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Questions >> ISC XII Math >> Model Papers

The mathematical aptitude score (MAS) of ten computer programmers with job performance rating (JPR) is given below.Calculate Spearman's rating of rank correlation and state whether those who have aptitude for maths are likely to be better programmers.

asked Apr 19, 2013 by sreemathi.v

0 answers

If a,b,c are elements of Boolean Algebra,prove that $ab+c(a'+b')=ab+c$.

asked Apr 19, 2013 by sreemathi.v

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Write the Boolean expression for the following circuit :

asked Apr 19, 2013 by sreemathi.v

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Prove the right cancellation law in a group.

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,$x\in S$.

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 $2\overrightarrow{i}+3\overrightarrow{j}+\overrightarrow{k}$.

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.

asked Apr 19, 2013 by sreemathi.v

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If $x=\sin^3t$ and $y=a\cos^3t$,find $\large\frac{dy}{dx}$.

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.

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.

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$

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).

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 $5x-4y+z=5.$

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 $2x+3y-z-5\sqrt{14}=0.$

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 $0^{\circ}$.

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, $A^n=\begin{pmatrix}1+2n&-4n\\n &1-2n\end{pmatrix}$

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 $C_0+C_2+C_4+.........=C_1+C_3+C_5+.....=2^{n-1}$

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 $xyz=-1$.

asked Apr 18, 2013 by sreemathi.v

0 answers

If $i=\sqrt{-1}$,prove the following : $(x+1+i)(x+1-i)(x-1+i)(x-1-i)=x^4+4$

asked Apr 18, 2013 by sreemathi.v

0 answers

Prove that $2(\tan^{-1}1+\tan^{-1}\large\frac{1}{2}\normalsize+\tan^{-1}\large\frac{1}{3}\normalsize)=\pi$

asked Apr 18, 2013 by sreemathi.v

0 answers

Integrate : $\int\large\frac{1+\tan^2x}{\sqrt{1+\tan^2x}}\normalsize dx$.

asked Apr 18, 2013 by sreemathi.v

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If the matrix $A=\begin{pmatrix}2 & 3\\5 & -2\end{pmatrix}$,show that $A^{-1}=\large\frac{1}{19}\normalsize A.$

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 $\overrightarrow{b}$.

asked Apr 18, 2013 by sreemathi.v

0 answers

What is the probability that a leap year has 53 Sundays?

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 $x+y+2z=0.$

asked Apr 18, 2013 by sreemathi.v

0 answers

If $x^yy^x$=5 show that $\large\frac{dy}{dx}=-\begin{pmatrix}\large\frac{\log y+\Large\frac{y}{x}}{\log x+\Large\frac{x}{y}}\end{pmatrix}$

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 $\large\frac{1}{\sqrt 2}$

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 : $x^2+pxy-2y^2+3gx+3fy=0.$

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?

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.

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 :

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?

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?

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?

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 :

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 :

asked Apr 18, 2013 by sreemathi.v

0 answers

Prove that $\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})\times (\overrightarrow{a}+2\overrightarrow{b}+3\overrightarrow{c})=[\overrightarrow{a}\;\overrightarrow{b}\;\overrightarrow{c}].$

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 $\overrightarrow{b}.$

asked Apr 17, 2013 by sreemathi.v

0 answers

Find the least distance of the plane $12x+4y+3z=327$ from the sphere $x^2+y^2+z^2+4x-2y-6z=155.$

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.

asked Apr 17, 2013 by sreemathi.v

1 answer

Solve the differential equation : $\tan x\large\frac{dy}{dx}\normalsize+2y=\sec x$

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 $-2^{\large\frac{n+2}{2}}$

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.

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.

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.

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 :

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.

asked Apr 17, 2013 by sreemathi.v

0 answers

Prove that $\int_0^{\large\frac{\pi}{2}}\large\frac{3\sin\theta+4\cos\theta}{\sin\theta+\cos\theta}\normalsize d\theta=\large\frac{7\pi}{4}$

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.

asked Apr 17, 2013 by sreemathi.v

0 answers

Examine the validity and conclusion of Rolle's theorem for the function $f(x)=e^x\sin x,\forall x\in [0,\pi]$.

asked Apr 17, 2013 by sreemathi.v

0 answers

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