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Recent questions tagged 2012

Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: $ f (x) = \sin x+\cos x, x \in [0,\pi] $

asked Aug 7, 2013 by sreemathi.v

1 answer

Show that of all the rectangles with a given perimeter,the square has the largest area.

asked Jul 25, 2013 by sreemathi.v

0 answers

Differentiate \(( x \cos \: x )^x + ( x\sin\: x )^{\Large\frac{1}{x}}\) w.r.t. \( x \).

asked Jul 25, 2013 by sreemathi.v

1 answer

Find the value of x from the following : $\begin {vmatrix} x & 4 \\ 2 & 2x \end {vmatrix} = 0 $

asked Jul 19, 2013 by sreemathi.v

1 answer

Obtain the inverse of the following matrix using elementary operations :$A=\begin{bmatrix}3 & 0 & -1\\2 & 3 & 0\\0 & 4& 1\end{bmatrix}$

asked Jul 18, 2013 by sreemathi.v

1 answer

Calculate the 5 yearly moving averages of the number of students in a college from the following data and plot them on a graph paper :

asked Apr 11, 2013 by sreemathi.v

0 answers

Find the consumer price index number for the year 2010 using year 2000 as the base year by using method of weighted aggregates :

asked Apr 10, 2013 by sreemathi.v

0 answers

If total cost function is given by $C=a+bx+cx^2$,where x is the quantity of output.Show that : $\frac{d}{dx}(AC)=\frac{1}{x}(MC-AC),$where $MC$ is the marginal cost and $AC$ is the average cost.

asked Apr 10, 2013 by sreemathi.v

1 answer

A bill of Rs. 1000 drawn on 7th May,2011 for six months was discounted on 29th August,2011 for cash payment of Rs. 988.Find the rate of interest charged by the bank.

asked Apr 10, 2013 by sreemathi.v

0 answers

A machine costs Rs 97,000 and its effective life is estimated to be 12 years.If scrap realises Rs. 2,000 only,what amount should be retained out of profits at the end of each year to accumulate at compound interest of 5% per annum in order to buy a new machine after 12 years?(use $1.05^{12}=1.769$)

asked Apr 10, 2013 by sreemathi.v

0 answers

Two tailors P and Q earn Rs. 150 and Rs. 200 per days respectively.P can stitch 6 shirts and 4 trousers a day,while Q can stitch 10 shirts and 4 trousers per day.How many days should each work to produce at least 60 shirts and 32 trousers at minimum labour cost?

asked Apr 10, 2013 by sreemathi.v

0 answers

The probability that a bulb produced by a factory will fuse in 100 days of use is 0.05.Find the probability that out of 5 such bulbs,after 100 days of use :

asked Apr 10, 2013 by sreemathi.v

0 answers

In a class of 75 students,15 are above average,45 are average and the rest below average achievers.The probability that an above average achieving student fails is 0.005,then an average achieving student fails is 0.05 and the probability of a below average achieving student failing is 0.15.If a student is known to have passed,what is the probability that he is a below average achiever?

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the equation of the plane passing through the line of intersection of the planes $x+2y+3z-5=0$ and $3x-2y-z+1=0$ and cutting off equal intercepts on the x and z axes.

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the shortest distance between the lines : $\large \frac{x-8}{3}=\frac{y+9}{-16}=\frac{z-10}{7}$ and $\large \frac{x-15}{3}=\frac{y-29}{8}=\frac{5-z}{-5}$

asked Apr 10, 2013 by sreemathi.v

0 answers

In any triangle ABC,prove by vector method : $\large \frac{a}{sin\;A}=\frac{b}{sin\;B}=\frac{c}{sin\;C}$

asked Apr 10, 2013 by sreemathi.v

0 answers

For any three vectors $\overline{a},\overline{b},\overline{c}$ prove :$[\;\overline{a}-\overline{b}\;\overline{b}-\overline{c}\;\overline{c}-\overline{a}\;]=0.$

asked Apr 10, 2013 by sreemathi.v

0 answers

Solve the differential equation :$\Large \frac{dy}{dx}\normalsize -3y cot\;x=sin \;2x$,given y=2,when $x=\Large \frac{\pi}{2}$

asked Apr 10, 2013 by sreemathi.v

0 answers

Using De Moivre's theorem prove that : $\bigg(\large \frac{1+cos\; \theta+isin\;\theta}{1+cos\; \theta-i sin\;\theta}\bigg)^n\normalsize$$ =cos \;n\theta+i \sin n\theta,$where $i=\sqrt {-1}.$

asked Apr 10, 2013 by sreemathi.v

0 answers

A box contains 30 bolts and 40 nuts .Half of the bolts and half of the nuts are rusted.If two items are drawn at random from the box,what is the probability that either both are rusted or both are bolts?

asked Apr 10, 2013 by sreemathi.v

0 answers

A bag contains 8 red and 5 white balls.Two successive draws of 3balls are made at random from the bag without replacements.Find the probability that the first draw yields 3 white balls and the second draw 3 red balls.

asked Apr 10, 2013 by sreemathi.v

0 answers

The following results were obtained with respect to two variable x and y :$\sum x=30,\sum y=42,\sum xy=199,\sum x^2=184,\sum y^2=318,n=6.$

asked Apr 10, 2013 by sreemathi.v

1 answer

Ten candidates received percentage marks in two marks in two subjects as follows:

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the area of the region bounded by the curves $x=4y-y^2$ and the y-axis.

asked Apr 10, 2013 by sreemathi.v

0 answers

Evaluate :$ \Large \int \frac{dx}{x\{6(log x)^2+7log x+2\}}$

asked Apr 10, 2013 by sreemathi.v

0 answers

A printed page is to have a total area of 80 sq.cm with a margin of 1 cm at the top and on each side and a margin of 1.5 cm at the bottom.What should be the dimensions of the page so that the printed area will be maximum?

