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Recent questions tagged sec-b

Prove that $\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})\times (\overrightarrow{a}+2\overrightarrow{b}+3\overrightarrow{c})=[\overrightarrow{a}\;\overrightarrow{b}\;\overrightarrow{c}].$

asked Apr 17, 2013 by sreemathi.v

0 answers

$\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors such that $2\overrightarrow{a}-4\overrightarrow{b}$ and $10\overrightarrow{a}+8\overrightarrow{b}$ are perpendicular to each other.Find the angle between the vectors $\overrightarrow{a}$ and $\overrightarrow{b}.$

asked Apr 17, 2013 by sreemathi.v

0 answers

Find the least distance of the plane $12x+4y+3z=327$ from the sphere $x^2+y^2+z^2+4x-2y-6z=155.$

asked Apr 17, 2013 by sreemathi.v

0 answers

A plane passes through the point (4,2,4) and is perpendicular to the planes $2x+5y+4z+1=0$ and $4x+7y+6z+2=0$.Find the equation of the plane.

asked Apr 17, 2013 by sreemathi.v

1 answer

The table below gives details of the electricity generated in million kilowatt hours in each quarter for the years 2002 to 2004.

asked Apr 17, 2013 by sreemathi.v

0 answers

The quotations for four different commodities for the years 2000 and 2005 are given below.Calculate the index number for 2005 with 2000 as the base year by using the weighted average of price relatives method.

asked Apr 17, 2013 by sreemathi.v

0 answers

The vectors $\hat{i}+3\hat{j},5\hat{k}$ and $\lambda\hat{i}-\hat{j}$ are coplanar.Find the value of $\lambda$.

asked Apr 17, 2013 by sreemathi.v

0 answers

The vectors $-2\hat{i}+4\hat{j}+4\hat{k}$ and $-4\hat{i}-2\hat{k}$ represent the diagonals BD and AC of a parallelogram ABCD.Find the area of the parallelogram.

asked Apr 17, 2013 by sreemathi.v

0 answers

Show that the equation to a sphere passing through three points (2,0,0),(0,2,0) and (0,0,2) and having its centre on the plane $2x+3y+4z=27$ is $x^2+y^2+z^2-6x-6y-6z+8=0.$

asked Apr 17, 2013 by sreemathi.v

0 answers

Find the equations to be two planes passing through the points (0,4,-3) and (6,-4,3),if the sum of their intercepts on the three axes is zero.

asked Apr 17, 2013 by sreemathi.v

0 answers

The production of a soft drink company in thousands of litres during each month of a year is as follows :

asked Apr 16, 2013 by sreemathi.v

1 answer

Calculate the index number for 2005 with 2000 as the base year by the weighted aggregate method.

asked Apr 16, 2013 by sreemathi.v

1 answer

Find a unit vector perpendicular to the vectors $4i+3j+k$ and $2i-j+2k$.Determine the sine angle between these two vectors.

asked Apr 16, 2013 by sreemathi.v

0 answers

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three vectors,show that : $(\overrightarrow{a}+\overrightarrow{b}).\{(\overrightarrow{b}+\overrightarrow{c})\times (\overrightarrow{c}+\overrightarrow{a})\}=2[\overrightarrow{a}\; \overrightarrow{b}\;\overrightarrow{c}]$

asked Apr 16, 2013 by sreemathi.v

0 answers

Prove that the plane $x+2y-z=4$ cuts the sphere $x^2+y^2+z^2-x+z-2=0$ in a circle whose radius is unity.

asked Apr 16, 2013 by sreemathi.v

0 answers

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

asked Apr 16, 2013 by sreemathi.v

0 answers

Given $\overrightarrow{a}=i-2j+k,\overrightarrow{b}=2i+j+k$ and $\overrightarrow{c}=i+2j-k$.Find $\overrightarrow{a}\times(\overrightarrow{b}\times \overrightarrow{c})$

asked Apr 15, 2013 by sreemathi.v

0 answers

Find $\overrightarrow{a}.\overrightarrow{b}$ if $ \mid\overrightarrow{a}\mid=2, \mid\overrightarrow{b}\mid=5$ and $\mid \overrightarrow{a}\times \overrightarrow{b}\mid$=8.

