Recent questions tagged kvquestionbank2012

$\Large \frac {1}{x(x^4-1)^4}=$\[(a)\;\log \bigg[\frac{x^4}{x^4-1}\bigg]\qquad (b)\;\frac{1}{2}\log \bigg[\frac{x^2+1}{x^2+1}\bigg]\qquad(c)\;\frac{1}{4} log \bigg[\frac{x^4-1}{x^4}\bigg]\qquad(d)\;\log \frac{x(x^2-1}{x^2+1}\bigg]\]

asked Jan 31, 2013 by meena.p

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$\Large \frac {3^xdx}{\sqrt{1-9^x}} =$\[(a)\;\log _e 3\sin^{-1}(3^x) \qquad (b)\;\frac{1}{log_e^3} \sin^{-1}(3^x)\qquad(c)\;\log_e3\sin^{-1}(3^{x/2})\qquad(d)\;\frac{1}{log _e3} \sin^{-1}(3^{x/2}\]

asked Jan 31, 2013 by meena.p

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$\Large\int \frac {2xdx}{1+x^4}=$\[(a)\;\tan^{-1} (x^2) \qquad (b)\;\frac{1}{2}\tan^{-1} x^2 \qquad(c)\;log (1+x^4)\qquad(d)\;\tan^{-1} \bigg(\frac{1}{x^2}\bigg)\]

asked Jan 31, 2013 by meena.p

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$\int \sqrt {1+x^2} d(x^2)=$\[(a)\;\frac{2}{3x}(1+x^2)^{3/2}\qquad (b)\;\frac{2}{3}(1+x^2)^{3/2}\qquad(c)\;\frac{2x}{3}(1+x^2)^{3/2}\qquad(d)\;\frac{2x}{3}(1+x^2)\]

asked Jan 31, 2013 by meena.p

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$\Large\int \frac {dx}{x-X^3}=$\[(a)\;\frac{1}{2}log \frac{x^2}{1-x^2}\qquad (b)\;\frac{1}{2}log \frac{1-x^2}{x^2}\qquad(c)\;log \frac{(1-x)}{x(1+x)}\qquad(d)\;log x(1-x^2)\]

asked Jan 31, 2013 by meena.p

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$\Large\int \frac {dx}{x\sqrt{1-x^3}} =$\[\begin {array} {1 1} (a)\;\frac{1}{3} log \bigg | \frac {\sqrt {1-x^2}+1}{\sqrt {1-x^2}-1}\bigg | & \quad (b)\;\frac{1}{3} log \bigg |\frac{\sqrt {1-x^2}-1}{\sqrt {1-x^2}+1}\bigg| & \quad \\(c)\;\frac{2}{3} log \bigg |\frac{1}{\sqrt {1-x^3}}\bigg| & \quad(d)\;\frac{1}{3} log | 1-x^3 | \end {array}\]

asked Jan 31, 2013 by meena.p

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$\Large\int \frac {\sin^2x-\cos^2x}{\sin^2x-\cos^2x} \normalsize dx=$\[(a)\;\tan x+\cot x \qquad (b)\;\tan x-\cot x \qquad(c)\;\tan x+\sec x \qquad(d)\;\tan x+cosec x\]

asked Jan 31, 2013 by meena.p

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$\Large\int \frac {x+\sin x}{1+\cos x} \normalsize dx=$\[(a)\;\tan \frac{x}{2}\qquad (b)\;x\tan \frac{x}{2}\qquad(c)\;\cot \frac{x}{2}\qquad(d)\;x \cot \frac{x}{2}\]

asked Jan 31, 2013 by meena.p

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$\int x\tan^{-1}x dx=$ \[(a)\;\bigg(\frac{x^2+1}{2}\bigg) \tan^{-1}x- \frac{x}{2} \qquad (b)\;\bigg(\frac{x^2+1}{2}\bigg)+\tan^{-1}x-x \qquad(c)\;(x^2+1)\tan^{-1}x-x \qquad(d)\;(x^2+1) \tan^{-1}x+x \]

asked Jan 30, 2013 by meena.p

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$\Large\int \frac {x \sin^{-1}x}{\sqrt{1-x^2}} \normalsize dx=$\[(a)\;\sqrt{1-x^2}\sin^{-1}x\qquad (b)\;x\sin^{-1}x\qquad(c)\;x-\sqrt{1-x^2}\sin^{-1}x\qquad(d)\;(\sin^{-1}x)^2\]

