Recent questions tagged q9

Compute $ P (A/B)$if, $P(B)=0.5, P(A \cap B)=0.32.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

A swimming pool is to be drained for cleaning .If L represents the number of litres of water in the pool seconds after the pool has been plugged off to drain and $L=200(10-t)^2$.How fast is the water running out at the end of 5 seconds?What is the average rate at which the water flows out during the first 5 seconds?

asked Jan 11, 2013 by sreemathi.v

1 answer

If $ | \overrightarrow a | = \sqrt 3, | \overrightarrow b | = 2 \: and \: \overrightarrow a . \overrightarrow b = 3. $ Find angle between $ \overrightarrow a \: and \: \overrightarrow b $.

asked Jan 10, 2013 by thanvigandhi_1

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Find a unit vector in the direction of $ \overrightarrow a = 3\hat i - 2\hat j + 6\hat k.$

asked Jan 10, 2013 by thanvigandhi_1

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Write the unit vector in the direction of $ \overrightarrow a = 2\hat i - 6\hat j + 3\hat k $.

asked Jan 9, 2013 by thanvigandhi_1

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Let $E_1$ and $E_2$ be the two independent events.Such that $P(E_1)=p_1$ and $P(E_2)=p_2$.

asked Jan 8, 2013 by sreemathi.v

1 answer

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

asked Jan 8, 2013 by thanvigandhi_1

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Find the angle between the vectors $ \overrightarrow a = \hat i - \hat j + 4\hat k \: and \: \overrightarrow b = \hat i + \hat j - \hat k $

asked Jan 6, 2013 by thanvigandhi_1

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If P(A) = 0.8, P(B) = 0.5 and P(B/A) = 0.4. Find$ (i)\: P(A \cap B ) (ii)\: P(A/B) (iii)\: P(A \cup B). $

asked Jan 4, 2013 by thanvigandhi_1

0 answers

If the line drawn from the point $(-2,-1,-3)$ meets a plane at right angle at the point $(1,-3,3)$ find the equation of the plane.

asked Jan 3, 2013 by sreemathi.v

1 answer

If A and B one the events associated with a random experiment and $ P(A) = 0.2, P(B) = 0.3, P (A \cup B ) = 0.4$, find $ (i) P( A \cap B ) and (ii) P( A / B ) $

asked Jan 3, 2013 by thanvigandhi_1

0 answers

Find the sum of the vectors : $ \overrightarrow a = \hat i - 2\hat j + \hat k, \overrightarrow b = -2\hat i + 4\hat j + 5\hat k \: and \: \overrightarrow c = \hat i - 6\hat j - 7\hat k $

asked Jan 2, 2013 by thanvigandhi_1

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Find the scalar and vector components of the vector with initial point ( 2, 1 ) and terminal point ( -5, 7 ).

asked Jan 2, 2013 by thanvigandhi_1

1 answer

Find whether $f(x)$ is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{x^2}{2}, & if\;0\leq x\leq 1\\2x^2-3x+\large\frac{3}{2}\normalsize,& if\;0< x\leq 2\end{array}\right.$ at $x=1$.

asked Dec 31, 2012 by sreemathi.v

1 answer

Find the value of $ \lambda $ for which the vector $ \overrightarrow a = 3\hat i + \hat j - 2\hat k $ and $ \overrightarrow b = \hat i + \lambda\hat j - 3\hat k $ are perpendicular to each other.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

If $ \overrightarrow a = 2\hat i - \hat j + 3\hat k \: and \: \overrightarrow b = (6\hat i + \lambda\hat j + 9\hat k )$ and $ \overrightarrow a | | \overrightarrow b, $ find the value of $ \lambda $.

asked Dec 26, 2012 by thanvigandhi_1

0 answers

Find $ | \overrightarrow a $ x $ \overrightarrow b |$, if $ \overrightarrow a = \hat i - 7\hat j + 7\hat k$ and $ \overrightarrow b = 3\hat i - 2\hat j + 2\hat k $

asked Dec 25, 2012 by thanvigandhi_1

0 answers

The interval in which $y = x^2 e^{–x}$ is increasing is \[ \begin{array} ((A)\: (– ∞, ∞) \quad & (B)\: (–2, 0) \\ (C) \:(2, ∞) \quad & (D)\: (0, 2) \end{array} \]

asked Dec 24, 2012 by thanvigandhi_1

0 answers

If $A=\begin{bmatrix}0 & 1\\1& 1\end{bmatrix}\;and\;B=\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix},\;show\;that\;(A+B)(A-B)\neq A^2-B^2$

asked Dec 22, 2012 by sreemathi.v

1 answer

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

asked Dec 21, 2012 by thanvigandhi_1

0 answers

If $2\tan^{-1}(\cos x)=\tan^{-1}(2cosecx)$,then what is the value of $x$?

