\int \large \frac{( x)}{\sqrt x+1}$$dx \quad(Hint:Put\;\sqrt x=z)$

asked Jan 14, 2013 by sreemathi.v

1 answer

Evaluate : $ P(A \cup B)$ if $2P(A) = P(B)=\large\frac{5}{13}\: and \: $$P(A/B) =\large \frac{2}{5} $.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

The volume of a cube increases at a constant rate.Prove that the increase in its surface area varies inversely as the length of the side.

asked Jan 11, 2013 by sreemathi.v

1 answer

Find the equation of the plane which is perpendicular to the plane $ 5x+3y+6z+8=0$ and which contains the line of intersection of the planes $ x+2y+3z-4=0 \: and \: 2x+y-z+3=0.$

asked Jan 10, 2013 by thanvigandhi_1

0 answers

For what value of $ \lambda $ are the vectors $ \overrightarrow a = 2\hat i + \lambda \hat j + \hat k \: and \: \overrightarrow b = \hat i - 2 \hat j + 3\hat k $ perpendicular to each other?

asked Jan 10, 2013 by thanvigandhi_1

0 answers

Scalar product of the vector $ \hat i + \hat j + \hat k $ with the unit vector along the sum of vectors $ 2\hat i + 4\hat j -5\hat k $ and $ \lambda \hat i + 2\hat j + 3\hat k $ is equal to one, find the value of $ \lambda $.

asked Jan 9, 2013 by thanvigandhi_1

0 answers

A discrete random variable X has the probability distribution given as below:

asked Jan 8, 2013 by sreemathi.v

1 answer

Write the value of $\overrightarrow P $ for which $ \overrightarrow a = 3\hat i + 2\hat j + 9\hat k \: and \: \overrightarrow b = \hat i + p\hat j + 3\hat k$ are parallel vectors.

asked Jan 8, 2013 by thanvigandhi_1

0 answers

If $ \overrightarrow a = \hat i + 2\hat j - \hat k\: and \: \overrightarrow b =( 3\hat i + \hat j - 5\hat k)$, find a unit vector in the direction of $ \overrightarrow a - \overrightarrow b.$

asked Jan 6, 2013 by thanvigandhi_1

0 answers

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and $ P(E \cap F)$. = 0.2. Find P(E/F) and P(F/E).

asked Jan 4, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane through the points (2,1,0),(3,-2,-2) and (3,1,7).

asked Jan 3, 2013 by sreemathi.v

1 answer

In a class having 70% boys, 20% of the boys and 10% of the girls are players. A student is selected at random from the class and is found to be a player. Find the probability that the selected student is a girl.

asked Jan 3, 2013 by thanvigandhi_1

0 answers

Find the equation of the plane passing through the point ( 1, -1, 2 ) having ( 2, 3, 2 ) as direction ratios of normal to the plane?

asked Jan 2, 2013 by thanvigandhi_1

0 answers

Write the direction cosines of a line equally inclined to the three coordinate axes.

asked Jan 2, 2013 by thanvigandhi_1

0 answers

Find whether f(x) is continuous or discontinuous at the indicated point $f(x)= x ^2+x-1\;at\;x=1.$

asked Dec 31, 2012 by sreemathi.v

1 answer

Find the value of $ \lambda $ such that the line $\large \frac{x-2}{9} = \large\frac{y-1}{\lambda} = \large\frac{z+3}{-6} $ is perpendicular to the plane $ 3x - y - 2z = 7 $.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Find the distance of the point (a, b, c) from x - axis.

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Find the cartesian equation of line which passes through the point ( -2, 4, -5 ) and parallel to the line given by $ \large\frac{x+3}{3} = \frac{y-4}{5} = \frac{z+8}{6} $

asked Dec 25, 2012 by thanvigandhi_1

0 answers

$ \int\: xsec^2xdx $ is equal to \[ \begin{array} ((A)\: tanx^2+C \quad & (B)\: tanx^2+C \\ (C)\: x\: tanx - log\: sin\: x \quad & (D)\: x\: tanx + log\: cos\: x+C \end{array} \]

asked Dec 24, 2012 by thanvigandhi_1

0 answers

Find the value of $x$ if $\begin{bmatrix}1 & x &1\end{bmatrix}\begin{bmatrix}1 & 3 & 2\\2 & 5 & 1\\15 & 3 & 2\end{bmatrix}\begin{bmatrix}1\\2\\x\end{bmatrix}=0$.

asked Dec 22, 2012 by sreemathi.v

1 answer

If $ \overrightarrow P $ is a unit vector and $ ( \overrightarrow x - \overrightarrow p ). ( \overrightarrow x + \overrightarrow p ) = 80$, then find $ | \overrightarrow x | $.

