Recent questions tagged isc

A straight line is parallel to the x-axis and passes through the intersection of the lines $x+2y+1=0$ and $y=x+7$.Find the equation of the straight line.

asked Apr 16, 2013 by sreemathi.v

1 answer

Solve for x and y : $\begin{bmatrix}x^2\\y^2\end{bmatrix}+2\begin{bmatrix}2x\\3y\end{bmatrix}=3\begin{bmatrix}7\\-3\end{bmatrix}$

asked Apr 16, 2013 by sreemathi.v

0 answers

The fixed cost of a new product is Rs.18,000 and the variable cost is Rs.550 per unit.If the demand function $p(x)=4000-150x$,find break even points.

asked Apr 16, 2013 by sreemathi.v

1 answer

An insurance company insured 1500 scooter drivers,2500 car drivers and 4500 truck drivers.The probability of a scooter ,a car and a truck meeting with an accident is 0.01,0.02 and 0.04 respectively.If one of the insured persons meets with an accident,find the probability that he is a scooter driver.

asked Apr 16, 2013 by sreemathi.v

1 answer

In a binomial distribution,the sum of its mean and the variance is 1.8.Find the probability of two successes if the event was conducted 5 times.

asked Apr 16, 2013 by sreemathi.v

0 answers

Mr.Mohan took a loan of Rs. 7,500 on 1st Jan.2005 and agreed to pay Rs.2,250 after 1month,Rs.2,400 after 3 months,Rs.3000 after 4 months and Rs.750 after 5 months in full redemption of his debit.Find the rate of interest charged.

asked Apr 16, 2013 by sreemathi.v

0 answers

A person borrowed a sum of money and paid it back in 3 equal annual installments of Rs.2,160 each.If the rate of interest charged is 20% p.a. compounded annually,calculate :(i)The sum borrowed (ii) The total interest charged.

asked Apr 16, 2013 by sreemathi.v

0 answers

A bill was drawn on 14th June 2006 at 8 months after date and was discounted on 24th September 2006 at 5% p.a.If the banker's gain on the basis of simple interest is Rs. 3,calculate the sum for which the bill was drawn.

asked Apr 16, 2013 by sreemathi.v

0 answers

The production of a soft drink company in thousands of litres during each month of a year is as follows :

asked Apr 16, 2013 by sreemathi.v

1 answer

Calculate the index number for 2005 with 2000 as the base year by the weighted aggregate method.

asked Apr 16, 2013 by sreemathi.v

1 answer

Find a unit vector perpendicular to the vectors $4i+3j+k$ and $2i-j+2k$.Determine the sine angle between these two vectors.

asked Apr 16, 2013 by sreemathi.v

0 answers

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are three vectors,show that : $(\overrightarrow{a}+\overrightarrow{b}).\{(\overrightarrow{b}+\overrightarrow{c})\times (\overrightarrow{c}+\overrightarrow{a})\}=2[\overrightarrow{a}\; \overrightarrow{b}\;\overrightarrow{c}]$

asked Apr 16, 2013 by sreemathi.v

0 answers

Prove that the plane $x+2y-z=4$ cuts the sphere $x^2+y^2+z^2-x+z-2=0$ in a circle whose radius is unity.

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the equation of the plane through the point (1,2,3) and perpendicular to the planes $x+y+2z=3$ and $3x+2y+z=4$.

asked Apr 16, 2013 by sreemathi.v

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Solve the differential equation : $x\large\frac{dy}{dx}\normalsize-y=\sqrt {x^2+y^2}$.

asked Apr 16, 2013 by sreemathi.v

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Prove that $(1+i\sqrt 3)^8+(1-i\sqrt 3)^8=-2^8$ by using De Moiver's Theorem.

asked Apr 16, 2013 by sreemathi.v

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Assuming that on an average one telephone out of 10 is busy,seven telephone numbers are randomly selected and called.Find the probability that three of them will be busy.

asked Apr 16, 2013 by sreemathi.v

1 answer

The bag 'A' contains 3 white and 2 black balls while the bag 'B' contains 2 white and 5 black balls.One of the bags is chosen at random and a ball is drawn from it.What is the probability that the balls is white.

asked Apr 16, 2013 by sreemathi.v

0 answers

Given two regression lines $4x+3y+7=0$ and $3x+4y+8=0$,determine :

asked Apr 16, 2013 by sreemathi.v

0 answers

Calculate the coefficient of correlation between X and Y from the following data using Karl Pearson's method :

asked Apr 16, 2013 by sreemathi.v

1 answer

Find the area enclosed by the curves $y^2=x$ and $y^2=4-3x$.

asked Apr 16, 2013 by sreemathi.v

1 answer

Evaluate : $\int_0^{\large \frac{\pi}{4}}\normalsize \log (1+\tan x)dx.$

asked Apr 16, 2013 by sreemathi.v

0 answers

Show that the semi-vertical angle of a cone of maximum volume and of given slant height is $\tan^{-1}(\sqrt 2).$

asked Apr 16, 2013 by sreemathi.v

0 answers

Verify Lagrange's mean value theorem for the function $f(x)=3x^2-5x+1$ defined in interval $[2,5].$

asked Apr 16, 2013 by sreemathi.v

0 answers

If $\sin y=x\sin (a+y),$show that $\large\frac{dy}{dx}=\large\frac{\sin^2(a+y)}{\sin a}$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Prove that : $2\tan^{-1}\bigg(\large\frac{1}{3}\bigg)\normalsize +\cot ^{-1}(4)=\tan^{-1}\bigg(\large\frac{16}{13}\bigg).$

asked Apr 16, 2013 by sreemathi.v

0 answers

Show that the bisectors of the angles between the pair of straight lines $11x^2-16xy-y^2=0$ are parallel and perpendicular to $x+2y+5=0.$