asked Apr 15, 2013 by sreemathi.v

0 answers

Coded monthly sales figures of a particular brand of T.V. for 18 months commencing January 1,2005 are as follows :

asked Apr 15, 2013 by sreemathi.v

0 answers

A small industrial concern used three raw materials A,B and C in its manufacturing process.The prices of the materials was as shown below :

asked Apr 15, 2013 by sreemathi.v

0 answers

If $A(-1,4,-3)$ is one end of a diameter $AB$ of the sphere $x^2+y^2+z^2-2y+2z-15=0$ then find the coordinates of the other end point B.

asked Apr 15, 2013 by sreemathi.v

0 answers

Find the coordinates of the point where the line joining the points (1,-2,3) and (2,-1,5) cuts the plane $x-2y+3z=19$.Hence,find the distance of this point from the point (5,4,1).

asked Apr 15, 2013 by sreemathi.v

0 answers

Draw a rough sketch of the curve $y^2+1=x,x\leq 2$.Find the area enclosed by the curve and the line $x=2$.

asked Apr 15, 2013 by sreemathi.v

1 answer

An insurance company insured 4000 doctors,8000 teachers and 12,000 engineers.The probabilities of a doctor,a teacher and an engineer dying before the age of 58 years are 0.01 ,0.03 and 0.05 respectively.If one of the insured persons dies before the age of 58 years,find the probability that he is a doctor.

asked Apr 15, 2013 by sreemathi.v

0 answers

The mean and variance of a binomial distribution are 4 and 2 respectively .Find the probability of at least 6 successes.

asked Apr 15, 2013 by sreemathi.v

0 answers

(i) Prove by vector method that the diameter of a circle will subtend a right angle at a point on its circumference.(ii) If $\overrightarrow {a},\overrightarrow {b}$ and $\overrightarrow {c}$ represent the position vectors of the points with co-ordinates $(2,-10,2),(3,1,2)$ and $(2,1,3)$ respectively,find the value of $\overrightarrow {a}\times (\overrightarrow {b}\times \overrightarrow {c})$.

asked Apr 15, 2013 by sreemathi.v

0 answers

Find the area of a parallelogram whose diagonals are determined by the vectors $\overrightarrow{a}=3i+j-2k$ and $\overrightarrow{b}=i-3j+4k$

asked Apr 15, 2013 by sreemathi.v

0 answers

Find the equation of the sphere which passes through the circle $x^2+y^2-6z-4=0,x+2y+2z=0$ and whose centre lies on the plane $2x-y+z=1.$

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the equation of the plane which contains the line $\large\frac{x-1}{2}=\large\frac{y+1}{-1}=\large\frac{z-3}{4}$ and is perpendicular to the plane $x+2y+z=12.$

asked Apr 12, 2013 by sreemathi.v

0 answers

Five bad eggs are mixed with 10 good ones.If three eggs are drawn one by one with replacement ,find the probability distribution of the number of goods eggs drawn.

asked Apr 12, 2013 by sreemathi.v

1 answer

A factory has three machines A,B and C producing 1,500,2,500 and 3,000 bulbs per day,respectively.Machine A produces 1.5% defective bulbs,machine B produces 2% defective bulbs and machine C produces 2.5% defective bulbs.At the end of the day,a bulb is drawn at random and is found to be defective.What is the probability that this defective bulb has been produced by machine B?

asked Apr 12, 2013 by sreemathi.v

1 answer

Find the equation of the plane passing through the line of intersection of the planes $x+2y+3z-4=0$ and $3z-y=0$ and perpendicular to the plane $3x+4y-2z+6=0$.

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the shortest distance between the lines whose vector equations are :$\overrightarrow{r}=(4\hat{i}-\hat{j}+2\hat{k})+\lambda(\hat{i}+2\hat{j}-3\hat{k})$ and $\overrightarrow{r}=(2\hat{i}+\hat{j}-\hat{k})+\mu(3\hat{i}+2\hat{j}-4\hat{k})$.

asked Apr 12, 2013 by sreemathi.v

0 answers

In any $\Delta ABC$,prove by vector method that $\cos B=\large\frac{c^2+a^2-b^2}{2ca}$.

