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Recent questions tagged sec3

If area of triangle is $35\; sq\; units$ with vertices $(2, -6), (5, 4)$ and $(k, 4)$. Then $k$ is

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find equation of line joining (1, 2) and (3, 6) using determinants

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find the value of $k$ if area of triangle is $4\; sq. units$ and vertices are: $(k, 0), (4, 0), (0, 2)$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Show that the points A (a, b + c), B (b, c + a), C (c, a + b) are collinear.

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find area of the triangle with vertices at the point given in (1, 0), (6, 0), (4, 3)

asked Nov 28, 2012 by balaji.thirumalai

1 answer

If A and B are two events such that \(A ⊂ B\) and \(P(B) ≠ 0\), then which of the following is correct?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Probability that A speaks truth is $\large \frac{4}{5} $ . A coin is tossed. A reports that a head appears. The probability that actually there was head is?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver? (Note, in 2014, this was modified to ask for the probability that he is a car driver also).

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive ?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

In answering a question on a multiple choice test, a student either knows the answer or guesses. Let $ \frac{3}{4} $ be the probability that he knows the answer and $\frac{1}{4} $ be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability $ \frac{1}{4} $ . What is the probability that the student knows the answer given that he answered it correctly?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostlier?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Choose the correct answer in the line $y = x + 1$ is a tangent to the curve $y^2 = 4x$ at the point

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the slope of the normal to the curve $ y = 2x^2 + 3 \sin\: x$ at $x = 0$ is

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the transpose of each of the following matrices : $$ \text{ (i) } \begin{bmatrix} 5 \\ \tfrac{1}{2} \\ -1 \end{bmatrix} \qquad \qquad (ii) \begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix} \qquad \qquad (iii)\begin{bmatrix} -1 & 5 & 6 \\ \sqrt{3} & 5 & 6 \\ 2 & 3 & -1 \end{bmatrix} $$

asked Nov 25, 2012 by pady_1

1 answer

if $ A = \begin{bmatrix} -1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1 \end{bmatrix} \text{, then verify that } $ $$ \text{ (i) } (A+B)' = A' + B' $$

asked Nov 25, 2012 by pady_1

1 answer

If $ A' = \begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -1 & 2 &1 \\ 1 & 2 & 3 \end{bmatrix} \text{ , then verify that } $$ \text{ (i) } (A + B )' = A' + B' \qquad \qquad $

asked Nov 25, 2012 by pady_1

1 answer

If $A' = \begin{bmatrix} -2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 0 \\ 1 & 2 \end{bmatrix}$, then find $(A + 2B)'$

asked Nov 25, 2012 by pady_1

1 answer

For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (i) } A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix} \text{ , } B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix} \qquad $$

asked Nov 25, 2012 by pady_1

1 answer

$ (i) A = \begin{bmatrix} cos\alpha & sin\alpha \\ -sin\alpha & cos\alpha \end{bmatrix}$ then verify that $A'A = I$

asked Nov 25, 2012 by pady_1

1 answer

$ (i)$ Show that the matrix $A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix}$ is a symmetric matrix.

asked Nov 25, 2012 by pady_1

1 answer

For the matrix $ A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix} $ , verify that $ (i) (A+A') $ is a symmetric matrix.

asked Nov 25, 2012 by pady_1

1 answer

Find $ \frac{1}{2}(A + A')$ and $\frac{1}{2}(A - A')$ , when $ A = \begin{bmatrix} 0 & a & b \\ -a & 0 & c \\ -b & -c & 0 \end{bmatrix} $

asked Nov 25, 2012 by pady_1

1 answer

Express the following matrices as the sum of a symmetric and a skew symmetric matrix: $ \quad \begin{bmatrix} 3 & 5 \\ 1 & -1 \end{bmatrix}$

asked Nov 25, 2012 by pady_1

1 answer

Find the equation of the tangent to the curve $y = \sqrt {3x - 2}$ which is parallel to the line $4x - 2y + 5 = 0 $.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equations of the tangent and normal to the hyperbola $\large {\frac{x^2}{a^2}} -\large { \frac{y^2}{b^2}} =\normalsize 1$ at the $ (x_0, \: y_0)$.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Prove that the curves \(x = y^2\) and \(xy = k\) cut at right angles* if \(8k^2 = 1.\)

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equations of the tangent and normal to the parabola $y^2 = 4ax$ at the point $(at^2, 2at)$.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equation of the normals to the curve $y = x^3 + 2x + 6$ which are parallel to the line $x + 14y + 4 = 0$.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equation of the normal at the point \((am^2,am^3)\) for the curve \(ay^2 = x^3.\)

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the points on the curve \(x^2 + y^2 - 2x - 3 = 0\) at which the tangents are parallel to the \(x\) - axis.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

For the curve $y = 4x^3 – 2x^5$, find all the points at which the tangent passes through the origin.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the points on the curve $y = x^3$ at which the slope of the tangent is equal to the $y$ - coordinate of the point.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Show that the tangents to the curve \(y = 7x^3 + 11\) at the points where \(x = 2\) and \(x = -2\) are parallel.

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equation of the tangent line to the curve $y = x^2 - 2x +7$ which is $(a)$ parallel to the line $2x - y + 9 = 0$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find the equations of the tangent and normal to the given curves at the indicated points: $ y = x^4 - 6x^3 + 13x^2 - 10x + 5\; at \;(0, 5)$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

Find points on the curve $ \large\frac{x^2}{9} + \frac{y^2}{16} = 1$ at which the tangents are $(i)\; parallel\; to\; x - axis$

asked Nov 24, 2012 by thanvigandhi_1

1 answer

If $A, B$ are symmetric matrices of the same order, then $AB - BA$ is

asked Nov 23, 2012 by pady_1

1 answer

if $A = \begin{bmatrix} cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{bmatrix} $ then $ A + A' = I, $ if the value of $\alpha$ is

asked Nov 23, 2012 by pady_1

1 answer

Find the equation of all lines having slope $0$ that are tangents to the curve $ y=\large \frac{1}{x^2-2x+3}$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the equation of all lines having slope \(2\) that are tangents to the curve $ y= \large\frac{1}{x-3}, $$\: x \neq 3$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the equation of all lines having slope $–1$ that are tangents to the curve $ y= \large\frac{1}{x-1}, $$ \: x \neq 1$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the point on the curve $y = x^3 - 11x + 5$ at which the tangent is $y = x -11$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find a point on the curve $y = (x – 2)^2 $ at which the tangent is parallel to the chord joining the points $(2, 0)$ and $(4, 4)$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

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