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Recent questions tagged 2010

$(1+2x+3x^2)^{10}=a_0+a_1x+a_2x^2+..........+a_{20}x^{20}=>\large\frac{a_2}{a_1}$=

asked Sep 26, 2013 by meena.p

1 answer

A polygon has 54 diagonals. Then the number of its sides is :

asked Sep 26, 2013 by meena.p

2 answers

Let $a_n=\large\frac{10^n}{n !}$ for $n=1,2,3.......$ Then the greatest value of $n$ for which $a_n$ is the greatest is :

asked Sep 26, 2013 by meena.p

1 answer

Let $n= 1 !+ 4 !+7 !+.............+400 !$. Then ten's digits of $n$ is :

asked Sep 26, 2013 by meena.p

1 answer

The numbers $a_n=6^n-5n$ for $n=1,2,3,.....$ when divided by 25 leave the remainder:

asked Sep 26, 2013 by meena.p

1 answer

Let R denotes the set of all real numbers and $R^{+}$ denote the set of all positive real numbers. For the subsets $A$ and $B$ of R define $f:A \to B$ by $f(x)=x^2$ for $x \in A$. Observe the two lists given below:

asked Sep 26, 2013 by meena.p

1 answer

If $f(0),f(1)=1,f(2)=2$ and $f(x)=f(x-2)+f(x-3)$ for $x=3,4,5,........$ then $f(9)=$

asked Sep 26, 2013 by meena.p

1 answer

Find the locus of a complex number $z=x+iy$,satisfying the relation $\mid 3z-4i\mid \leq \mid 3z+2\mid.$Illustrate the locus in the Argand plane.

asked Apr 12, 2013 by sreemathi.v

0 answers

Solve the differential equation : $(y+\log x)dx-xdy=0$,given that $y=0$,when $x=1$.

asked Apr 12, 2013 by sreemathi.v

0 answers

Consider the following data :

asked Apr 12, 2013 by sreemathi.v

0 answers

The index number for the following data,for the year 2008,taking 2004 as base year was found to be 116.The simple aggregate method was used for calculation.Find the numerical values of x and y if the sum of the prices in the year 2008 is Rs. 203.

asked Apr 12, 2013 by sreemathi.v

0 answers

The average cost function AC for a commodity is given by $AC=x+5+\large\frac{36}{x}$ in terms of output x.Find the :

asked Apr 12, 2013 by sreemathi.v

0 answers

A bill of exchange for Rs. 722 was drawn on the 3rd April,2009,payable three months after date.It was discounted on 15th April,2009 at 4.75% per annum.What was the discounted value of the bill?

asked Apr 12, 2013 by sreemathi.v

0 answers

At the beginning of each quarter,a sum of Rs. 1,500 is deposited into a savings account that pays 12% per annum compounded quarterly.Find the amount in the account at the end of four years.

asked Apr 12, 2013 by sreemathi.v

0 answers

A company produces two types of items,P and Q.Manufacturing of both items requires the metals gold and copper.Each unit of item P requires 3 gms of gold and 1 gm of copper while that of item Q requires 1 gm of gold and 2 gms of copper.The company has 9 gms of gold and 8 gms of copper in its store.If each unit of item P makes a profit of Rs. 50 and each unit of item Q makes profit of Rs. 60,determine the number of units of each item that the company should produce to maximize profit.What is the maximum profit?

asked Apr 12, 2013 by sreemathi.v

0 answers

Five bad eggs are mixed with 10 good ones.If three eggs are drawn one by one with replacement ,find the probability distribution of the number of goods eggs drawn.

asked Apr 12, 2013 by sreemathi.v

1 answer

A factory has three machines A,B and C producing 1,500,2,500 and 3,000 bulbs per day,respectively.Machine A produces 1.5% defective bulbs,machine B produces 2% defective bulbs and machine C produces 2.5% defective bulbs.At the end of the day,a bulb is drawn at random and is found to be defective.What is the probability that this defective bulb has been produced by machine B?

asked Apr 12, 2013 by sreemathi.v

1 answer

Find the equation of the plane passing through the line of intersection of the planes $x+2y+3z-4=0$ and $3z-y=0$ and perpendicular to the plane $3x+4y-2z+6=0$.

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the shortest distance between the lines whose vector equations are :$\overrightarrow{r}=(4\hat{i}-\hat{j}+2\hat{k})+\lambda(\hat{i}+2\hat{j}-3\hat{k})$ and $\overrightarrow{r}=(2\hat{i}+\hat{j}-\hat{k})+\mu(3\hat{i}+2\hat{j}-4\hat{k})$.

asked Apr 12, 2013 by sreemathi.v

0 answers

In any $\Delta ABC$,prove by vector method that $\cos B=\large\frac{c^2+a^2-b^2}{2ca}$.