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the value of $\lambda$ for which the four points with position vectors $2\hat{i}+5\hat{j}+\hat{k},-\hat{j}-4\hat{k},3\hat{i}+\lambda\hat{j}+8\hat{k}$ and $-4\hat{i}+3\hat{j}+4\hat{k}$ are coplanar.

asked Apr 12, 2013 by sreemathi.v

2 answers

Bag contains 2 white,1 black and 3 red balls,Bag B contains 3 white ,2 black and 4 red balls and Bag C contains 4 white ,3 black and 2 red balls.One Bag is chosen at random and 2 balls are drawn at random from that Bag.If the randomly drawn balls happen to be red and black,what is the probability that both balls come from Bag B?

asked Apr 11, 2013 by sreemathi.v

1 answer

A box contains 4 red and 5 black marbles.Find the probability distribution of the red marbles in a random draw of three marbles.Also find the mean and standard deviation of the distribution.

asked Apr 11, 2013 by sreemathi.v

1 answer

Find the equation of the plane passing through the points $A(2,1,-3),B(-3,-2,1)$ and $C(2,4,-1).$

asked Apr 11, 2013 by sreemathi.v

0 answers

Find the vector equation of the line passing through the points $(-1,2,1)$ and parallel to the line $\overrightarrow{r}=2\hat{i}+3\hat{j}-\hat{k}+\lambda\big(\overrightarrow{i}-2\hat{j}+\hat{k}\big)$.Also,find the distance between these lines.

asked Apr 11, 2013 by sreemathi.v

0 answers

If D,E,F are mid-points of the sides of a triangle ABC,Prove by vector method that : Area of ADEF=$\frac{1}{4}$(Area of $\Delta$ABC).

asked Apr 11, 2013 by sreemathi.v

0 answers

Prove that : $\begin{bmatrix}\overrightarrow{a}+\overrightarrow{b}& \overrightarrow{b}+\overrightarrow{c}&\overrightarrow{c} +\overrightarrow{a}\end{bmatrix}=2\begin{bmatrix}\overrightarrow{a}&\overrightarrow{b}&\overrightarrow{c}\end{bmatrix}$

asked Apr 11, 2013 by sreemathi.v

0 answers

The probability that a bulb produced by a factory will fuse in 100 days of use is 0.05.Find the probability that out of 5 such bulbs,after 100 days of use :

asked Apr 10, 2013 by sreemathi.v

0 answers

In a class of 75 students,15 are above average,45 are average and the rest below average achievers.The probability that an above average achieving student fails is 0.005,then an average achieving student fails is 0.05 and the probability of a below average achieving student failing is 0.15.If a student is known to have passed,what is the probability that he is a below average achiever?

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the equation of the plane passing through the line of intersection of the planes $x+2y+3z-5=0$ and $3x-2y-z+1=0$ and cutting off equal intercepts on the x and z axes.

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the shortest distance between the lines : $\large \frac{x-8}{3}=\frac{y+9}{-16}=\frac{z-10}{7}$ and $\large \frac{x-15}{3}=\frac{y-29}{8}=\frac{5-z}{-5}$

asked Apr 10, 2013 by sreemathi.v

0 answers

In any triangle ABC,prove by vector method : $\large \frac{a}{sin\;A}=\frac{b}{sin\;B}=\frac{c}{sin\;C}$

asked Apr 10, 2013 by sreemathi.v

0 answers

For any three vectors $\overline{a},\overline{b},\overline{c}$ prove :$[\;\overline{a}-\overline{b}\;\overline{b}-\overline{c}\;\overline{c}-\overline{a}\;]=0.$

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the vector cartesian equation of the plane passing through the points with position vectors $\overrightarrow{3i}+\overrightarrow{4j}+\overrightarrow{2k}, \overrightarrow{2i}-\overrightarrow{2j}-\overrightarrow{2k},$ and $\overrightarrow{7i}+\overrightarrow{k}.$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the area of the triangle where vertices are $A(11,7),B(5,5)\; and\; C(-1,3)$

asked Apr 8, 2013 by meena.p

1 answer

Show that $A=\begin{bmatrix} 1 & log_x\;y & log_x\;z \\ log_y\;x & 1 & log_y\;z \\ log_z\;x & log_z\;y & 1 \end{bmatrix}=0$

asked Apr 6, 2013 by meena.p

1 answer

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