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Recent questions tagged isc
Questions
Write the Boolean expression for the following circuit :
isc
class12
modelpaper
2004
part-2
sec-b
q10
q10-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Prove the right cancellation law in a group.
isc
class12
modelpaper
2004
part-2
sec-b
q9
q9-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Consider the non empty set S={0,1,2,3,4}.Show that $(S,\oplus_5)$ is a group where $\oplus_5$ represents addition modulo 5.Also find 'x' if $x\oplus_5$ 3=4,$x\in S$.
isc
class12
modelpaper
2004
part-2
sec-b
q9
q9-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Find the unit vector perpendicular to the two vectors $\overrightarrow{i}+2\overrightarrow{j}-\overrightarrow{k}$ and $2\overrightarrow{i}+3\overrightarrow{j}+\overrightarrow{k}$.
isc
class12
modelpaper
2004
part-2
sec-b
q8
q8-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Show that the sum of the squares on the sides a parallelogram is equal to the sum of the squares on the diagonals of the parallelogram.
isc
class12
modelpaper
2004
part-2
sec-b
q8
q8-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
If $x=\sin^3t$ and $y=a\cos^3t$,find $\large\frac{dy}{dx}$.
isc
class12
modelpaper
2004
part-2
sec-a
q7
q7-b
asked
Apr 19, 2013
by
sreemathi.v
0
answers
Sketch and shade the area of the region lying in the first quadrant and bound by $y=9x^2,x=0,y=1$ and $y=4$.Find the area of the shaded region.
isc
class12
modelpaper
2004
part-2
sec-a
q7
q7-a
asked
Apr 19, 2013
by
sreemathi.v
0
answers
A closed circular cylinder has a volume of 2156c.c.What will be the radius of its base so that its total surface area is minimum.Find the height of the cylinder when its total surface area is minimum.
isc
class12
modelpaper
2004
part-2
sec-a
q6
asked
Apr 19, 2013
by
sreemathi.v
1
answer
Evaluate :$\Large \int_{\normalsize 0}^{\large \frac{1}{2}} \large \frac{\sin^{-1}x}{(1-x^2)^\frac{3}{2}}$$dx$
isc
class12
modelpaper
2004
part-2
sec-a
q5
q5-b
asked
Apr 18, 2013
by
sreemathi.v
0
answers
show that the function $f(x)=x^2-6x+1$ satisfies the Lagrange's Mean value Theoem.Also find the co-ordinate of a point at which the tangent to the curve represented by the above function is parallel to the chord joining A(1,-4) and B(3,-8).
isc
class12
modelpaper
2004
part-2
sec-a
q5
q5-a
asked
Apr 18, 2013
by
sreemathi.v
1
answer
Find the equation of a plane through the point (-1,-1,2) and perpendicular to the planes $3x+2y-3z=1$ and $5x-4y+z=5.$
isc
class12
modelpaper
2004
part-2
sec-a
q4
q4-b
asked
Apr 18, 2013
by
sreemathi.v
0
answers
Find the radius of the circular section of the sphere $x^2+y^2+z^2=49$ cut by a plane $2x+3y-z-5\sqrt{14}=0.$
isc
class12
modelpaper
2004
part-2
sec-a
q4
q4-a
asked
Apr 18, 2013
by
sreemathi.v
0
answers
Find the equation of a pair of straight lines represented by $8x^2+8xy+2y^2+26x+13y+5=0$ and show that the angle between them is $0^{\circ}$.
isc
class12
modelpaper
2004
part-2
sec-a
q3
q3-b
asked
Apr 18, 2013
by
sreemathi.v
0
answers
If $A=\begin{pmatrix}3 & -4\\1 & -1\end{pmatrix}$,show by mathematical induction that for any positive integer n, $A^n=\begin{pmatrix}1+2n&-4n\\n &1-2n\end{pmatrix}$
isc
class12
modelpaper
2004
part-2
sec-a
q3
q3-a
asked
Apr 18, 2013
by
sreemathi.v
0
answers
If $C_0,C_1,C_2..........C_n$ denote the coefficient of successive terms in the expansion of the binomial $(1+x)^n$ prove that $C_0+C_2+C_4+.........=C_1+C_3+C_5+.....=2^{n-1}$
isc
class12
modelpaper
2004
part-2
sec-a
q2
q2-b
asked
Apr 18, 2013
by
sreemathi.v
0
answers
If $x\neq y\neq z$ and $\begin{vmatrix}x& x^2 & 1+x^3\\y & y & 1+y^3\\z & z^2 & 1+z^3\end{vmatrix}=0$.Then show that $xyz=-1$.
isc
class12
modelpaper
2004
part-2
sec-a
q2
q2-a
asked
Apr 18, 2013
by
sreemathi.v
0
answers
If $i=\sqrt{-1}$,prove the following : $(x+1+i)(x+1-i)(x-1+i)(x-1-i)=x^4+4$
isc
class12
modelpaper
2004
part-1
sec-a
q1
q1-10
asked
Apr 18, 2013
by
sreemathi.v
0
answers
Prove that $2(\tan^{-1}1+\tan^{-1}\large\frac{1}{2}\normalsize+\tan^{-1}\large\frac{1}{3}\normalsize)=\pi$
isc
class12
modelpaper
2004
part-1
sec-a
q1
q1-9
asked
Apr 18, 2013
by
sreemathi.v
0
answers
Integrate : $\int\large\frac{1+\tan^2x}{\sqrt{1+\tan^2x}}\normalsize dx$.
