Recent questions in Model Papers

If $x^py^q=(x+y)^{p+q}$.Prove that $\large\frac{dy}{dx}=\large\frac{y}{x}$.

asked Apr 17, 2013 by sreemathi.v

0 answers

Prove that : $\cot \begin{pmatrix}\large\frac{\pi}{4}\normalsize -2\cot^{-1}3\end{pmatrix}=7.$

asked Apr 17, 2013 by sreemathi.v

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Find the angle and the equation of the bisectors of the angle between the pair of lines given by $2x^2-7xy+3y^2=0$.

asked Apr 17, 2013 by sreemathi.v

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The equation $2x^2-3xy-py^2+x+qy=0$ represents two perpendicular lines.Find the values of $p$ and $q$.

asked Apr 17, 2013 by sreemathi.v

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Given the matrix $A=\begin{vmatrix}1 & 0 & 2\\-2 & 1 & 0\\0 & -1 & 2\end{vmatrix}$,compute $A^{-1}$.

asked Apr 17, 2013 by sreemathi.v

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Using properties of determinants,show that $\begin{vmatrix}a^2+1 & ab & ac\\ba & b^2+1 & bc\\ca & cb & c^2+1\end{vmatrix}=a^2+b^2+c^2+1$

asked Apr 17, 2013 by sreemathi.v

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Solve the following differential equation : $\large\frac{dy}{dx}\normalsize-e^{y+x}=e^{x-y}$

asked Apr 17, 2013 by sreemathi.v

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Find the amplitude of the complex number $\sin\large\frac{6\pi}{5}\normalsize+i\begin{pmatrix}1-\cos\large\frac{6\pi}{5}\end{pmatrix}$.

asked Apr 17, 2013 by sreemathi.v

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A performance test was conducted among seven candidates.They scored the following marks : 7,10,12,15,17,19,25.Calculate the interquartile range and the standard deviation.

asked Apr 17, 2013 by sreemathi.v

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Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random.What is the probability that the ticket has a number which is a multiple of 3 or 7.

asked Apr 17, 2013 by sreemathi.v

1 answer

The points (0,4) and (0,2) are the vertex and focus of a parabola.Find the equation of the parabola.

asked Apr 17, 2013 by sreemathi.v

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Evaluate $\int\large\frac{\cos x}{\sin x+\sqrt \sin x}\normalsize dx.$

asked Apr 17, 2013 by sreemathi.v

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If $\sin(xy)+\cos(xy)=1$ and $\tan(xy)\neq 1$,then show that $\large\frac{dy}{dx}=-\frac{y}{x}$

asked Apr 17, 2013 by sreemathi.v

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Find the foci and latus rectum for the hyperbola $\large\frac{x^2}{4}-\frac{y^2}{5}=\frac{1}{2}$

asked Apr 17, 2013 by sreemathi.v

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A straight line $y=mx$ passes through the intersection of the straight lines $x+2y-1=0$ and $2x-y+3=0.$Find the value of m.

asked Apr 17, 2013 by sreemathi.v

1 answer

Given that $A=\begin{bmatrix}\cos x & \sin x\\-\sin x& \cos x\end{bmatrix}$ and $A(adj. A)=K\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$,find the value of K.

asked Apr 17, 2013 by sreemathi.v

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A company has two plants which manufacture scooters.Plant I manufactures 80% of the scooters while Plant II manufactures 20% of the scooters.At plant I ,85 out of 100 scooters are rated as being of standard quality,while at Plant II only 65 out of 100 scooters are rated as being of standard quality.If a scooter is of standard quality,what is the probability that it came from Plant I?

asked Apr 17, 2013 by sreemathi.v

1 answer

Four dice are thrown simultaneously.If the occurrence of an odd number in a single dice is considered a success,find the probability of at most 2 successes.

asked Apr 17, 2013 by sreemathi.v

0 answers

A television manufacturer finds that the total cost for the production and marketing of $x$ number of television sets is : $c(x)=300x^2+4200x+13,500.$Each product is sold for Rs.8,400.Determine the break-even points.

asked Apr 17, 2013 by sreemathi.v

2 answers

Mr.Agarwal buys goods worth Rs.2,800 payable 8 months. Hence he pays Rs.400 at the end of the second month and Rs.600 at the end of the third month.Find the number of months after which the balance will become due.

asked Apr 17, 2013 by sreemathi.v

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The price of a tape recorder is Rs. 1,561.A person purchases it by paying Rs. 300 in cash and the balance is to be paid with due interest in 3 half yearly equal installments.If the dealer charges interest at the rate of 10% per annum compounded half yearly,find the value of each installment.

asked Apr 17, 2013 by sreemathi.v

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Find the Banker's discount and the discounted value of a bill worth Rs.600 drawn on May 15,2005 for 3 months and discounted on July 20,2005 at 5% per annum.

asked Apr 17, 2013 by sreemathi.v

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The table below gives details of the electricity generated in million kilowatt hours in each quarter for the years 2002 to 2004.

asked Apr 17, 2013 by sreemathi.v

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The quotations for four different commodities for the years 2000 and 2005 are given below.Calculate the index number for 2005 with 2000 as the base year by using the weighted average of price relatives method.

