Recent questions tagged easy

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

Are the following set of ordered pairs function?If so,examine whether the mapping is injective or subjective $\;\{(x,y)\;:\;x \;is \;a \;person,y\; is\; the\; mother\; of\; x\}$

asked Dec 18, 2012 by sreemathi.v

1 answer

Is $g=\{(1,1),(2,3),(3,5),(4,7)\}$ a function?If g is described by $g(x)=\alpha x+\beta$,then what value should be assigned to $\alpha\;and\;\beta.$

asked Dec 18, 2012 by sreemathi.v

1 answer

Let A={a,b,c,d} and the function f={(a,b),(b,d),(c,a),(d,c)},Write $f^{-1}$.

asked Dec 18, 2012 by sreemathi.v

1 answer

If $ P(A) = \large \frac{6}{11} , P(B) =\large \frac{5}{11}\:$ and $ P(A \cup B) = \large \frac{7}{11}$ , find (i) $P(A \cap B) , (ii) P(A|B) , (iii) P(B|A)$

asked Dec 18, 2012 by thanvigandhi_1

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 Dec 18, 2012 by thanvigandhi_1

1 answer

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 Dec 18, 2012 by thanvigandhi_1

1 answer

There are three coins. One is a two headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows heads, what is the probability that it was the two headed coin ?

asked Dec 18, 2012 by thanvigandhi_1

1 answer

In each of the following cases,determine the direction cosines of the normal to the plane and the distance from the origin. $(a)\; z = 2 $

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the Cartesian equation of the plane $\;(a)\; \overrightarrow r. (\hat i + \hat j - \hat k) = 2$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane $(a)\; 2x + 3y + 4z -12 = 0$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the vector and cartesian equations of the planes that passes through the point $(1, 0, -2)$ and the normal to the plane is $ \hat i+\hat j - \hat k $

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the equations of the planes that passes through three points. $(1, 1, -1), (6, 4, -5), (-4, -2, 3) $

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the intercepts cut off by the plane $2x + y -z = 5.$

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the equation of the plane with intercept 3 on the y - axis and parallel to ZOX plane.

asked Dec 15, 2012 by thanvigandhi_1

1 answer

Find the angle between the planes whose vector equations are $ \overrightarrow r. ( 2\hat i + 2\hat j - 3\hat k ) = 5 \: and\: \overrightarrow r. ( 3\hat i - 3\hat j + 5\hat k ) = 3. $

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Determine whether the given planes are parallel or perpendicular, and in case they are neither, then find the angles between them. $(a)\; 7x + 5y + 6z + 30 = 0 \: and \: 3x -y -10z + 4 = 0 $

asked Dec 14, 2012 by thanvigandhi_1

1 answer

In the following cases,find the distance of each of the given points from the corresponding given plane (a)Point(0,0,0),Plane $3x-4y+12z-3=0$

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the angle between the following pair of lines: $ \frac{\large x-2}{\large 2} = \frac{\large y-1}{\large 5} = \frac{\large z + 3}{\large -3} \: and\: \frac{\large x+2}{\large -1} = \frac{\large y-4}{\large 8} = \frac{\large z - 5}{\large 4} $

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Find the shortest distance between the lines whose vector equations are $ \overrightarrow r = ( 1 - t ) \hat i + ( t - 2 )\hat j + ( 3 - 2t )\hat k$ and $ \overrightarrow r = ( s + 1 )\hat i + ( 2s - 1 )\hat j - (2s + 1)\hat k $

asked Dec 14, 2012 by thanvigandhi_1

1 answer

Show that the lines $ \frac{ \large x - 5 }{ \large 7} = \frac{ \large y + 2}{ \large -5} = \frac{ \large z}{ \large 1}$ and $ \frac{ \large x }{ \large 1} = \frac{ \large y}{ \large 2} = \frac{ \large z}{ \large 3}$ are perpendicular to each other.

asked Dec 14, 2012 by thanvigandhi_1

1 answer