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the value of 'k' so that the second degree equation $12x^2-10xy+ky^2+14x-5y+2=0$ may represent a pair of straight lines.For this value of 'k' find the angle between the lines represented by the above equation.

asked Apr 16, 2013 by sreemathi.v

0 answers

Solve the following system of equations using matrices : $x+y+z=6,x-y+z=2,2x+y-z=1$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Using the properties of determinants ,show that $\begin{vmatrix}x-y-z & 2x & 2x\\2y & y-z-x & 2y\\2z & 2z & z-x-y\end{vmatrix}=(x+y+z)^3$

asked Apr 16, 2013 by sreemathi.v

0 answers

Solve the differential equation $\tan y dx+\sec^2y\tan x dy=0$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the modulus and amplitude of the complex number $\large\frac{2+3i}{3+2i}$.

asked Apr 16, 2013 by sreemathi.v

0 answers

Five students scored marks as follows : 8,10,15,20,22.

asked Apr 16, 2013 by sreemathi.v

0 answers

Kamal and Monika appear for an interview for two vacancies.The probability of Kamal's selection is $\large\frac{1}{3}$ and that of Monika's selection is $\large\frac{1}{5}$.Find the probability that only one of them will be selected.

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the equation of the ellipse whose minor axis is 4 and which has a distance of 6 units between its foci.

asked Apr 16, 2013 by sreemathi.v

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Solve $\int\large\frac{1}{x\cos^2(1+\log x)}\normalsize dx$.

asked Apr 16, 2013 by sreemathi.v

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If $e^{x+y}=xy,$show that $\large\frac{dy}{dx}\normalsize=\large\frac{y(1-x)}{x(y-1)}$.

asked Apr 16, 2013 by sreemathi.v

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Find the equation of the parabola having focus at (3,-4) and directrix as $x+y=2.$

asked Apr 16, 2013 by sreemathi.v

0 answers

Find the equation of the line passing through the intersection of the straight lines $2x+3y=1$ and $3x+4y=6$ and perpendicular to the line $5x-2y=7$.

asked Apr 16, 2013 by sreemathi.v

0 answers

If $A\begin{bmatrix}1 & 2\\2 & 1\end{bmatrix}$,show that $A^2-3I=2A$.

asked Apr 16, 2013 by sreemathi.v

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A class consists of 50 students out of which there are 10 girls.In the class 2 girls and 5 boys are rank holders in an examination.If a student is selected at random from the class and is found to be a rank holder,what is the probability that the student selected is a girl?

asked Apr 15, 2013 by sreemathi.v

1 answer

Eight coins are thrown simultaneously.

asked Apr 15, 2013 by sreemathi.v

0 answers

The average cost function associated with producing and marketing $x$ units of an item is given by $AC=2x-11+\large\frac{50}{x}$.Find : (i) The total cost function and marginal cost function. (ii) The range of values of the output $x$ for which AC is increasing.

asked Apr 15, 2013 by sreemathi.v

0 answers

A manufacturer produces two types of steel trunks.He has two machines,A and B.The first type of trunk requires 3 hours on machine A and 3 hours on machine B.The second type requires 3 hours on machine A and 2 hours on machine B.Machines A and B can work at most for 18 hours and 15 hours per day respectively.He earns a profit of Rs. 30 per trunk on the first type of trunk and Rs. 25 per trunk on the second type.Formulate a Linear Programming Problem to find out how many trunks of each type he must make each day to maximise his profit.

asked Apr 15, 2013 by sreemathi.v

1 answer

Mr.Aggarwal buys a house at Rs. 30,00,000 for which he agrees to make equal payments at the end of each year for 10 years.If money is worth 10% p.a., find the amount of each installment.[Take $(1.1)^{-10}=0.3855]$

asked Apr 15, 2013 by sreemathi.v

0 answers

The banker's gain on a certain bill due 6 months hence is Rs. 100,the rate of interest being 10% per annum.Find the face value of the bill.

asked Apr 15, 2013 by sreemathi.v

0 answers

Given $\overrightarrow{a}=i-2j+k,\overrightarrow{b}=2i+j+k$ and $\overrightarrow{c}=i+2j-k$.Find $\overrightarrow{a}\times(\overrightarrow{b}\times \overrightarrow{c})$

asked Apr 15, 2013 by sreemathi.v

0 answers

Find $\overrightarrow{a}.\overrightarrow{b}$ if $ \mid\overrightarrow{a}\mid=2, \mid\overrightarrow{b}\mid=5$ and $\mid \overrightarrow{a}\times \overrightarrow{b}\mid$=8.

asked Apr 15, 2013 by sreemathi.v

0 answers

Coded monthly sales figures of a particular brand of T.V. for 18 months commencing January 1,2005 are as follows :

asked Apr 15, 2013 by sreemathi.v

0 answers

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

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