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Show that $\cos\bigg(2\tan^{-1}{\frac{1}{7}}\bigg)=\sin\bigg(4\tan^{-1}{\frac{1}{3}}\bigg)$

asked Dec 20, 2012 by sreemathi.v

1 answer

For what value of $ \lambda$ are the vectors $ \overrightarrow a = 2\hat i + \lambda\hat j + \hat k $ and $ \overrightarrow b = \hat i - 2\hat j + 3\hat k $ perpendicular to each other?

asked Dec 20, 2012 by thanvigandhi_1

0 answers

Let C be the set of complex numbers.Prove that the mapping $f\; :\;C \rightarrow R\;given\;by\;f(z)=|\;z\;|,\forall\; z \in C,$is neither one-one nor onto.

asked Dec 18, 2012 by sreemathi.v

1 answer

Find the vector equation of the plane passing through the intersection of the planes $ \overrightarrow r .(2\hat i + 2 \hat j - 3\hat k) = 7, \overrightarrow r .(2\hat i + 5\hat j + 3\hat k ) = 9$ and through the point $(2, 1, 3).$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the angle between the pairs of lines: $ \overrightarrow r = 2\hat i - 5 \hat j + \hat k + \lambda (3\hat i + 2\hat j + 6\hat k)\: and \: \overrightarrow r = 7\hat i - 6 \hat k+ \mu (\hat i + 2\hat j + 2\hat k) $

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Show that the differential equation is homogeneous and solve :$ \bigg( 1 + e^{\Large\frac{x}{y}} \bigg) dx + e^{\Large\frac{x}{y}} \bigg( 1 -\large \frac{x}{y} \bigg) $$dy= 0 $

asked Dec 12, 2012 by thanvigandhi_1

1 answer

Write the following function in the simplest form:\[ tan^{-1} \bigg( \frac{3a^2x-x^3}{a^3-3ax^2} \bigg), a > 0 ; \frac{-a}{\sqrt 3} \leq x \leq \frac{a}{\sqrt 3} \]

asked Dec 10, 2012 by thanvigandhi_1

1 answer

The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is:

asked Dec 7, 2012 by sreemathi.v

2 answers

Find a vector in the direction of vector $5\hat i − \hat j + 2\hat k$ which has magnitude $8$ units.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the integral $\Large \int \normalsize\bigg(\sqrt x-\frac{1}{\sqrt x}\bigg)^2\;dx$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integral $\large \int \frac{\sec^2x}{\large cosec^2x}$$dx$

asked Dec 6, 2012 by sreemathi.v

1 answer

If $\overrightarrow a = 2\hat i + 2\hat j + 3\hat k,\: \overrightarrow b = − \hat i + 2\hat j + \hat k$ and $ \overrightarrow c = 3\hat i + \hat j$ are such that $\overrightarrow a + λ\overrightarrow b $ is perpendicular to $ \overrightarrow c $ , then find the value of $λ.$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Integrate the function $\frac{\large 1}{\large x-\sqrt x}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\sin^4x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{1}{\sqrt{x^2+2x+2}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions\[\frac{2x-3}{(x^2-1)(2x+3)}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the area of the parallelogram whose adjacent sides are determined by the vectors $ \overrightarrow a = \hat i - \hat j + 3\hat k$ and $\overrightarrow b = 2\hat i - 7 \hat j + \hat k$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

The two adjacent sides of a parallelogram are $2\hat i - 4\hat j + 5\hat k$ and $ \hat i - 2\hat j - 3\hat k$ . Find the unit vector parallel to its diagonal. Also, find its area.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the function $(\sin^{-1}x)^2$

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the region enclosed by the parabola $x^2 = y$, the line $y = x + 2$ and the $x$ - axis.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in $\Large \int \normalsize \sqrt{1+x^2}dx$ is equal to \[\begin{array}{l}(A)\;\frac{x}{2}\sqrt{1+x^2}+\frac{1}{2}log\LARGE\mid\normalsize\bigg(x+\sqrt{1+x^2}\bigg)\LARGE\mid\normalsize+C \\(B)\;\frac{2}{3}(1+x^2)^\frac{3}{2}+C\qquad \\ (C)\;\frac{2}{3}x(1+x^2)^\frac{3}{2}+ C \\ (D)\;\frac{x^2}{2}\sqrt{1+x^2}+\frac{1}{2}x^2log\LARGE\mid\normalsize x+\sqrt{1+x^2}\LARGE\mid\normalsize+C \end{array}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Evaluate the definite integral\[\int\limits_0^1\frac{dx}{1+x^2}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

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