asked Jan 30, 2013 by meena.p

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$\Large\int x^3 e^{x^2} dx=$ \[(a)\;x^2(e^{x^2}-1) \qquad (b)\;\frac{1}{2}x^2(e^{x^2}-1)\qquad(c)\;\frac{1}{2}e^{x^2}(x^2-1) \qquad(d)\;\frac{1}{2}(e^x-1)\]

asked Jan 30, 2013 by meena.p

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$\Large\int \frac {\sqrt x}{\sqrt{a^3-x^3}} dx=$\[(a)\;\frac{2}{3}\bigg(\frac{x}{a}\bigg)^{3/2} \qquad (b)\;\frac{2}{3}\sin^{-1}\bigg(\frac{x}{a}\bigg)^{3/2} \qquad(c)\;\frac{2}{3}\cos {-1}\bigg(\frac{x}{a}\bigg)^{3/2} \qquad(d)\;\frac{2}{3}\sin^{-1}\bigg(\frac{a}{x}\bigg)^{3/2}\]

asked Jan 30, 2013 by meena.p

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$\Large\int \frac {e^xdx} {e^{2x}+1}=$\[(a)\;log (e^x+e^{-x}) \qquad (b)\;log (e^{2x}+1)\qquad(c)\;\tan^{-1}(e^x) \qquad(d)\;\tan^{-1}(2e^x)\]

asked Jan 30, 2013 by meena.p

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$\Large\int \frac {\sin^2xdx}{a^2\cos ^2x+b^2\sin^2x \sin^2 x} =$\begin{array}{1 1}(a)\;(b-a)log(a^2\cos ^2x+b^2\sin^2x) & \quad (b)\;\frac{1}{b-a}log(a^2\cos ^2x+b^2\sin^2x) & \\(c)\;\frac{1}{b^2-a^2}log(a^2\cos ^2x+b^2\sin^2x) & \quad(d)\;\frac{1}{a^2+b^2}log(a^2\cos ^2x+b^2\sin^2x)\end{array}

asked Jan 30, 2013 by meena.p

0 answers

$\Large\int \frac {dx}{\sin x+\sqrt 3 \cos x} =$ \begin{array}{1 1}(a)\;\frac{1}{2} log \tan \bigg [\frac{\pi}{2}+\frac{\pi}{6}\bigg] & \quad (b)\;\frac{1}{2} log \bigg\{cosec \bigg(x+\frac{\pi}{3}\bigg)-\cot \bigg(x+\frac{\pi}{3}\bigg)\bigg\} & \\ (c)\;\frac{1}{2} log \bigg\{\sec \bigg(x-\frac{\pi}{6}\bigg)+\tan \bigg(x-\frac{\pi}{6}\bigg)\bigg\} & \quad (d)\;-\frac{1}{2} log \bigg\{cosec \bigg(x+\frac{\pi}{3}\bigg)+\cot \bigg(x+\frac{\pi}{3}\bigg)\bigg\}\end{array}

asked Jan 30, 2013 by meena.p

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$\Large\int \frac {\sqrt {\tan x}}{\sin x \cos x} \normalsize dx=$\[(a)\;2\sqrt {\tan x} \qquad (b)\;2\sqrt {\cot x} \qquad(c)\;\sqrt {\cot x} \qquad(d)\;\sqrt {\tan x}\]

asked Jan 30, 2013 by meena.p

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$\Large\int \frac {\tan (log)x} {x} dx=$\[(a)\;log\cos (log x) \qquad (b)\;log\sec (log x)\qquad(c)\;log\sin (log x) \qquad(d)\;-log\cos (log x)\]

asked Jan 30, 2013 by meena.p

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choose the correct alternative$ \int \large\frac {\cos \sqrt x}{\sqrt x} dx=$\[(a)\;\sin \sqrt x \qquad (b)\;2\cos \sqrt x\qquad(c)\;2\sin \sqrt x \qquad(d)\;\large\frac{\sqrt \cos x}{x}\]

asked Jan 30, 2013 by meena.p

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Find the maximum profit that a company can make if the profit function is given by \[P(x)=41-24x-18x^2\]

asked Jan 30, 2013 by meena.p

1 answer

Find the sides of a rectangle of greatest area that can be inscribed in the ellipse $ x^2+4y^2=16$

asked Jan 30, 2013 by meena.p

1 answer

A poster is to contain $50cm^2$ of matter with borders of 4 cm at top and bottom and of 2 cm on each side. Find the dimensions if the total area of the poster is minimum.

asked Jan 30, 2013 by meena.p

1 answer

Two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of 3cm/sec. How fast is the area decreasing when the two equal sides are equal to the base?

