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Recent questions tagged 2009

If $f:[2,3] \to R$ is defined by $f(x) =x^3+3x-2,$ then the range $f(x) $ is contained in the interval:

asked Oct 8, 2013 by meena.p

1 answer

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

0 answers

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

0 answers

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

0 answers

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

0 answers

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

0 answers

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

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

An article manufactured by a company consists of two parts A and B .In the process of manufacture of part A,9 out of 104 parts may be defective.Similarly,5 out of 100 are likely to be defective in the manufacture of part B.Calculate the probability that the article manufactured will not be defective.

asked Apr 12, 2013 by sreemathi.v

0 answers

Bag A contains 5 white and 4 black balls,and bag B contains 7 white and 6 black balls.One ball is drawn from the bag A and with out noticing its color,is put in the bag B.If a ball is then drawn from bag B,find the probability that it is black in colour.

asked Apr 12, 2013 by sreemathi.v

0 answers

If the two regression lines of a bivariate distribution are $4x-5y+33=0$ and $20x-9y-107=0$,

asked Apr 12, 2013 by sreemathi.v

1 answer

An examination of 8 applicants for a clerical post was taken by a firm.The marks obtained by the applicants in the Reasoning and Aptitude tests are given below :

asked Apr 12, 2013 by sreemathi.v

2 answers

Draw a rough sketch of the curve $x^2+y=9$ and find the area enclosed by the curve,the x-axis and the lines $x+1=0$ and $x-2=0$.

asked Apr 12, 2013 by sreemathi.v

0 answers

(i) Evaluate $\int_0^{\large\frac{\pi}{2}}\log(\tan x)dx$.(ii) Evaluate $\int_0^5\big(x+\frac{1}{2}\big)dx$ as a limit of a sum.

asked Apr 12, 2013 by sreemathi.v

0 answers

A wire of length 20m is available to fence off a flower bed in the form of a sector of a circle.What must be the radius of the circle,if we wish to have a flower bed with the greatest possible area?

asked Apr 12, 2013 by sreemathi.v

1 answer

It is given that Rolle's theorem holds good for the function : $f(x)=x^3+ax^2+bx,x\in [1,2]$ at the point $x=\large\frac{4}{3}$.Find the values of a and b.

asked Apr 12, 2013 by sreemathi.v

1 answer

Using a suitable substitution find the derivative of $\tan^{-1}\large\frac{4\sqrt x}{1-4x}$ with respect to x.

asked Apr 12, 2013 by sreemathi.v

0 answers

If $\sin^{-1}x+\sin^{-1}y+\sin^{-1}z=\pi,$prove that : $x^2-y^2-z^2+2yz\sqrt{1-x^2}=0.$

asked Apr 12, 2013 by sreemathi.v

0 answers

$P$ , $Q$ and $R$ represent switches in 'on' positions and P',Q' and R' represent switches in 'off' positions.Construct a switching circuit representing the polynomial $PR+Q(Q'+R)(P+QR).$Use Boolean algebra to prove that the above circuit can be simplified to an expression in which,when $P$ and $R$ are 'on' or $Q$ and $R$ are 'on',the light is on.Construct an equivalent circuit.

asked Apr 12, 2013 by sreemathi.v

0 answers

Prove that the following equation represents a pair of straight lines.Find their point of intersection and the angle between them :$2x^2+7xy+3y^2+2(4x+7y+4)=0.$

asked Apr 12, 2013 by sreemathi.v

0 answers

Solve the following linear equations using the matrix method : $x+y+z=9,2x+5y+7z=52,2x+y-z=0$.

asked Apr 12, 2013 by sreemathi.v

1 answer

By using properties of determinants ,prove that :$\begin{vmatrix}1+\sin^2x& \cos ^2x&4\sin 2x\\\sin^2x & 1+cos^2 x& 4\sin 2x\\\sin^2 x& \cos ^2x &1+4\sin 2x\end{vmatrix}=2+4\sin 2x$.

asked Apr 12, 2013 by sreemathi.v

0 answers

Solve the following differential equation : $(x\cos y)dy=e^x(x\ log x+1)dx$.

