Recent questions tagged modelpaper

A small industrial concern used three raw materials A,B and C in its manufacturing process.The prices of the materials was as shown below :

asked Apr 15, 2013 by sreemathi.v

0 answers

If $A(-1,4,-3)$ is one end of a diameter $AB$ of the sphere $x^2+y^2+z^2-2y+2z-15=0$ then find the coordinates of the other end point B.

asked Apr 15, 2013 by sreemathi.v

0 answers

Find the coordinates of the point where the line joining the points (1,-2,3) and (2,-1,5) cuts the plane $x-2y+3z=19$.Hence,find the distance of this point from the point (5,4,1).

asked Apr 15, 2013 by sreemathi.v

0 answers

Solve the following $(x^{2}+y^{2})\;dy$ =$ xy \;dx$

asked Apr 15, 2013 by poojasapani_1

1 answer

Solve : $(x^2+y^2)dx-2xydy=0$,given that $y=0$,when $x=1$.

asked Apr 15, 2013 by sreemathi.v

0 answers

If the ratio $\large\frac{z-i}{z-1}$ is purely imaginary,prove that the point $z$ lies on the circle whose centre is the point $\large\frac{1}{2}\normalsize(1+i)$ and radius is $\large\frac{1}{\sqrt 2}$.

asked Apr 15, 2013 by sreemathi.v

0 answers

The probability that a teacher will give an unannounced test during any class meeting is $\large\frac{1}{5}$.If a student is absent twice,find the probability that the student will miss at least one test.

asked Apr 15, 2013 by sreemathi.v

0 answers

There are 3 urns A,B and C.Urn A contains 4 red balls and 3 black balls.Urn B contains 5 red balls and 4 black balls.Urn C contains 4 red balls and 4 black balls.One ball is drawn from each of these urns.What is the probability that the 3 balls drawn consist of 2 red balls and 1 black ball?

asked Apr 15, 2013 by sreemathi.v

0 answers

Solve the following $(x+y)^2 \large\frac{dy}{dx}$=$1$

asked Apr 15, 2013 by poojasapani_1

1 answer

The data for marks in Physics and History obtained by ten students are given below :

asked Apr 15, 2013 by sreemathi.v

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The data for marks in Physics and History obtained by ten students are given below :

asked Apr 15, 2013 by sreemathi.v

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Draw a rough sketch of the curve $y^2+1=x,x\leq 2$.Find the area enclosed by the curve and the line $x=2$.

asked Apr 15, 2013 by sreemathi.v

1 answer

Evaluate $\int_0^9f(x)$ dx,where f(x) is defined by $f(x)=\left\{\begin{array}{1 1}\sin x;if 0\leq x\leq \large\frac{\pi}{2}\\1;\large\frac{\pi}{2}\normalsize\leq x\leq 5\\e^{x-5};5\leq x\leq 9\end{array}\right.$

asked Apr 15, 2013 by sreemathi.v

0 answers

An open box with a square base is to be made out of a given quantity of cardboard whose area is $c^2$ square units.Show that the maximum volume of the box is $\large\frac{c^3}{6\sqrt 3}$cubic units.

asked Apr 15, 2013 by sreemathi.v

0 answers

Use Lagrange's mean value theorem to be determine a point P on the curve $y=\sqrt{x-2}$ defined in the interval [2,-3],where the tangent is parallel to the chord joining the end points on the curve.

asked Apr 15, 2013 by sreemathi.v

1 answer

Find $\large\frac{dy}{dx}$ if $y=\tan^{-1}\large \frac{\sqrt{1-x^2}-1}{x}$

asked Apr 15, 2013 by sreemathi.v

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Solve for x : $\tan^{-1}(x-1)+\tan^{-1}x+\tan^{-1}(x+1)=\tan^{-1}3x.$

asked Apr 15, 2013 by sreemathi.v

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(i) Write down the Boolean expression corresponding to the switching circuit given below : (ii) Simplify the expression and construct the switching circuit for the simplified expression.

