Recent questions tagged q9

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(iv)\;\; a \ast b = (a-b)^2$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(iii)\;\; a \ast b = a+ab$ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $(ii)\;\; a \ast b = a^2+b^2 $ Find which of the binary operations are commutative and which are associative.

asked Mar 13, 2013 by sreemathi.v

1 answer

Show that the relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $(ii) R = \{(a,b): a=b\}$ is an equivalence relation. Find the set of all elements related to 1.

asked Mar 8, 2013 by balaji.thirumalai

1 answer

If the binary operation * on the set of integers Z, is defined by $ab=( a+3b^2)$ then find the value of $24$

asked Feb 17, 2013 by thanvigandhi_1

1 answer

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 Feb 15, 2013 by thanvigandhi_1

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 Feb 11, 2013 by thanvigandhi_1

1 answer

If $ | \overrightarrow a |=13 | \overrightarrow b |=5\: and \: \overrightarrow a.\overrightarrow b=60$ then find $ |\overrightarrow a$ x $ \overrightarrow b|$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

Find $ \overrightarrow a.\overrightarrow b\: if \: \overrightarrow a = 3\hat i - \hat j + 2\hat k\: and \: \overrightarrow b = 2\hat i + 3\hat j + 3\hat k$

asked Feb 9, 2013 by thanvigandhi_1

1 answer

If a line makes angles $ 90^{\circ}, 135^{\circ}, 45^{\circ}$ with the x, y and z axes respectively, find its direction cosines.

asked Feb 8, 2013 by thanvigandhi_1

1 answer

Write the perpendicular distance of the plane $ \overrightarrow r.(2\hat i - \hat j + 2\hat k)=12$ from the origin.

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Find the value of p for which $ p(\hat i + \hat j + \hat k) $ is a unit vector.

asked Feb 7, 2013 by thanvigandhi_1

0 answers

Write $ fog,$ if $ f : R \rightarrow R $ and $ g: R \rightarrow R$ are given by $ f(x) = | x| \: and \: g(x) = | 5x-2 | $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

If $ \overrightarrow a.\overrightarrow a=0\: and \: \overrightarrow a.\overrightarrow b = 0$, then what can be concluded about the vector $ \overrightarrow b$?

asked Feb 6, 2013 by thanvigandhi_1

1 answer

Suppose X has a binomial distribution B(6,1/2) show that X = 3 is the most likely outcome.

asked Feb 5, 2013 by meena.p

0 answers

Determine graphically the minimum value of the objective function.\[z=-50x+20y\] subject to constraints \[2x-y\geq-5\]\[3x+y\geq3\]\[2x-3y\leq12\]\[x\geq0,y\geq0\]

asked Feb 5, 2013 by meena.p

0 answers

Write the projection of the vector $ \hat i - \hat j $ on the vector $ \hat i + \hat j $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Find the image of the point (1,2,3) in the plane x+2y+4z = 38.

asked Feb 5, 2013 by meena.p

0 answers

Show that in a triangle ABC the perpendicular of the point $ C $ from the line joining $ the\:points\:A\:and\:B\:is\;\Large\frac{|\bar{a} \times \bar{b}+\bar{b} \times \bar{c}+\bar{c} \times \bar{a}|}{|\bar{b}-\bar{a}|}$(Hint : use area of triangle =$\frac{1}{2}$bh)

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[ydx-(x+2y)^2dy=0\]

asked Feb 4, 2013 by meena.p

1 answer

Write the value of $ \tan^{-1} \bigg[\tan\large \frac{3\pi}{4} \bigg] $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Sketch the region bounded by the curves $ y=x^2\;and\;y=\large\frac{2}{1+x^2}$ and find its area.

asked Feb 4, 2013 by meena.p

0 answers

Write the direction cosines of the vector $ -2\hat i + \hat j - 5\hat k $.

asked Feb 4, 2013 by thanvigandhi_1

1 answer

If $( \overrightarrow a \: and \: \overrightarrow b)$ are two vectors such that $( | \overrightarrow a. \overrightarrow b| = | \overrightarrow a x \overrightarrow b |)$, then what is the angle between $( \overrightarrow a \: and \: \overrightarrow b)?$

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find the angle between two vectors $ \overrightarrow a \: and \: \overrightarrow b$ if $ |\overrightarrow a |=3, |\overrightarrow b|=4\: and \: |\overrightarrow a * \overrightarrow b |=6 $

asked Feb 3, 2013 by thanvigandhi_1

0 answers

If vectors $ 2\hat i-5\hat j + b\hat k$ and $ 2\hat i + a\hat j + 4\hat k$ are parallel, find the values of a and b.

asked Feb 3, 2013 by thanvigandhi_1

0 answers

A coin is tossed twice, where E : Tail appear on one coin and F : one coin shows head. Find P(E/F).

asked Feb 2, 2013 by thanvigandhi_1

0 answers

If vectors $ 2\hat i - 5\hat j + b\hat k \: and \: 2\hat i + a\hat j+4\hat k $ are parallel, find the values of a and b.

asked Jan 31, 2013 by thanvigandhi_1

0 answers

$\Large\int \frac {x \sin^{-1}x}{\sqrt{1-x^2}} \normalsize dx=$\[(a)\;\sqrt{1-x^2}\sin^{-1}x\qquad (b)\;x\sin^{-1}x\qquad(c)\;x-\sqrt{1-x^2}\sin^{-1}x\qquad(d)\;(\sin^{-1}x)^2\]

asked Jan 30, 2013 by meena.p

0 answers

Find the real value $ '\lambda' $ such that $ |\lambda \overrightarrow a | = 5, \overrightarrow a $ being a non-zero vector.