isc
class12
modelpaper
2004
part-1
sec-a
q1
q1-8
asked
Apr 18, 2013
by
sreemathi.v
0
answers
If the matrix $A=\begin{pmatrix}2 & 3\\5 & -2\end{pmatrix}$,show that $A^{-1}=\large\frac{1}{19}\normalsize A.$
isc
class12
modelpaper
2004
part-1
sec-a
q1
q1-7
asked
Apr 18, 2013
by
sreemathi.v
0
answers
If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two vectors such that $\mid \overrightarrow{a}+\overrightarrow{b}\mid=\mid\overrightarrow{a}\mid $ then show that vector $(2\overrightarrow{a}+\overrightarrow{b})$ is perpendicular to $\overrightarrow{b}$.
isc
class12
modelpaper
2004
part-1
sec-a
q1
q1-6
asked
Apr 18, 2013
by
sreemathi.v
0
answers
What is the probability that a leap year has 53 Sundays?
isc
class12
modelpaper
2004
part-1
sec-a
q1
q1-5
asked
Apr 18, 2013
by
sreemathi.v
0
answers
Find the angle between the line $\large\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$ and the plane $x+y+2z=0.$
isc
class12
modelpaper
2004
part-1
sec-a
q1
q1-4
asked
Apr 18, 2013
by
sreemathi.v
0
answers
If $x^yy^x$=5 show that $\large\frac{dy}{dx}=-\begin{pmatrix}\large\frac{\log y+\Large\frac{y}{x}}{\log x+\Large\frac{x}{y}}\end{pmatrix}$
isc
class12
modelpaper
2004
part-1
sec-a
q1
q1-3
asked
Apr 18, 2013
by
sreemathi.v
0
answers
The directrix of a conic section is $3x+4y=1$ and focus is (2,3).Find the equation of the conic section if its eccentricity is $\large\frac{1}{\sqrt 2}$
isc
class12
modelpaper
2004
part-1
sec-a
q1
q1-2
asked
Apr 18, 2013
by
sreemathi.v
0
answers
Find the value of 'p' for which the following equation represents a pair of straight lines : $x^2+pxy-2y^2+3gx+3fy=0.$
isc
class12
modelpaper
2004
part-1
sec-a
q1
q1-1
asked
Apr 18, 2013
by
sreemathi.v
0
answers
A coin is tossed 5 times.What is the probability of getting at least three heads?
isc
class12
modelpaper
2005
sec-c
q15
q15-b
asked
Apr 18, 2013
by
sreemathi.v
0
answers
A manufacturing firm produces steel pipes in three plants A,B and C with daily production of 500,1000 and 2000 units respectively.The fractions of defective steel pipes output produced by the plants A,B and C are respectively .005, .008 and .010.If a pipe is selected from a day's total production and found to be defective,find out the probability that it came from the first plant.
isc
class12
modelpaper
2005
sec-c
q15
q15-a
asked
Apr 18, 2013
by
sreemathi.v
1
answer
A company is selling a certain product.The demand function of the product is linear.The company can sell 2000 units when the price is Rs.8 per unit and when the price is Rs.4 per unit,it can sell 3000 units,Determine :
isc
class12
modelpaper
2005
sec-c
q14
q14-b
asked
Apr 18, 2013
by
sreemathi.v
1
answer
How much should a company set aside at the end of each year if it has to buy a machine expected to cost Rs.100,000 at the end of 4 years and the rate of interest is 5% per annum compounded annually?
isc
class12
modelpaper
2005
sec-c
q14
q14-a
asked
Apr 18, 2013
by
sreemathi.v
0
answers
Find the amount of an ordinary annuity if payment of Rs.600.00 is made at the end of every quarter for 10 years at the rate of 4% per year compounded quarterly?
isc
class12
modelpaper
2005
sec-c
q13
q13-b
asked
Apr 18, 2013
by
sreemathi.v
0
answers
A bill of exchange for Rs.750.00 was drawn on 3rd April,2000 payable at 3 months after date.It was discounted on 24th April,2000 at 5% per annum.What was the discounted value of the bill?