asked Apr 10, 2013 by sreemathi.v

0 answers

If,$e^y(x+1)=1$,then show that : $\large \frac{d^2y}{dx^2}=\bigg(\frac{dy}{dx}\bigg)^2$

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the equation of the ellipse with its centre at $(4,-1)$ focus at $(1,-1)$ and given that it passes through $(8,0).$

asked Apr 10, 2013 by sreemathi.v

0 answers

Verify Rolle's theorem for the function : $f(x)=log\left \{\Large \frac{x^2+ab}{(a+b)+x}\right\}$ in the interval [a,b] where,$0 \notin [a,b]$.

asked Apr 10, 2013 by sreemathi.v

0 answers

$\begin{array}{1 1}(i)\text{ Write the Boolean expression corresponding to the circuit given below} : \\(ii) \text{ Simplify the expression using laws of Boolean Algebra and constract the simplified circuit.}\end{array}$

asked Apr 10, 2013 by sreemathi.v

0 answers

Prove that : $cos^{-1}\frac{63}{65}+2tan^{-1}\frac{1}{5}=sin^{-1}\frac{3}{5}$

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the product of the matrices A and B where : $A=\begin{pmatrix}-5 & 1 & 3\\7 & 1 &-5\\1 & -1 & 1\end{pmatrix},B=\begin{pmatrix}1 & 1 & 2\\3 & 2 & 1\\2 & 1& 3 \end{pmatrix}$Hence,solve the following equations by matrix method:$x+y+2z=1,3x+2y+z=7,2x+y+3z=2.$

asked Apr 10, 2013 by sreemathi.v

0 answers

Using properties of determinants,prove that : $\begin{vmatrix}a & a+b & a+b+c\\2a & 3a+2b & 4a+3b+2c\\3a & 6a+3b & 10a+6b+3c\end{vmatrix}=a^3$

asked Apr 10, 2013 by sreemathi.v

0 answers

Solve the differential equation : $(xy^2+x)dx+(x^2y+y)dy=0.$

asked Apr 10, 2013 by sreemathi.v

0 answers

Three persons A,B and C shoot to hit a target.If in trials,A hits the target 4 times in 5 shots,B hits 3 times in 4 shots and C hits 2 times in 3 trials.Find the probability that :

asked Apr 10, 2013 by sreemathi.v

1 answer

Evaluate : $\Large \int_1^2 \frac{\sqrt x}{\sqrt{3-x}+\sqrt x}\normalsize dx.$

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the locus of the complex number,Z=x+iy given $\bigg/ \Large \frac{x+iy-2i}{x+iy+2}\bigg/ \normalsize =\sqrt 2$.

asked Apr 10, 2013 by sreemathi.v

0 answers

Evaluate : $\lim_{x\to \Large {\frac{\pi}{2}}}(cos.log\;tan\;x).$

asked Apr 10, 2013 by sreemathi.v

0 answers

Evaluate : $\int e^x(tan \;x+log \;sec x)dx.$

asked Apr 10, 2013 by sreemathi.v

0 answers

If a matrix has 7 elements, what are the possible order it can have?

asked Apr 10, 2013 by sreemathi.v

1 answer

From the equations of the two regression lines,4x+3y+7=0 and 3x+4y+8=0,find :

asked Apr 10, 2013 by sreemathi.v

0 answers

Find the equation of the hyperbola whose Transverse and Conjugate axes are the x and y axes respectively,given that the length of conjugate axis is 5 and distance between the foci is 13.

asked Apr 10, 2013 by sreemathi.v

0 answers

Prove that $sec^2(tan^{-1}2)+cosec^2(cot ^{-1}3)=15.$

asked Apr 10, 2013 by sreemathi.v

0 answers

Solve for x and y if $\left(\begin{array}{c}x^2\\y^2\end{array}\right)+2\left(\begin{array}{c}2x\\3y\end{array}\right)=3\left(\begin{array}{c}7\\-3\end{array}\right)$

asked Apr 10, 2013 by sreemathi.v

0 answers

In the matrix $A=\begin{bmatrix} 2 & 5 & 19 & -7 \\ 35 & -2 & \frac{5}{2} & 12 \\ \sqrt 3 & 1 & -5 & 17 \end{bmatrix} $Write (iii) Write the elements $a_{13},a_{21}.a_{33},a_{24},a_{23}$ .

asked Apr 3, 2013 by sreemathi.v

1 answer

In the matrix $A=\begin{bmatrix} 2 & 5 & 19 & -7 \\ 35 & -2 & \frac{5}{2} & 12 \\ \sqrt 3 & 1 & -5 & 17 \end{bmatrix} $Write (ii) The number of elements .

asked Apr 3, 2013 by sreemathi.v

1 answer

Find the transpose of each of the following matrices : $ (iii)\begin{bmatrix} -1&5&6 \\ \sqrt 3 & 5&6\\2 &3&-1 \end{bmatrix} $.

asked Apr 3, 2013 by sreemathi.v

1 answer

Find the transpose of each of the following matrices : \( (ii)\begin{bmatrix} 1&-1 \\ 2 & 3 \end{bmatrix} \).

asked Apr 3, 2013 by sreemathi.v

1 answer

Find the value of x if : $ \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} = \begin{bmatrix} x & 3 \\ 2x & 5 \end{bmatrix} $

asked Apr 2, 2013 by sreemathi.v

1 answer

Write a unit vector in the direction of \( \overrightarrow a = 2\hat i - 6\hat j + 3\hat k.\)

asked Feb 17, 2013 by thanvigandhi_1

1 answer

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