Recent questions in ISC XII Math

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

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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

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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

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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

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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

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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

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

asked Apr 10, 2013 by sreemathi.v

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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

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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

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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

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

asked Apr 10, 2013 by sreemathi.v

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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

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

asked Apr 10, 2013 by sreemathi.v

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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

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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

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

asked Apr 10, 2013 by sreemathi.v

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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

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