asked Apr 12, 2013 by sreemathi.v

0 answers

If $(-2+\sqrt {-3})(-3+2\sqrt{-3})=a+ib$,find the real numbers a,b.With these values of a and b ,also find the modulus of $a+ib.$

asked Apr 12, 2013 by sreemathi.v

0 answers

The mean weight of 70 students in a class is 60 kg.The mean weight of the girls in the class is 53 kg and that of the boys is 70.5 kg.Find the number of girls in the class.

asked Apr 12, 2013 by sreemathi.v

0 answers

Two horses are considered for a race.The probability of selection of the first horse is $\large\frac{1}{4}$ and that of the second is $\large\frac{1}{3}$.What is the probability that :

asked Apr 12, 2013 by sreemathi.v

1 answer

Evaluate the following limit : $\lim_{x\to \large\frac{\pi}{4}}\large\frac{1-\tan x}{\cos 2x}$

asked Apr 12, 2013 by sreemathi.v

0 answers

Evaluate the following integral : $\int \large\frac{e^{2x}}{2+e^x}\normalsize dx.$

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the derivative of $\sin x^2$ with respect to $x^3$.

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the equations of the tangents of the parabola $y^2+12x=0$ from the point (3,8).

asked Apr 12, 2013 by sreemathi.v

0 answers

The lines $x-2y+6=0$ and $2x-y-10=0$ intersect at the point A.Find the equation of the line making an angle $45^{\circ}$ with the positive direction of the x-axis and passing through the point A.

asked Apr 12, 2013 by sreemathi.v

0 answers

If $M(\theta)=\begin{bmatrix}\cos \theta & \sin\theta\\-\sin\theta &\cos\theta\end{bmatrix}$,show that $M(x)M(y)=M(x+y).$

asked Apr 12, 2013 by sreemathi.v

1 answer

Obtain the inverse of the following matrix using elementary operation $A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} $

asked Feb 7, 2013 by thanvigandhi_1

1 answer

Obtain the inverse of the following matrix, using elementary operations $ A = \begin{bmatrix} 3 & 0 & -1 \\ 2 & 3 & 0 \\ 0 & 4 & 1 \end{bmatrix} $

asked Feb 6, 2013 by thanvigandhi_1

1 answer

A manufacturer can sell x items at a price of Rs. \( \bigg( 5 - \large \frac{x}{100} \bigg) \) each. The cost price of x items is Rs. $ \bigg( \large\frac{x}{5}$$ + 500 \bigg) $. Find the number of items he should sell to earn the maximum profit.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Solve for x : $ 2\tan^{-1} ( \cos x ) = \tan^{-1} (2 cosec x) $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int \mathrm \: x \sin^{-1}x \: dx $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

If \( (\cos x)^y = (\sin y)^x \), find \( \large\frac{dy}{dx} \)

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Find the intervals in which the function f given by $ f(x) = \sin x + \cos x, 0 \leq \: x \leq \: 2\pi, $is strictly increasing or strictly decreasing.

asked Dec 29, 2012 by thanvigandhi_1

0 answers

If \( A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end {bmatrix} \), find \( A^{-1} \) . Using \( A^{-1} \) , solve the system of equations : $ 2x – 3y + 5z = 11 ,3x + 2y – 4z = –5 ,x + y – 2x = –3. $

asked Dec 29, 2012 by thanvigandhi_1

0 answers

Find the value of x, if \[ \begin {bmatrix} 3x+y & -y \\ 2y-x & 3 \end {bmatrix} = \begin {bmatrix} 1 & 2 \\ -5 & 3 \end {bmatrix} \]

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Let * be a binary operation on N given by a * b = HCF (a, b) , a, b \( \in \) N. Write the value of 22 * 4.

asked Dec 21, 2012 by thanvigandhi_1

0 answers

Evaluate : $ \int_0^{\Large\frac{1}{\sqrt 2}} \mathrm \: \frac{\large 1}{\large \sqrt{1-x^2}} dx $

asked Dec 21, 2012 by thanvigandhi_1

0 answers

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