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Recent questions tagged q13

Integrate the functions\[\frac{1}{\sqrt{(x-1)(x-2)}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions\[\frac{2}{(1-x)(1+x^2)}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

The scalar product of the vector \(\hat i + \hat j + \hat k\) with a unit vector along the sum of vectors \(2\hat i + 4 \hat j − 5\hat k\) and \(λ\hat i + 2 \hat j + 3\hat k\) is equal to one. Find the value of \( λ.\)

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the function $\tan^{-1}x$

asked Dec 4, 2012 by sreemathi.v

1 answer

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B(4, 5) and C(6, 3).

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the area of the region bounded by the curve $y^2 = 4x,\; y$ - axis and the line $y = 3$ is

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Evaluate the definite integral $\begin{align}\int\limits_2^3\frac{xdx}{x^2+1} \end{align}$

asked Dec 4, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals,evaluate the integral $\begin{align}\int\limits_\frac{\Large -\pi}{\Large 2}^\frac{\Large \pi}{\Large 2}\sin^7\;x\;dx \end{align}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function $\int\large\frac{e^x}{(1+e^x)(2+e^x)}$

asked Dec 3, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition $\cos\bigg(\large\frac{dy}{dx}\bigg)$$=a\;(a\;\in\;R);y=2\;when\;x=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find a particular solution satisfying the given condition$\large\frac{dy}{dx}$$+2y\tan x=\sin x;\;y=o\;when\;x=\large\frac{\pi}{3}$

asked Nov 29, 2012 by sreemathi.v

1 answer

Using properties of determinants, prove that: $\begin{vmatrix} 3a&-a+b&-a+c\\ -b+a&3b&-b+c\\ -c+a&-c+b&3c \end{vmatrix}= 3(a+b+c)(ab+bc+ca)$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:\[\] \[2x+3y+3z=5\] \[x-2y+z=-4\] \[3x-y-2z=3\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

\[ \text{If A = } \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}, \text{show that } A^{2} -5A +7I = 0. \text{ Hence find } A^{-1}\]

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the following \[2tan^{-1} (cos x) = tan^{-1} (2\, cosec\, x) \]

asked Nov 29, 2012 by vaishali.a

1 answer

Find a particular solution of the differential equation $\frac{dy}{dx} + y\cot x=4x\:cosec\:x$, $(x\neq0)$, given that $y = 0$ when $x = \large\frac{\pi}{2}$

asked Nov 28, 2012 by sreemathi.v

1 answer

By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1+a^2-b^2&2ab&-2b \\ 2ab&1-a^2+b^2&2a \\ 2b&-2a&1-a^2-b^2 \end{vmatrix} = (1+a^2+b^2)^3 \end{array} \]

asked Nov 28, 2012 by balaji.thirumalai

1 answer

If $ \sin^{-1} x=y$ then:

asked Nov 28, 2012 by vaishali.a

1 answer

Find the points at which the function \(f\) given by \(f (x) = (x – 2)^4 (x + 1)^3\) has a (i) local maxima, (ii) local minima and the (iii) point of inflexion.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.

asked Nov 27, 2012 by balaji.thirumalai

2 answers

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

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red. (ii) first ball is black and second is red. (iii) one of them is black and other is red.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find two numbers whose sum is 24 and whose product is as large as possible.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

if $ F( x ) = \begin{bmatrix} cos\;x & -sin\;x & 0 \\ sin\;x & cos\;x & 0 \\ 0 & 0 & 1 \end{bmatrix}, $ show that $ F( x )\; F( y ) = F( x + y ). $

asked Nov 25, 2012 by pady_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

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

asked Nov 23, 2012 by pady_1

1 answer

On which of the following intervals is the function $f $ given by $f (x) = x^{100} + sin x –1$ strictly decreasing ?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A balloon, which always remains spherical, has a variable diameter $\large\frac{3}{2}$$(2x+1)$. Find the rate of change of its volume with respect to $x.$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

Given a non-empty set \( X,\) let \(\ast :\; P(X)\; \times\; P(X) \to P(X) \) be defined as \(A \ast B = \; ( A-B)\; \cup \; (B-A),\; \forall A, B \in \; P(X).\). Show that the empty set \(\emptyset \) is the identity for the operation $\ast$ and all the elemnets \(A\) of \( P(X) \) are invertible with \( A^{-1} \;= A\).

asked Nov 22, 2012 by vaishali.a

1 answer

Consider a binary operation $\ast$ on $N$ defined as $a \ast b = a^3 + b^3$. Choose the correct answer:

asked Nov 21, 2012 by vaishali.a

1 answer

Find \(\large \frac{dy}{dx} \), if \( y = \sin^{-1}x + \sin^{-1} \: \sqrt {1-x^2} , -1 \leq x \leq 1 \)

asked Nov 21, 2012 by thanvigandhi_1

1 answer

If \( y = 3 \cos \: (\log x ) + 4 \sin ( \log x )\), show that \(x^2y_2 + xy_1 + y = 0\)

asked Nov 20, 2012 by thanvigandhi_1

1 answer

If $f: R\to R$ be given by $f(x)=(3-x^3)^\frac {1}{3} $, then $fof(x)$ is

asked Nov 19, 2012 by vaishali.a

1 answer

Find $\large\frac{dy}{dx}$ of the functions given in $ y^{\large x} = x^{\large y} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Find \( \large\frac {dy}{dx} \) in the following: $ y = cos^{-1} \left(\large\frac{2x}{1 + x^2}\right), -1 < x < 1 $

asked Nov 15, 2012 by thanvigandhi_1

1 answer

Is the function defined by $ f(x) = \left\{ \begin{array} {1 1} x + 5 ,& \quad\text{ if $ x $ \(\leq 1\)}\\ x - 5,& \quad \text{if $x$ > 1}\\ \end{array} \right. $ a continuous function?

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Show that the relation \(R\) defined in the set \(A\) of all polygons as \(R = \{(P_1, P_2) :\: P_1\ and \;P_2\) have same number of sides\(\}\), is an equivalence relation. What is the set of all elements in \(A\) related to the right angle triangle \(T\) with sides \(3, 4\) and \(5\)?

asked Nov 8, 2012 by vaishali.a

1 answer

Show that each of the relation $R$ in the set $A=\{x\in Z: 0 \leq x \leq 12\}$, given by $(i) R = \{(a,b) |a-b|$ is a multiple of 4 $\}$ is an equivalence relation. Find the set of all elements related to 1.

asked Nov 7, 2012 by vaishali.a

1 answer

Find the equation of the plane passing through the point $( -1, 3, 2)$ and perpendicular to each of the planes $x + 2y + 3z = 5$ and $3x + 3y + z = 0$.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

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