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Recent questions tagged q6

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 0&a&-b \\ -a&0&-c \\ b&c&0 \end{vmatrix} = 0 \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

If $A = \begin{bmatrix} 1&1&-2\\ 2&1&-3 \\5&4&-9 \end{bmatrix}$, then find $|A|$

asked Nov 28, 2012 by balaji.thirumalai

1 answer

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

asked Nov 28, 2012 by vaishali.a

2 answers

Find the intervals in which the function \(f\) given by $ f(x) =\large \frac{4sin\: x - 2x - xcos \: x}{2+cos\:x}$ is (i) increasing (ii) decreasing.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Determine order and degree (if defined) of differential equation $(y''')^2+(y'')^3+(y')^4+y^5=0$

asked Nov 27, 2012 by sreemathi.v

1 answer

Show that { $\bigl(\begin{smallmatrix} 1 & 0 \\ 0 & 1 \end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} \omega & 0 \\ 0 & \omega^2\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} \omega^2 & 0 \\ 0 & \omega\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & 1 \\ 1 & 0\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & \omega^2\\ \omega & 0\end{smallmatrix} \bigr) $, $\bigl(\begin{smallmatrix} 0 & \omega\\ \omega^2 & 0\end{smallmatrix} \bigr) $} where $\omega^3 = 1, \omega \neq 1$ form a group with respect to matrix multiplication.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that $p \rightarrow q$ and $q \rightarrow p$ are not equivalent.

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

In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6 . What is the probability that he will knock down fewer than 2 hurdles?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Let E and F be events with $P (E) = \frac{3}{5} , P (F)= \frac{3}{10} $ and $P (E \cap F) = \frac{1}{5} $ . Are E and F independent?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the maximum profit that a company can make, if the profit function is given by $ p(x) = 41 - 72x - 18x^2$

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Simplify $\cos\theta\begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$ + $\sin\theta\begin{bmatrix} \sin\theta & -\cos\theta \\ \cos\theta & \sin\theta \end{bmatrix} $

asked Nov 26, 2012 by pady_1

1 answer

If the radius of a sphere is measured as $7 \: m$ with an error of $0.02 \: m$, then find the approximate error in calculating its volume.

asked Nov 26, 2012 by thanvigandhi_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

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} $

asked Nov 23, 2012 by pady_1

1 answer

Find the slope of the normal to the curve $ x = 1 - a \sin\theta, y = b \cos^2\theta$ at $ \theta = \Large {\frac{\pi}{2}}$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Find the values of $x, y, z $ if the matrix $ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} $ satisfy the equation $A'A = I $

asked Nov 23, 2012 by pady_1

1 answer

Find the intervals in which the following functions are strictly increasing or decreasing: $(a) \;x^2 + 2x - 5$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

The radius of a circle is increasing at the rate of $0.7\; cm/s$. What is the rate of increase of its circumference?

asked Nov 22, 2012 by thanvigandhi_1

1 answer

Give examples of two functions \(f : N \to Z \) and \(g: Z \to Z\) such that \(g\;o\;f\) is injective but \(g\) is not injective.

asked Nov 21, 2012 by vaishali.a

1 answer

Differentiate w.r.t. x the function $cot^{-1} \begin{bmatrix} \frac{{\sqrt {1+sin \: x}} + {\sqrt{1-sin \: x}}} {{\sqrt {1+sin \: x}} - {\sqrt{1-sin \: x}}} \\[0.3em] \end{bmatrix}$, where $0 < x < \frac{\pi}{2}$

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Let \(\ast\) be the binary operation on \(N\) given by \(a\ast b=L.C.M\,.of\,a\,and\,b\). Find $\begin{array}{1 1}(i)\;\; 5 \ast7,\; 20 \ast 16 & (ii)\;\; Is\; \ast \;commutative?\\(iii)\;\; Is\; \ast \;associative? & (iv)\;\; Find\, the\,identity \, of \ast \, in N\\(v)\;\; Which \, elements\, of \, N\, are\, invertible\, for\, the\, operaation\,\ast ? & \;\end{array}$

asked Nov 21, 2012 by vaishali.a

2 answers

Examine the applicability of Mean Value Theorem for all three functions given in $(i)\;f (x) = [x] \;for\; x \: \in [5,9]$

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the function $(e^{\large x} \sin 5x)$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $x = a ( \theta - \sin \theta ), y = a ( 1 +\cos \theta) $ without eliminating the parameter, Find $\large\frac{dy}{dx}$

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ (x + \large\frac{1}{x})^{\large x}$$ + x ^{\large (1 + \Large\frac{1}{x})} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $x : e^x + e^{x^2} + \: ... + e^{x^5} $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?

asked Nov 16, 2012 by fingeazy

1 answer

Two godowns A and B have grain capacity of 100 quintals and 50 quintals respectively. They supply to 3 ration shops, D, E and F whose requirements are 60, 50 and 40 quintals respectively.

asked Nov 15, 2012 by fingeazy

1 answer

Show that $f : [-1,1]$ $ \rightarrow R$, given by $f(x) =\frac {x } { (x+2)}$ is one-one. Find the inverse of of the $f : [-1,1] \rightarrow $ Range $ f$.

asked Nov 14, 2012 by vaishali.a

1 answer

Find $ \frac {dy}{dx} $ in the following: $ x^3 +x^2y + xy^2 +y^3 = 81 $

asked Nov 11, 2012 by thanvigandhi_1

1 answer

Differentiate the functions with respect to x: $ cos \; x^3. sin^2 (x)^5 $

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Let \(A=\{1,2,3\},\; B = \{4,5,6,7\}\) and let \(f = \{(1,4),(2,5),(3,6)\}\)be a function from \(A\) to \(B\). Show that \(f\) is one-one.

asked Nov 8, 2012 by vaishali.a

1 answer

Find all points of discontinuity of $f$, where $f$ is defined by $f(x) = \left\{ \begin{array} {1 1} 2x + 3,& \quad\text{ if $ x $ \(\leq 2\)}\\ 2x - 3,& \quad \text{if $x$ > 1}\\ \end{array} \right. $

asked Nov 7, 2012 by thanvigandhi_1

1 answer

Show that the relation \(R\) in the set {1,2,3} given by R={(1,2), (2,1)} is symmetric but neither reflexive nor transitive.

asked Nov 7, 2012 by vaishali.a

1 answer

If the lines $\large\frac{x-1} {-3} = \frac{y-2}{2k} = \frac{z-3}{2}$ and $\large\frac{x-1}{3k} = \frac{y-1}{1} = \frac{z-6}{-5}$ are perpendicular, find the value of $k$.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

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