asked Apr 15, 2013 by sreemathi.v

0 answers

(i) Show that the second degree equations $x^2-5xy+4y^2+x+2y-2=0$ represents a pair of straight lines.(ii) Find the equations of the individual lines and their point of intersection.

asked Apr 15, 2013 by sreemathi.v

1 answer

If $A=\begin{vmatrix}1 & -2 & -3\\2 & 3 & 2\\3 &-3 & -4\end{vmatrix},$find $A^{-1}$ and hence solve the following system of linear equations : $x+2-3z=-4,2x+3y+2z=2,3x-3y-4z=11.$

asked Apr 15, 2013 by sreemathi.v

0 answers

Prove that :$ \begin{vmatrix}a & b & ax+by\\b & c & bx+cy\\ax+by & bx+cy & 0\end{vmatrix}=(b^2-ac)(ax^2+2bxy+cy^2).$

asked Apr 15, 2013 by sreemathi.v

0 answers

Solve the differential equation : $(x+1)\large\frac{dy}{dx}\normalsize-y=e^{3x}(x+1)^2$.

asked Apr 15, 2013 by sreemathi.v

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Find the value of $x$,$y$,given that $(x+iy)(2-3i)=4+i.$

asked Apr 15, 2013 by sreemathi.v

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In a standard deviation of the numbers,2,3,11 and x is $3\large\frac{1}{2}$,find the value of $x$.

asked Apr 15, 2013 by sreemathi.v

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In a single throw of two dice,find the probability of getting a total of at most 9.

asked Apr 15, 2013 by sreemathi.v

1 answer

Find the equation of tangents to the hyperbola $3x^2-y^2=3$ which are perpendicular to the line $x+3y=2$.

asked Apr 15, 2013 by sreemathi.v

0 answers

Evaluate $\int \large\frac{x^2}{(x^2-4)}\normalsize dx.$

asked Apr 15, 2013 by sreemathi.v

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If $y=\sqrt{\large\frac{1-\cos x}{1+\cos x}}$,find $\large\frac{dy}{dx}$.

asked Apr 15, 2013 by sreemathi.v

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Find the equation of the normal to the ellipse $5x^2+3y^2=137$ at the point where the ordinate is 2.

asked Apr 15, 2013 by sreemathi.v

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Find the equation of the straight line through origin and passing through the intersection of lines $x-2y+3=0$ and $3x+5y+6=0$.

asked Apr 15, 2013 by sreemathi.v

0 answers

Find $x$ and $y$,if $x+y=\begin{bmatrix}7 & 0\\2 & 5\end{bmatrix}$ and $x-y=\begin{bmatrix}3 & 0\\0 & 3\end{bmatrix}$.

asked Apr 15, 2013 by sreemathi.v

0 answers

A propeller costs Rs. 1,80,000 and its effective life is estimated to be 10 years.A sinking fund is created for replacing the propeller by a new model at the end of its life time,when its scrap realizes a sum of Rs. 34,000 only.The price of the new model is estimated to be 30% more than the price of the present one.What amount should be put into the sinking fund at the end of each year,if it accumulates at 4% per annum compound interest?(Take $(1.04)^{10}=1.480$).

asked Apr 15, 2013 by sreemathi.v

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Calculate the index number for the year 2006 with 1996 as the base year by the weighted average of price relatives method from the following data.

asked Apr 15, 2013 by sreemathi.v

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The cost of manufacturing of certain items consists of Rs. 1600 as overheads,Rs. 30 per item as the cost of the material and the labour cost $Rs. \large\frac{x^2}{100}$ for x items produced.How many items must be produced to have a minimum average cost?

asked Apr 15, 2013 by sreemathi.v

0 answers

A new cereal,formed of a mixture of bran and rice,contains at least 88 grams of protein and at least 36 milligrams of iron.Knowing that bran contains 80 grams of protein and 40 milligrams of iron per kilogram,and rice contains 100 grams of protein and 30 milligrams of iron per kilogram,find the minimum cost of producing a kilogram of this new cereal if bran costs Rs. 28 per kilogram and rice costs Rs. 25 per kilogram.