asked Apr 17, 2013 by sreemathi.v

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The vectors $\hat{i}+3\hat{j},5\hat{k}$ and $\lambda\hat{i}-\hat{j}$ are coplanar.Find the value of $\lambda$.

asked Apr 17, 2013 by sreemathi.v

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The vectors $-2\hat{i}+4\hat{j}+4\hat{k}$ and $-4\hat{i}-2\hat{k}$ represent the diagonals BD and AC of a parallelogram ABCD.Find the area of the parallelogram.

asked Apr 17, 2013 by sreemathi.v

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Show that the equation to a sphere passing through three points (2,0,0),(0,2,0) and (0,0,2) and having its centre on the plane $2x+3y+4z=27$ is $x^2+y^2+z^2-6x-6y-6z+8=0.$

asked Apr 17, 2013 by sreemathi.v

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Find the equations to be two planes passing through the points (0,4,-3) and (6,-4,3),if the sum of their intercepts on the three axes is zero.

asked Apr 17, 2013 by sreemathi.v

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

asked Apr 16, 2013 by sreemathi.v

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Find the cube roots of -27 and show that the sum of the cube roots is equal to zero.

asked Apr 16, 2013 by sreemathi.v

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A card is drawn at random from a pack of 52 playing cards.What is the probability that the card drawn is neither a spade nor a queen?

asked Apr 16, 2013 by sreemathi.v

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A and B throw two dice each.If A gets a sum of 9 on his two dice ,then find the probability of B getting a higher sum.

asked Apr 16, 2013 by sreemathi.v

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The following table shows the sales and advertisement expenditure of a firm :

asked Apr 16, 2013 by sreemathi.v

1 answer

Calculate Spearman's rank correlation coefficient between the advertisement cost and sales from the following data :

asked Apr 16, 2013 by sreemathi.v

1 answer

The region bounded by the curve $y^2=x(x-1)^2$,the x-axis and the lines $x=1,x=0$,is rotated through four right angles about the x-axis.Calculate the volume of the solid of revolution so formed.

asked Apr 16, 2013 by sreemathi.v

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Prove that $\int_0^{2\pi}\large\frac{x\cos x}{1+\cos x}\normalsize dx=2{\pi}^2.$

asked Apr 16, 2013 by sreemathi.v

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Find the volume of the largest cone that can be inscribed in a sphere of radius R.

asked Apr 16, 2013 by sreemathi.v

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Verify Rolle's theorem for the function $f(x)=e^{2x}(\sin 2x-\cos 2x)$ defined in the interval $\begin{bmatrix}\large\frac{\pi}{8},\frac{5\pi}{8}\end{bmatrix}$

asked Apr 16, 2013 by sreemathi.v

1 answer

If $y=\large\frac{\sin^{-1}x}{\sqrt{1-x^2}}$,prove that $(1-x^2)\large\frac{dy}{dx}-\normalsize xy=1.$

asked Apr 16, 2013 by sreemathi.v

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Show that : $\sin^{-1}\bigg(\large\frac{1}{\sqrt {17}}\bigg)\normalsize+\cos^{-1}\bigg(\large\frac{9}{\sqrt{85}}\bigg)\normalsize=\tan^{-1}\bigg(\large\frac{1}{2}\bigg).$

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the equation of the bisectors of the angle between the pair of lines given by $(4ax+3by)^2=3(3bx-4ay)^2$

asked Apr 16, 2013 by sreemathi.v

0 answers

Show that the equation $x^2-3xy+2y^2+3x-5y+2=0$ represents two straight lines.Find the angle between them.

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the adjoint of the matrix A=$\begin{bmatrix}1 & 0 & -1\\3 & 4 & 5\\0 &-6 &-7\end{bmatrix}$ and hence find the matrix $A^{-1}$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Show that : $\begin{vmatrix}1 & 1 & 1\\{\alpha}^2 &{\beta}^2 &{\gamma}^2\\{\alpha}^3 &{\beta}^3 &{\gamma}^3\end{vmatrix}=(\alpha-\beta)(\beta-\gamma)(\gamma-\alpha)(\alpha\beta+\beta\gamma+\alpha\gamma)$.

asked Apr 16, 2013 by sreemathi.v

0 answers

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

asked Apr 16, 2013 by sreemathi.v

0 answers

Express $\large\frac{1-2i}{2+i}+\frac{3+i}{2-i}$ in the form $ a+ib$.

asked Apr 16, 2013 by sreemathi.v

0 answers

One set of 100 observations has the mean as 15 and another set of 150 observations has the mean as 16.Find the mean of 250 observations by combining the two sets of given observations.

asked Apr 16, 2013 by sreemathi.v

1 answer

The probability of A,B and C solving a problem are $\large\frac{1}{3},\frac{2}{7}$ and $\large\frac{3}{8}$respectively.If all the three try and solve the problem simultaneously,find the probability that only one of them will solve it.

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the equation of the ellipse whose eccentricity is $\large\frac{1}{2}$ and whose foci are the points $(\pm 2,0).$

asked Apr 16, 2013 by sreemathi.v

0 answers

Evaluate $\int x^2(e^{x^3})\cos (2e^{x^3})dx.$

asked Apr 16, 2013 by sreemathi.v

0 answers

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