asked Jan 30, 2013 by meena.p

1 answer

Find the local maximum and local minimum value of the function. \[f(x)=\sin x+\frac{1}{2}\cos 2x\;in\;[0,\pi/2]\]

asked Jan 30, 2013 by meena.p

1 answer

Find two positive numbers x and y such that their sum is 16 and sum of whose cubes is minimum.

asked Jan 30, 2013 by meena.p

1 answer

Find the interval in which $ y=x^2e^{-x}$ is increasing.

asked Jan 30, 2013 by meena.p

1 answer

Find the intervals in which f(x) = logcosx is strictly decreasing and strictly increasing.

asked Jan 30, 2013 by meena.p

1 answer

At what point in the interval $ [0,2\pi] $ does the function $\sin2x$ attain its maximum value?

asked Jan 30, 2013 by meena.p

1 answer

Without using derivatives find the maximum and minimum value of $ f(x) = \sin2x+7 $

asked Jan 30, 2013 by meena.p

1 answer

Without using derivatives find the maximum or minimum value of $ f(x)=-| x+5 |+3$

asked Jan 30, 2013 by meena.p

0 answers

Find the maxima or minima if any of the function $f(x)=\Large\frac{1}{x^2+2}$

asked Jan 30, 2013 by meena.p

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FInd the local maxima and local minima if any of the function $f(x)=e^{5x}$

asked Jan 30, 2013 by meena.p

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The curve $ y=ax^3+6x^2+bx+5$ touches the x-axis at P(-2,0) and cuts the y-axis at a point Q where its gradient is 3. Find a,b,c.

asked Jan 30, 2013 by meena.p

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Find the maximum and minimum value of $ f(x)=| (\sin 4x+5) |$ without using derivatives.

asked Jan 30, 2013 by meena.p

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Find the maximum and minimum values of 'f', if any of the function $ f(x) = | x |,x \in R$

asked Jan 30, 2013 by meena.p

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Find the approximate value of $ 2x^4-160=0 $

asked Jan 30, 2013 by meena.p

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Using differentials evaluate $\tan 44^\circ approximately, 1^\circ=0.07145^\circ$

asked Jan 30, 2013 by meena.p

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Use differentials to evaluate $ \bigg(\large\frac{17}{81}\bigg)^{1/4}$ approximately.

asked Jan 30, 2013 by meena.p

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Find the appropriate change in volume of a cube when side increases by 1%.

asked Jan 30, 2013 by meena.p

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If $ y=x^4-10 $ and if x changes from 2 to 1.97, what is the appropriate change in y ?

asked Jan 30, 2013 by meena.p

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Using differentials find the appropriate value of $(82)^{1/4}$

asked Jan 30, 2013 by meena.p

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Find the angle between the parabolas $ y^2=4ax\;and\;x^2=4by$ at their point of intersection other than the origin.

asked Jan 30, 2013 by meena.p

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FInd the equation of the tangent to the curve $\sqrt x+ \sqrt y =a$ at the point $\bigg(\large\frac{a^2}{4},\frac{a^2}{4}\bigg)$

asked Jan 30, 2013 by meena.p

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FInd the equation of tangent and normal to the curve $ y^2=\large\frac{x^3}{4-x}$ at (2,-2)

asked Jan 30, 2013 by meena.p

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Find the equations of the normal lines to the curve $ y=4x^3-3x+5$ which are parallel to the line $9y+x+3=0$

asked Jan 30, 2013 by meena.p

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Find equation of tangents to the curve $ x=a\cos ^3 \theta,y=b\sin ^3 \theta $ at $\theta=\pi/4$

asked Jan 30, 2013 by meena.p

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Find the points on the curve $\large\frac{x^2}{4}+\frac{y^2}{25}=1$ at which the tangents are parallel to x-axis and parallel to y-axis.

asked Jan 30, 2013 by meena.p

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Find the interval on which the function $ \large\frac{x}{log x}$ is increasing or decreasing.

asked Jan 29, 2013 by meena.p

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FInd the interval in which $f(x)=8+36x+3x^2-2x^3$ is increasing or decreasing.

asked Jan 29, 2013 by meena.p

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Find the interval in[0,2\pi] in which the function $ \Large\frac{-4.\sin x+2x+x \cos x}{2+\cos x}$ is increasing or decreasing.

asked Jan 29, 2013 by meena.p

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Find whether $ f(x)=\cos (2x+\pi/4)\:is\:increasing\:or\:decreasing\:in\:(\frac{3\pi}{8},\frac{5\pi}{8})$ .

asked Jan 29, 2013 by meena.p

0 answers

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