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Recent questions tagged q10

Find the area bounded by the curve $x^2 = 4y$ and the line $x = 4y - 2$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Choose the correct answer If f(x)=$\int\limits_0^x t\sin t\;dt,$ then f'(x) is

asked Dec 3, 2012 by sreemathi.v

1 answer

By using the properties of definite integrals, evaluate the integral $\int\limits_0^\frac{\Large \pi}{\Large 2}(2 \log \sin x-\log \sin 2x)\;dx$

asked Dec 3, 2012 by sreemathi.v

1 answer

Integrate the function\[\int\frac{\sin^8x-\cos^8x}{1-2\sin^2x\cos^2x}\]

asked Dec 3, 2012 by sreemathi.v

1 answer

Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=\sqrt{a^2-x^2}\;x\in\;(-a,a):\;x+y\;\large\frac{dy}{dx}$$=0(y\neq0)$

asked Nov 30, 2012 by sreemathi.v

1 answer

Form the differential equation of the family of circles having centre on $y$-axis and radius $3$ units.

asked Nov 30, 2012 by sreemathi.v

2 answers

Find the general solution $e^x\tan y\;dx+(1-e^x)\sec ^2y\;dy=0$

asked Nov 30, 2012 by sreemathi.v

1 answer

Find the general solution of the differential equation $(x+y)\large\frac{dy}{dx}$$=1$

asked Nov 29, 2012 by sreemathi.v

1 answer

Find the direction cosines of a line which makes equal angles with the coordinate axes.

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Evaluate $\begin{vmatrix} 1 & x & y\\ 1 & x+y & y\\ 1 & x & x+y \end{vmatrix}$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve system of linear equations, using matrix method:<br>$5x+2y=3$ <br> $3x+2y=5$

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Show that the minimum of Z occurs at more than two points. Maximise $Z = x + y$, subject to$\; x $– $y\leq –1, -x + y \leq 0, x, y \geq 0.$

asked Nov 29, 2012 by fingeazy

1 answer

Prove that \[cot^{-1} \left ( \frac {{\sqrt {1+sinx}}+{\sqrt {1-sinx}}}{{\sqrt {1+sinx}}-{\sqrt {1-sinx}}} \right ) = \frac {x}{2} , x \in \left ( 0, \frac{\pi}{4} \right )\]

asked Nov 29, 2012 by vaishali.a

1 answer

Find the inverse of the matrix (if it exists): $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \\ \end{bmatrix} $

asked Nov 29, 2012 by balaji.thirumalai

1 answer

Solve the differential equation$y\;e^{\large\frac{x}{y}}\;dx=\bigg(x\;e^{\Large\frac{x}{y}}+y^2\bigg)dy\;(y\neq0)$

asked Nov 29, 2012 by sreemathi.v

1 answer

By using the properties of determinants show that $ (i) \begin{vmatrix} x+4&2x&2x \\ 2x&x+4&2x \\ 2x&2x&x+4 \end{vmatrix} = (5x+4)(4-x)^2 $

asked Nov 28, 2012 by balaji.thirumalai

1 answer

Determine order and degree (if defined) of differential equation $y''+2y'+\sin y=0$

asked Nov 28, 2012 by sreemathi.v

1 answer

Find the principal values of the following: <br> $ \mathrm{cosec}^{-1} (-\sqrt 2) $

asked Nov 28, 2012 by vaishali.a

2 answers

The sum of the perimeter of a circle and square is \(k\), where \(k\) is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle.

asked Nov 28, 2012 by thanvigandhi_1

1 answer

Find the order of each element in the group $ (Z_5 − \{[0]\}, _.5)$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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

asked Nov 27, 2012 by balaji.thirumalai

0 answers

How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $ \frac{1}{100}$. What is the probability that he will win a prize (a) at least once (b) exactly once (c) at least twice?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the mean number of heads in three tosses of a fair coin.