isc
class12
modelpaper
2005
sec-c
q13
q13-a
asked
Apr 18, 2013
by
sreemathi.v
0
answers
The average number,in lakhs,of working days lost in strikes during each year of the period 1981-90 was :
isc
class12
modelpaper
2005
sec-b
q12
q12-b
asked
Apr 18, 2013
by
sreemathi.v
0
answers
Calculate the index number for the year 1979 with 1970 as base from the following data using weighted average of price relatives :
isc
class12
modelpaper
2005
sec-b
q12
q12-a
asked
Apr 18, 2013
by
sreemathi.v
0
answers
Prove that $\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})\times (\overrightarrow{a}+2\overrightarrow{b}+3\overrightarrow{c})=[\overrightarrow{a}\;\overrightarrow{b}\;\overrightarrow{c}].$
isc
class12
modelpaper
2005
sec-b
q11
q11-b
asked
Apr 17, 2013
by
sreemathi.v
0
answers
$\overrightarrow{a}$ and $\overrightarrow{b}$ are unit vectors such that $2\overrightarrow{a}-4\overrightarrow{b}$ and $10\overrightarrow{a}+8\overrightarrow{b}$ are perpendicular to each other.Find the angle between the vectors $\overrightarrow{a}$ and $\overrightarrow{b}.$
isc
class12
modelpaper
2005
sec-b
q11
q11-a
asked
Apr 17, 2013
by
sreemathi.v
0
answers
Find the least distance of the plane $12x+4y+3z=327$ from the sphere $x^2+y^2+z^2+4x-2y-6z=155.$
isc
class12
modelpaper
2005
sec-b
q10
q10-b
asked
Apr 17, 2013
by
sreemathi.v
0
answers
A plane passes through the point (4,2,4) and is perpendicular to the planes $2x+5y+4z+1=0$ and $4x+7y+6z+2=0$.Find the equation of the plane.
isc
class12
modelpaper
2005
sec-b
q10
q10-a
asked
Apr 17, 2013
by
sreemathi.v
1
answer
Solve the differential equation : $\tan x\large\frac{dy}{dx}\normalsize+2y=\sec x$
isc
class12
modelpaper
2005
sec-a
q9
q9-b
asked
Apr 17, 2013
by
sreemathi.v
0
answers
Using Demoivre's theorem,find the least value of $n\in N$ for which the expression $(i+1)^n+(1-i)^n$ is equal to $-2^{\large\frac{n+2}{2}}$
isc
class12
modelpaper
2005
sec-a
q9
q9-a
asked
Apr 17, 2013
by
sreemathi.v
0
answers
A candidate is selected for interview of management trainees for 3 companies.For the first company,there are 12 candidates,for the second there are 15 candidates and for the third,there are 10 candidates.Find the probability that he is selected in at least one of the companies.
isc
class12
modelpaper
2005
sec-a
q8
q8-b
asked
Apr 17, 2013
by
sreemathi.v
1
answer
In a certain city,the probability of not reading the morning newspaper by the residents is $\large\frac{1}{2}$ and that of not reading the evening newspaper is $\large\frac{2}{5}$.The probability of reading both the newspapers is $\large\frac{1}{5}$.Find the probability that a resident reads either the morning or evening or both the papers.
isc
class12
modelpaper
2005
sec-a
q8
q8-a
asked
Apr 17, 2013
by
sreemathi.v
0
answers
There are two series of index numbers : P for price index and S for stock of a commodity.The mean and standard deviation of P are 100 and 8 and of S are 103 and 4 respectively.The correlation coefficient between the two series is 0.4,with these data,obtain the regression lines of P on S and S on P.
isc
class12
modelpaper
2005
sec-a
q7
q7-b
asked
Apr 17, 2013
by
sreemathi.v
1
answer
Internal and External assessments were conducted on a group of 10 students who were studying in a post graduate class in a college.The following marks were obtained in the assessments :
isc
class12
modelpaper
2005
sec-a
q7
q7-a
asked
Apr 17, 2013
by
sreemathi.v
0
answers
Calculate the area bounded by the curve $y=x(2-x)$ and the lines $x=0,y=0,x=2$.This area is rotated through four right angles about the $x$-axis.Calculate the volume of the solid so formed.
isc
class12
modelpaper
2005
sec-a
q6
q6-b
asked
Apr 17, 2013
by
sreemathi.v
0
answers
Prove that $\int_0^{\large\frac{\pi}{2}}\large\frac{3\sin\theta+4\cos\theta}{\sin\theta+\cos\theta}\normalsize d\theta=\large\frac{7\pi}{4}$
isc
class12
modelpaper
2005
sec-a
q6
q6-a
asked
Apr 17, 2013
by
sreemathi.v
0
answers
Prove that the area of right-angled traingle of a given hypotenuse is maximum when the triangle is isosceles.
isc
class12
modelpaper
2005
sec-a
q5
q5-b
asked
Apr 17, 2013
by
sreemathi.v
0
answers
Examine the validity and conclusion of Rolle's theorem for the function $f(x)=e^x\sin x,\forall x\in [0,\pi]$.
isc
class12
modelpaper
2005
sec-a
q5
q5-a
asked
Apr 17, 2013
by
sreemathi.v
0
answers
If $x^py^q=(x+y)^{p+q}$.Prove that $\large\frac{dy}{dx}=\large\frac{y}{x}$.
isc
class12
modelpaper
2005
sec-a
q4
q4-b
asked
Apr 17, 2013
by
sreemathi.v
0
answers
Prove that : $\cot \begin{pmatrix}\large\frac{\pi}{4}\normalsize -2\cot^{-1}3\end{pmatrix}=7.$
isc
class12
modelpaper
2005
sec-a
q4
q4-a
asked
Apr 17, 2013
by
sreemathi.v
0
answers
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