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the value of $\lambda$ for which the four points with position vectors $2\hat{i}+5\hat{j}+\hat{k},-\hat{j}-4\hat{k},3\hat{i}+\lambda\hat{j}+8\hat{k}$ and $-4\hat{i}+3\hat{j}+4\hat{k}$ are coplanar.

asked Apr 12, 2013 by sreemathi.v

2 answers

There are two bags.One bag contains six green and three red balls.The second bag contains five green and four red balls.One ball is transferred from the first bag to the second bag.Then one ball is drawn from the second bag.Find the probability that it is a red ball.

asked Apr 12, 2013 by sreemathi.v

0 answers

Akhil and Vijay appear for an interview for two vacancies.The probability of Akhil's selection is $\large\frac{1}{4}$ and Vijay's selection is $\large\frac{2}{3}$.Find the probability that only one of them will be selected.

asked Apr 12, 2013 by sreemathi.v

1 answer

Calculate Spearman's coefficient of rank correlation from the following data and interpret the result :

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the equations of the two lines of regression for the following observations : $(3,6),(4,5),(5,4),(6,3),(7,2).$Find an estimate of $y$ for $x$ =2.5.

asked Apr 12, 2013 by sreemathi.v

0 answers

Draw a rough sketch of the curve $y=x^2-5x+6$ and find the area bounded by the curve and the $x$-axis.

asked Apr 12, 2013 by sreemathi.v

1 answer

Evaluate $\large \int \frac{2\sin 2 x -\cos x }{6-\cos^2x -4\sin x }$$dx$.

asked Apr 12, 2013 by sreemathi.v

1 answer

A closed right circular cylinder has volume $\large\frac{539}{2}$cubic units.Find the radius and the height of the cylinder so that the total surface area is minimum.

asked Apr 12, 2013 by sreemathi.v

1 answer

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

asked Apr 12, 2013 by sreemathi.v

0 answers

$x$,$y$ and $z$ represent three switches in an 'ON' position and $x',y'$ and $z'$ represent the same three switches in an 'OFF' position.Construct a switching circuit representing the polynomial $(x+y)(x'+z)+y(y'+z').$Using the laws of Boolean Algebra,show that the above polynomial is equivalent to $xz+y$ and construct an equivalent switching circuit.

asked Apr 12, 2013 by sreemathi.v

0 answers

Prove that : $\sin\begin{bmatrix}2 \tan^{-1}\frac{3}{5}-\sin^{-1}\frac{7}{25}\end{bmatrix}=\large\frac{304}{425}$

asked Apr 12, 2013 by sreemathi.v

0 answers

Find the equation of the parabola whose focus is (-1,-2) and the equation of the directrix is given by $4x-3y+2=0$.Also find the equation of the axis.

asked Apr 12, 2013 by sreemathi.v

0 answers

Using Rolle's theorem,find a point on the curve $y=\sin x+\cos x-1,x\in \begin{bmatrix}0,\large\frac{\pi}{2}\end{bmatrix}$ where the tangent is parallel to the x-axis.

asked Apr 11, 2013 by sreemathi.v

2 answers

Using matrix method,solve the following equations :$5x+3y+z=16,2x+y+3z,x+2y+4z=25$.

asked Apr 11, 2013 by sreemathi.v

0 answers

By using properties of determinants,prove that the determinant $\begin{vmatrix}a & \sin x& \cos x\\-\sin x & -a & 1\\\cos x & 1 & a\end{vmatrix}$ is independent of x.

asked Apr 11, 2013 by sreemathi.v

0 answers

Solve the differential equation : $cosec ^3x\; dy-cosec y\;dx=0.$

asked Apr 11, 2013 by sreemathi.v

0 answers

If 1,$\omega{,\omega}^2$ are the three cube roots of unity,then simplify :$(3+5\omega+3{\omega}^2)^2(1+2\omega+{\omega}^2).$

asked Apr 11, 2013 by sreemathi.v

0 answers

If the regression equation of $x$ on $y$ is given by $mx-y+10=0$ and the equation of $y$ on $x$ is given by $-2x+5y=14$,determine the value of 'm' if the coefficient of correlation between $x$ and $y$ is $\large\frac{1}{\sqrt {10}}$.

asked Apr 11, 2013 by sreemathi.v

1 answer

A fair die is thrown once.What is the probability that either an even number or a number greater than three will turn up?

asked Apr 11, 2013 by sreemathi.v

1 answer

Evaluate : $\int_{-3}^3\mid x+2\mid dx.$

asked Apr 11, 2013 by sreemathi.v

0 answers

Evaluate : $\int\large\frac{x}{(x+1)^2}\normalsize dx.$

asked Apr 11, 2013 by sreemathi.v

0 answers

Evaluate : $\lim_{x\to \large\frac{\pi}{2}}[x\tan x-\large\frac{\pi}{2}\normalsize\ sec x]$

asked Apr 11, 2013 by sreemathi.v

0 answers

Show that the line $y=x+\sqrt 7$ touches the hyperbola $9x^2-16y^2=144.$

asked Apr 11, 2013 by sreemathi.v

0 answers

Solve : $Cos^{-1}[\sin(\cos^{-1}X)]=\large\frac{\pi}{3}$

asked Apr 11, 2013 by sreemathi.v

0 answers

If a matrix $A=\begin{bmatrix}6 & x & 2\\-2 & -1 & 2\\-10 & 5 & 2\end{bmatrix}$ is a singular matrix,find the value of x.

asked Apr 11, 2013 by sreemathi.v

0 answers

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