asked Apr 15, 2013 by sreemathi.v

0 answers

An iPod is purchased on installment basis,such that Rs. 8,000 is to be paid on the signing of the contract and four yearly installments of Rs. 3000 each,payable at the end of the first,second,third and fourth years.If compound interest is charged at 5% per annum,what would be the cash price of the iPod?(Take $(1.05)^{-4}=0.8227).$

asked Apr 15, 2013 by sreemathi.v

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A bill of Rs. 84,150 is drawn on 22nd April,2002 at 11 months and is discounted on 11th january 2003.Find the banker's gain if the rate of interest is 10%.

asked Apr 15, 2013 by sreemathi.v

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An insurance company insured 4000 doctors,8000 teachers and 12,000 engineers.The probabilities of a doctor,a teacher and an engineer dying before the age of 58 years are 0.01 ,0.03 and 0.05 respectively.If one of the insured persons dies before the age of 58 years,find the probability that he is a doctor.

asked Apr 15, 2013 by sreemathi.v

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The mean and variance of a binomial distribution are 4 and 2 respectively .Find the probability of at least 6 successes.

asked Apr 15, 2013 by sreemathi.v

0 answers

(i) Prove by vector method that the diameter of a circle will subtend a right angle at a point on its circumference.(ii) If $\overrightarrow {a},\overrightarrow {b}$ and $\overrightarrow {c}$ represent the position vectors of the points with co-ordinates $(2,-10,2),(3,1,2)$ and $(2,1,3)$ respectively,find the value of $\overrightarrow {a}\times (\overrightarrow {b}\times \overrightarrow {c})$.

asked Apr 15, 2013 by sreemathi.v

0 answers

Find the area of a parallelogram whose diagonals are determined by the vectors $\overrightarrow{a}=3i+j-2k$ and $\overrightarrow{b}=i-3j+4k$

asked Apr 15, 2013 by sreemathi.v

0 answers

Prove that the tangent at any point to the rectangular hyperbola forms with the asymptotes a tringle of constant area.

asked Apr 14, 2013 by poojasapani_1

1 answer

Find the equation of rectangular hyperbola which has for one of its asymptotes the line $x+2y-5=0 $ and passes through the point $(6 , 0 ) $ and $(-3 , 0 )$ find its equation and asymptotes

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the equation of the hyperbola if its asymptotes are parallel to $x+2y-12=0$ and $x-2y+8=0, (2 , 4 ) $ is the centre of the hyperbola and it passes through $(2 , 0 )$

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the equation of the hyperbola if the asymptotes are $2x+3y-8=0$ and $3x-2y+1=0$ and $ (5 , 3 ) $ is a point on the hyperbola.

asked Apr 13, 2013 by poojasapani_1

1 answer

Prove that the line $5x+12y=9$ touches the hyperbola $x^{2}-9y^{2}=9$ and find its point of contact.

asked Apr 13, 2013 by poojasapani_1

1 answer

Find the equation of the sphere which passes through the circle $x^2+y^2-6z-4=0,x+2y+2z=0$ and whose centre lies on the plane $2x-y+z=1.$

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the equation of the plane which contains the line $\large\frac{x-1}{2}=\large\frac{y+1}{-1}=\large\frac{z-3}{4}$ and is perpendicular to the plane $x+2y+z=12.$

asked Apr 12, 2013 by sreemathi.v

0 answers

Solve the following differential equation for a particular solution : $dy=(5x-4y)dx;$ when $y=0$ and $x=0$.

asked Apr 12, 2013 by sreemathi.v

0 answers

If $z=\large\frac{13-5i}{4-9i}$,prove by using De Moivre's theorem that $z^6=-8i$.

asked Apr 12, 2013 by sreemathi.v

0 answers

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