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

Events A and B are such that $P (A) = \frac{1}{2} , P(B) = \frac{7}{12}$ and P(not A or not B) = $ \frac{1}{4} $ . State whether A and B are independent?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the maximum value of \(2x^3 – 24x + 107\) in the interval \([1, 3]\).

asked Nov 27, 2012 by thanvigandhi_1

1 answer

A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Solve the equation for $x, y, z$ and $t$ if $ 2\begin{bmatrix}x & z \\ y & t \end{bmatrix} + 3\begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix} = 3\begin{bmatrix} 3 & 5 \\ 4 & 6 \end{bmatrix} $

asked Nov 26, 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

Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 3 & -1 \\ -4 & 2 \end{bmatrix} $

asked Nov 23, 2012 by pady_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

Prove that the logarithmic function is strictly increasing on $(0, \infty).$

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?

asked Nov 23, 2012 by thanvigandhi_1

1 answer

A manufacturer produces three products \( x, y, z \) which he sells in two markets. Annual sales are indicated below: \[ \begin{array} { c c } \textbf{Market} & \textbf{Products} \\ I & 10,000 \quad 2,000 \quad 18,000 \\ II & 6,000 \quad 20,000 \quad 8,000 \end{array} \]
If unit sale prices of x, y and z are Rs 2.50, Rs 1.50 and Rs 1.00, respectively, find the total revenue in each market

asked Nov 22, 2012 by pady_1

1 answer

Find the number of all onto functions from the set $\{1, 2, 3, ... , n\}$ to itself.

asked Nov 22, 2012 by vaishali.a

1 answer

Find if the given operation has identity: $\;\; a \ast b = a^2 + b^2$

asked Nov 21, 2012 by vaishali.a

2 answers

Differentiate w.r.t. \(x\) the function in \( x^{\large x} + x^{\large a} + a^{\large x} + a^{\large a} \), for some fixed \( a > 0 \) and \( x > 0 \)

asked Nov 21, 2012 by thanvigandhi_1

1 answer

Find the second order derivatives of the functions given in $ \sin (\log x) $

asked Nov 20, 2012 by thanvigandhi_1

1 answer

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

asked Nov 20, 2012 by thanvigandhi_1

1 answer

Differentiate the functions given in w.r.t. $x : $ $ x^{\large x \cos x} + \large\frac{x^2 + 1}{x^2 - 1} $

asked Nov 17, 2012 by thanvigandhi_1

1 answer

Differentiate the following w.r.t. $ x: $ $ cos \: ( log\: x + e^x ), x > 0 $

asked Nov 16, 2012 by thanvigandhi_1

1 answer

There are two types of fertilisers \(F_{1} \) and \(F_{2} \). \(F_{1} \) consists of 10% nitrogen and 6% phosphoric acid and \(F_{2} \) consists of 5% nitrogen and 10% phosphoric acid. After testing the soil conditions, a farmer finds that she needs atleast 14 kg of nitrogen and 14 kg of phosphoric acid for her crop. If \(F_{1} \) costs Rs 6/kg and \(F_{2} \) costs Rs 5/kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost?

asked Nov 16, 2012 by fingeazy

1 answer

A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A. Further, the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?

asked Nov 16, 2012 by fingeazy

1 answer

Find $ \frac {dy}{dx}$ in the following: $y = tan^{-1} \left(\frac{3x - x^3}{1 - 3x^2}\right), - \; { \frac{1}{\sqrt3} } < x < \;{\frac{1}{\sqrt3} }\\ $

asked Nov 15, 2012 by thanvigandhi_1

1 answer

Let \(f : X \to Y\) be an invertible function. Show that \(f\) has unique inverse.

asked Nov 15, 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} x + 1,& \quad\text{ if $ x $ \(\geq 1\)}\\ x^2+1,& \quad \text{if $x$ < 1}\\ \end{array} \right. $

asked Nov 9, 2012 by thanvigandhi_1

1 answer

Let $A=R-\{3\}$ and $B=R-\{1\}$. Consider the function $ f:A \to B$ defined by $f(x)=\large\frac {x-2}{ x-3}$. Is $f$ one-one and onto?

asked Nov 9, 2012 by vaishali.a

1 answer

Prove that the greatest integer function defined by $ f(x) = [x], 0<x<3$ is not differentiable at $x = 1 $ and $ x = 2 $

asked Nov 8, 2012 by thanvigandhi_1

1 answer

Find the coordinates of the point where the line through $(5, 1, 6)$ and $(3, 4, 1)$ crosses the YZ-plane.

asked Nov 2, 2012 by balaji.thirumalai

1 answer

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