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Recent questions tagged q3

Show that the line through the points $(4, 7, 8), (2, 3, 4)$ is parallel to the line through the points $(-1, -2, 1), (1, 2, 5)$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

If a line has the direction ratios $-18, 12, -4,$ then what are its direction cosines?

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Evaluate $ \begin{vmatrix} cos\alpha \; cos\beta & cos\alpha \; sin\beta & -sin\alpha \\ -sin\beta & cos\beta & 0 \\ sin \alpha \; cos\beta & sin\alpha \; sin\beta & cos\alpha \end{vmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Examine the consistency of the system of equations:\[\] \[\quad x + 3y = 5 \] \[\quad 2x + 6y = 8\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Form the differential equation representing the family of curves given by $(x-a)^2+2y^2\;=\;a^2$, where $a$ is an arbitrary constant

asked Nov 29, 2012 by sreemathi.v

1 answer

Solve the following Linear Programming Problems graphically: Maximise $Z = 5x + 3y$ subject to $3x + 5y \leq 15, 5x + 2y \leq 10, x \geq 0, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Verify A (adj A)= (adj A) A = | A | I: \[ \begin{bmatrix} 2&3 \\ - 4&-6 \\ \end{bmatrix} \]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Using Cofactors of elements of second row, evaluate $ \Delta = \begin{vmatrix} 5&3&8 \\ 2&0&1 \\ 1&2&3 \end{vmatrix} $

asked Nov 29, 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

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 2&7&65 \\ 3&8&75 \\ 5&9&86 \end{vmatrix} = 0\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

\[ \text{If A = } \begin{bmatrix} 1&2 \\ 4&2 \end{bmatrix}, \text{then show that } |\;2A\;| = 4|\;A;|\]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find the principal values of the following: $cosec^{-1} (2) $

asked Nov 28, 2012 by vaishali.a

1 answer

Determine order and degree (if defined) of differential equation $\bigg(\frac{ds}{dt}\bigg)^4 +3s\frac{d^2s}{dt^2}=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

The two equal sides of an isosceles triangle with fixed base $b$ are decreasing at the rate of 3 cm per second. How fast is the area decreasing when the two equal sides are equal to the base ?

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Two bad oranges are accidentally mixed with ten good ones. Three oranges are drawn at random without replacement from this lot. Obtain the probability distribution for the number of bad oranges. and find the expected value of the distribution.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the set of all positive even integers forms a semi-group under the usual addition and multiplication. Is it a monoid under each of the above operations?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that p ↔ q ≡ (p → q) ∧ (q → p)

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Construct the truth tables for the following statement: ∼ (p ∨ q)

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?

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 box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: $ (i)\: f (x) = x^2 $

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Find the approximate value of \(f (5.001)\), where $f (x) = x^3 – 7x^2 + 15.$

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 1 & 3 \\ 2 & 7 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Find the slope of the tangent to curve $ y = x^3 - x + 1$ at the point whose $x$ - coordinate is $2$.

asked Nov 23, 2012 by thanvigandhi_1

1 answer

If $ A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$ then prove that $ A^n = \begin{bmatrix} 1+2n & -4n \\ n & 1 - 2n \end{bmatrix} $ , where $n$ is any positive integer.

asked Nov 23, 2012 by pady_1

1 answer

Show that the function given by $f (x) = \sin x$ is strictly decreasing in $(\large {\frac{\pi}{2}},$$ \pi)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that the function given by \(f (x) = \sin \;x\) is strictly increasing in $\left(0, \: \large {\frac{\pi}{2}}\right)$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The radius of a circle is increasing uniformly at the rate of $3\; cm/s.$ Find the rate at which the area of the circle is increasing when the radius is $10\; cm$.

asked Nov 22, 2012 by thanvigandhi_1

1 answer

If $(f:R \to R)$ is defined by $f(x) = x^2$ - $3x+2$. Find $f(f(x))$:

asked Nov 21, 2012 by vaishali.a

1 answer

Differentiate w.r.t. $x$ the function in $(5x)^{\large 3 \cos 2x} $

asked Nov 21, 2012 by thanvigandhi_1

1 answer

If \( f : [ -5,5] \rightarrow R \) is a differentiable function and if \( f' (x) \) does not vanish anywhere, then prove that \( f (-5) \: \neq \: f (5)\).

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Consider the binary operation \( \wedge\) on the set \(\{1, 2, 3, 4, 5\}\) defined by \(a \wedge b = min \{a, b\}\). Write the multiplication table of the operation \( \wedge\) .

asked Nov 20, 2012 by vaishali.a

1 answer

Find the second order derivatives of the functions given in $ x \; \cos x$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = \sin t, y = \cos 2t $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

asked Nov 19, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ ( \log \; x )^{\large cos \: x} $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : e^{x^{3} } $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftmans time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftmans time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsmans time. (i) What number of rackets and bats must be made if the factory is to work at full capacity? (ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.

asked Nov 16, 2012 by fingeazy

1 answer

Find $\frac {dy}{dx}$ in the following: $ax +by^2 = cos \: y$

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Find \( gof\) and \(fog\), if (i) \( f(x) = |\;x\;| \, and \, g(x) = |\;5x-2\;| \)

asked Nov 9, 2012 by vaishali.a

1 answer

Prove that the Greatest Integer Function \(f : R \to R\), given by \(f (x) = [x]\), is neither one-one nor onto, where \([x]\) denotes the greatest integer less than or equal to \(x\).

asked Nov 8, 2012 by vaishali.a

1 answer

Check whether the relation R defined in the set ${1, 2, 3, 4, 5, 6}$ as $R= {(a,b) : b= a+1}$ is reflexive, symmetric or transitive.

asked Nov 7, 2012 by vaishali.a

1 answer

Examine the following functions for continuity. $f(x) = | \;x - 5\;|$

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Examine the following functions for continuity $\; f(x) = \large \frac {x^2 - 25} {x + 5}$$, x\:\neq\: -5$

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Examine the following functions for continuity. $f(x) = \frac {1} { x - 5}, x \: \neq \: 5 $

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Examine the following functions for continuity. $f(x) = x-5$

asked Nov 6, 2012 by thanvigandhi_1

1 answer

A dietician wishes to mix together two kinds of food X and Y in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg food is given below: \[\]$\begin{array}{cccc} \textbf{Food} & \textbf{Vitamin A} & \textbf{Vitamin B}& \textbf{Vitamin C}\\ X & 1 & 2 &3 \\ Y & 2 & 2 &1 \end{array}$\[\] One kg of food X costs Rs 16 and one kg of food Y costs Rs 20. Find the least cost of the mixture which will produce the required diet?

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Find the angle between the lines whose direction ratios are $a, b, c$ and $b -c, c -a, a - b.$

asked Nov 2, 2012 by balaji.thirumalai

1 answer

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