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Recent questions tagged q1

Find the adjoint of the matrix: $\begin{bmatrix} 1&2 \\ 3&4 \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

For each of the differential equations given below,indicate its order and degree(if defined) $(i)\;\large\frac{d^2y}{dx^2}+5x\bigg(\frac{dy}{dx}\bigg)^2-6y=\log x$

asked Nov 28, 2012 by sreemathi.v

1 answer

Write Minors and Cofactors of the elements of following determinants: $ (i) \quad \begin{vmatrix} 2&-4 \\ 0&3 \end{vmatrix}$

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

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

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Evaluate the determinant:$ \begin{vmatrix} 2&4 \\ -5&-1 \end{vmatrix} $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Find the principal values of the following: <br> $ sin^{-1} \bigg( -\frac {1} {2}\bigg) $

asked Nov 28, 2012 by vaishali.a

2 answers

Determine order and degree (if defined) of differential equation $\frac{d^4y}{dx^4}+\sin(y''')=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

Find the probability distribution of the number of sixes in throwing three dice once.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Let $S$ be a non-empty set and o be a binary operation on $S$ defined by $xoy = x ; x, y \in S$. Determine whether o is commutative and associative.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Use the truth table to establish which of the following statements are tautologies and which are contradictions.

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

A and B are two events such that P (A) $\neq$ 0. Find P(B|A), if (i) A is a subset of B (ii) A $\cap$ B = $\phi$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A die is thrown 6 times. If getting an odd number is a success, what is the probability?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

State which of the following is a probability distributions of a random variable. Give reasons for your answer.

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

If $P(A) = \frac{3}{5} $ and $P(B) = \frac{1}{5} $ , find $P (A \cap B) $ if A and B are independent events.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the maximum and minimum values, if any, of the following functions given by?$\;f(x)=(2x-1)^2+3$

asked Nov 26, 2012 by thanvigandhi_1

1 answer

Using differentials, find the approximate value of each of the following up to $3$ places of decimal. $(i)\;\sqrt{25.3}$

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

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

asked Nov 23, 2012 by pady_1

1 answer

Let $A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} $, show that $ (aI + bA)^n = a^nI + na^{n-1}bA $, where $\;I\;$ is the identity matrix of order 2 and $n \in N$.

asked Nov 23, 2012 by pady_1

1 answer

Find the slope of the tangent to the curve $y = 3x^4 – 4x \; at\; x = 4.$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Show that the function given by \(f (x) = 3x + 17\) is strictly increasing on \(R\).

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Let \(f:R \to R\) be defined as \(f(x)=10x+7.\)Find the function \(g:R \to R\) such that \(g\;o\;f = f\;o\;g = I_R.\)

asked Nov 21, 2012 by vaishali.a

1 answer

Differentiate w.r.t. \(x\) the function in \( (3x^2 - 9x + 5)^9 \)

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Verify Rolle's theorem for the function \( f (x) =x^2 + 2x - 8, x \: \in [ -4 , 2 ]. \)

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ x^2 + 3x + 2 $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Determine whether or not each of the definition of $\ast$ given below gives a binary operation. In the event that $\ast$ is not a binary operation, give justification for this - On$ \; Z^+,\,$ defined $\,$ by$\; ab= a-b $

asked Nov 19, 2012 by vaishali.a

1 answer

If $x$ and $y$ are connected parametrically by the equations given in $ x = 2at^2, \: y = at^4 $ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ \cos \: x \: . \cos \: 2x \:. \cos \: 3x $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Find the rate of change of the area of a circle with respect to its radius r when $(a)\; r = 3 cm$

asked Nov 16, 2012 by kasturi.c

1 answer

Differentiate the following w.r.t. $x : \large \frac{e^x}{sin\;x}$

asked Nov 16, 2012 by thanvigandhi_1

1 answer

Reshma wishes to mix two types of Food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs 80/kg. Food P contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while Food Q contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture

asked Nov 16, 2012 by fingeazy

1 answer

Let $f:\{1,3,4\} \to \{1,2,5\} $ and $g:\{1,2,5\}\to\{1,3\}$ be given by $f = \{(1, 2), (3, 5), (4, 1)\}$ and $ g = \{(1, 3), (2, 3), (5, 1)\}$. Write down $gof$.

asked Nov 9, 2012 by vaishali.a

1 answer

Show that the function \(f : R_* \rightarrow R_* \) defined by \( f(x) = (\frac{1} {x})\) is one-one and onto, where \(R_* \) is the set of all non-zero real numbers. Is the result true, if the domain \(R_* \) is replaced by \(N\) with co-domain being same as \(R_*\)?

asked Nov 8, 2012 by vaishali.a

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

Prove that the function $f (x) = 5x-3$ is continuous at $x=0$, $x=-3$ and $x=5$.

asked Nov 5, 2012 by thanvigandhi_1

1 answer

Refer to Example 9 in book ( page 521 - copied below ). (Diet problem) A dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A. Each packet of the same quantity of food Q contains 3 units of calcium, 20 units of iron, 4 units of cholesterol and 3 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and at most 300 units of cholesterol. How many packets of each food should be used to minimise the amount of vitamin A in the diet? What is the minimum amount of vitamin A?How many packets of each food should be used to maximise the amount of vitamin A in the diet? What is the maximum amount of vitamin A in the diet?

asked Nov 2, 2012 by balaji.thirumalai

1 answer

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, – 1), (4, 3, – 1).

asked Nov 2, 2012 by balaji.thirumalai

1 answer

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