asked Jan 30, 2013 by thanvigandhi_1

0 answers

Find $ |\overrightarrow X |$, if for a unit vector $ \overrightarrow a.(\overrightarrow x-\overrightarrow a).(\overrightarrow x+\overrightarrow a)=15.$

asked Jan 29, 2013 by thanvigandhi_1

0 answers

If $f(x)= \left\{ \begin{array}{1 1} 3x^2+12x-1 & \quad :\;-1\leq x \leq 2 \\37-x & \quad :\;2<x\leq 3 \end{array} \right. $ then\[\begin{array}{1 1}(a)\;f(x)\; is\; increasing\; on\; [-1,2]\\(b)\;f(x)\; is\; continuous\; on\; [-1,3]\\(c)\;f'(2) doesn't \;exist\\(d)\;f(x)\; has\; the\; maximum\; value\; at x = 2\end{array}\]

asked Jan 28, 2013 by meena.p

0 answers

Show that the vectors $ 2\hat i - 3\hat j + 4\hat k\: and \: -4\hat i + 6\hat j - 8\hat k$ are collinear.

asked Jan 28, 2013 by thanvigandhi_1

0 answers

Find the angle between the lines $\large \frac{x+2}{1}=\frac{y}{2}=\frac{z-1}{0}$ and $\large\frac{x-1}{3}=\frac{y-4}{2}=\frac{z+5}{1} $

asked Jan 27, 2013 by thanvigandhi_1

0 answers

For two vectors $ \overrightarrow a \: and \: \overrightarrow b,$ show that $ \overrightarrow a.\overrightarrow b \leq |\overrightarrow a| \: |\overrightarrow b|.$

asked Jan 25, 2013 by thanvigandhi_1

0 answers

Find $\Large \frac{dy}{dx}$ when $ y=a^x.x^a$

asked Jan 25, 2013 by meena.p

1 answer

If $ \overrightarrow a = \hat i + 2\hat j - 3\hat k$, and $ \overrightarrow b = 2\hat i + 4\hat j - 5\hat k$. Find a unit vector parallel to $ \overrightarrow a + \overrightarrow b$.

asked Jan 25, 2013 by thanvigandhi_1

0 answers

If |A| = 5, where A is 3 x 3 matrix, find | adj A |.

asked Jan 24, 2013 by thanvigandhi_1

0 answers

Prove the determinant $\begin{vmatrix} x & -\sin\alpha & \cos\alpha \\ \sin\alpha & -x & 1 \\ \cos\alpha & 1 & x \end{vmatrix}$ is independent as $\alpha$

asked Jan 24, 2013 by meena.p

0 answers

If $x>0$ and $\sin^{-1}\bigg(\large{\frac{5}{x}}\bigg)+\sin^{-1}\bigg(\frac{12}{x}\bigg)=\large\frac{\pi}{2},$ than find the value of $x$.

asked Jan 23, 2013 by meena.p

1 answer

If angle between the two vectors $ \overrightarrow a \: and \: \overrightarrow b$ of same magnitude is $ 60^{\circ} $ and $ \overrightarrow a. \overrightarrow b = 32,$ then find $ |\overrightarrow a | \: and \: | \overrightarrow b |. $

asked Jan 23, 2013 by thanvigandhi_1

0 answers

If $f(x)=\frac{1+x}{1-x},$show that $f[f(\tan\theta)]= - cot\theta$

asked Jan 23, 2013 by meena.p

0 answers

For any two vectors $ \overrightarrow a \: and \: \overrightarrow b$ , prove that $ | \overrightarrow a + \overrightarrow b | = |\overrightarrow a - \overrightarrow b|, \: if \: \overrightarrow a \bot \overrightarrow b$.

asked Jan 22, 2013 by thanvigandhi_1

0 answers

Solve the differential equation $\Large \frac{dy}{dx}\normalsize=1+x+y^2+xy^2,$when y=0,x=0.

asked Jan 17, 2013 by sreemathi.v

1 answer

If |$ \overrightarrow a $ | =1 , | $ \overrightarrow b $ | = 2 and $ \overrightarrow a . \overrightarrow b$ = 1, find the angle between $ \overrightarrow a \: and \overrightarrow b.$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Find the angle between the vectors $2\hat i\;-\hat j\;-\hat k$ and $3\hat i\;+4\hat j\;+\hat k$.

asked Jan 17, 2013 by sreemathi.v

1 answer

If $ | \overrightarrow a$ x $ \overrightarrow b | = 4, | \overrightarrow a. \overrightarrow b |=2$ then find $| \overrightarrow a |^2 | \overrightarrow b |^2$.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Calculate the area under the curve $y=2\sqrt x$ included between the lines $x=0$ and $x=1$.

asked Jan 16, 2013 by sreemathi.v

1 answer

Show that the points A (1, 2, 7), B (2, 6, 3) and C(3, 10, -1) are collinear.

asked Jan 15, 2013 by thanvigandhi_1

0 answers

Evaluate the following $\int\sqrt{1+\sin x}\;dx$

asked Jan 14, 2013 by sreemathi.v

1 answer

Ask Questions, Get Answers