asked Dec 20, 2012 by sreemathi.v

1 answer

Find the angle between the vectors : $ \overrightarrow a = \hat i - \hat j + \hat k $ and $ \overrightarrow b = \hat i + \hat j - \hat k $

asked Dec 20, 2012 by thanvigandhi_1

0 answers

If the mappings f and g are given by\[f\;=\;\{(1,2),(3,5),(4,1)\} \;and\;g=\{(2,3),(5,1),(1,3)\},write\;f\;o\;g\]

asked Dec 18, 2012 by sreemathi.v

1 answer

Find the equation of the plane through the intersection of the planes $3x -y + 2z -4 = 0$ and $x + y + z -2 = 0$ and the point $(2, 2, 1).$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Write the following in the simplest form: $ \tan^{-1} \large \frac{x}{\sqrt {a^2 - x^2}},$$ | x | < a $

asked Dec 10, 2012 by thanvigandhi_1

1 answer

Let $f:\;N\;\to N\;be\;defined\;by\;f(n)= \left\{ \begin{array}{1 1} \frac{n+1}{2}, & if\;n\;is\;odd\\ \frac{n}{2}, & if\;is\;even\end{array} \right. \qquad for\;all\;n \in N$ \[\text{state whether the function f is bijective.Justify your answer.} \]

asked Dec 10, 2012 by sreemathi.v

1 answer

Which of the given values of x and y make the following pair of matrices equal:$\begin{bmatrix}3x+7 & 5\\y+1 & 2-3x\end{bmatrix},\begin{bmatrix}0 & y-2\\8 & 4\end{bmatrix} $

asked Dec 7, 2012 by sreemathi.v

1 answer

For given vectors, $ \overrightarrow a=2\hat i − \hat j + 2\hat k$ and $ \overrightarrow b=−\hat i + \hat j − \hat k$, find the unit vector in the direction of the vector $ \overrightarrow a +\overrightarrow b.$

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Find the integral $\int(2x^2+e^x)\;dx$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find $| \overrightarrow x |$, if for a unit vector $\overrightarrow a , (\overrightarrow x − \overrightarrow a) ⋅ (\overrightarrow x + \overrightarrow a) =12$.

asked Dec 6, 2012 by thanvigandhi_1

1 answer

Integrate the function$\frac{(\large log \; x)^2}{\large x}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Integrate the function $(4x+2)\sqrt{x^2+x+1}$

asked Dec 6, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\frac{\cos x}{1+\cos x}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{\sec^2x}{\sqrt{\tan^2x+4}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions\[\frac{3x+5}{x^3-x^2-x+1}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the area of the triangle with vertices $A(1, 1, 2), B(2, 3, 5)$ and $C(1, 5, 5)$.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are $(2\overrightarrow a + \overrightarrow b)$ and $(\overrightarrow a - 3\overrightarrow b)$ externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the function\[x\;\cos^{-1}x\]

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the smaller region bounded by the ellipse $\Large { \frac{ x^2}{ a^2}}+\Large { \frac{ y^2}{ b^2}} =\normalsize 1$ and the line $\Large { \frac{ x}{ a}}+\Large { \frac{y}{ b}} =\normalsize1$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Integrate the function\[\sqrt{1+\frac{x^2}{9}}\]

asked Dec 4, 2012 by sreemathi.v

1 answer

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

asked Dec 4, 2012 by sreemathi.v

1 answer

Find the area of the region bounded by the parabola $y = x^2$ and $y = \left | x \right | $.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the value of the integral$\begin{align}\int\limits_\frac{1}{3}^1\frac{(x-x^3)^\frac{1}{3}}{x^4}dx \end{align}$ is

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_0^2x\sqrt{2-x}dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\begin{align}\int\frac{\cos x}{\sqrt{4-\sin^2x}} \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of hyperbolas having foci on $x$-axis and centre at origin.

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution $\large\frac{dy}{dx}=$$\sin^{-1}x$

asked Nov 30, 2012 by sreemathi.v

1 answer

Show that the differential equation is homogeneous and solve $y\: dx+x\log\bigg(\large\frac{y}{x}\bigg)$$dy-2x\;dy=0$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+y-x+xy\cot x=0\;(x\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

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