Recent questions tagged sec-b

If y(x) is a solution of $\Large\frac{2-\sin x}{1-y}\bigg(\frac{dy}{dx}\bigg)\normalsize=-\cos x$ and y(0)=1,then find the value of $\frac{1}{2}.$

asked Jan 18, 2013 by sreemathi.v

1 answer

Find the general solution of $(x+2y^3)\Large \frac{dy}{dx}\normalsize =y \;dx$

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve the differential equation $\Large \frac{dy}{dx}\normalsize=1+x+y^2+xy^2,$when y=0,x=0.

asked Jan 17, 2013 by sreemathi.v

1 answer

Find the general solution of $\Large \frac{dy}{dx}\normalsize =ay-e^{mx}$

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve the differential equation $(x^2-1)\Large \frac{dy}{dx}\normalsize +2xy=\Large \frac{1}{x^2-1}$

asked Jan 17, 2013 by sreemathi.v

1 answer

If ${\mid\overrightarrow{a}\times\overrightarrow{b}\mid}^2$=${\mid\overrightarrow{a}.\overrightarrow{b}\mid}^2=144$ and$\mid\overrightarrow{a}\mid=4,$ then $\mid\overrightarrow{b}\mid$ is equal to ________.

asked Jan 17, 2013 by sreemathi.v

1 answer

The vector $\overrightarrow{a}+\overrightarrow{b}$ bisects the angle between the non-collinear vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ if__________.

asked Jan 17, 2013 by sreemathi.v

1 answer

For what value of k, the matrix $ \begin{bmatrix} k & 2 \\ 3 & 4 \end{bmatrix} $ has no inverse?

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Using properties of determinant, prove that $ \begin{bmatrix} 1 & x & y+z \\ 1 & y & z+x \\ 1 & z & x+y \end{bmatrix} = 0 $

asked Jan 17, 2013 by thanvigandhi_1

0 answers

If $\overrightarrow{a}=\hat i+\hat j+\hat k$ and $\overrightarrow{b}=\hat j-\hat k$,find a vector $\overrightarrow{c}$ such that $\overrightarrow{a}\times\overrightarrow{c}=\overrightarrow{b}$ and $\overrightarrow{a}.\overrightarrow{c}=3$.

asked Jan 17, 2013 by sreemathi.v

1 answer

Show that the area of the parallelogram whose diagonals are given by $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\mid \overrightarrow{a} \times \overrightarrow{b}\mid}{2}$.Also find the area of the parallelogram whose diagonals are $2\hat i+\hat j+\hat k$ and $\hat i+3\hat j+\hat k$.

asked Jan 17, 2013 by sreemathi.v

1 answer

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ represent the vertices of a triangle,then show that $\frac{1}{2}\mid\overrightarrow{b}\times\overrightarrow{c}+\overrightarrow{c}\times\overrightarrow{a}+\overrightarrow{a}\times\overrightarrow{b}\mid$ gives the vector area of the triangle .Hence deduce the condition that the three points $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are collinear.Also find the unit vector normal to the plane of the triangle.

asked Jan 17, 2013 by sreemathi.v

1 answer

Show that the relation R : N $ \rightarrow $ N defined by (a,b)R(c,d) $ \iff $ a+d = b+c for all (a,b), (c,d) $ \in $ N x N is an equivalence relation.

asked Jan 17, 2013 by thanvigandhi_1

0 answers

If $ cos^{-1}x+cos^{-1}y+cos^{-1}z=\pi$ prove that $ x^2+y^2+z^2+2xyz=1$

asked Jan 17, 2013 by thanvigandhi_1

1 answer

Solve: $ \tan^{-1}(x+1)+\tan^{-1}(x-1)=\tan^{-1}\large\frac{8}{31}$$;x > 0.$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

(i) The cost of 5 kg of sugar, 5kg of wheat and 2kg of rice is Rs. 340. The cost of 4 kg of rice, 2kg of sugar and 5kg of wheat is Rs. 270. Rs. 264 is the cost of 3kg of wheat, 2kg of rice and 4 kg of sugar. Represent the above problem by a system of linear equations and find the cost of each item per kg by matix method. (ii) How increase in the prices of essential commodities affect economic weaker section of society?

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Prove that in any triangle ABC,$ cos A=\large \frac{b^2+c^2-a^2}{2bc}$,$where \overrightarrow{a},\overrightarrow{b} and \overrightarrow{c}$ are the vectors of sides BC, CA and AB respectively.

asked Jan 17, 2013 by sreemathi.v

1 answer

Using vectors,prove that the parallelogram on the same base and between the same parallels are equal in area.

asked Jan 17, 2013 by sreemathi.v

1 answer

Using vectors,find the area of the triangle ABC with vertices $A(1,2,3),B(2,-1,4)$ and $C(4,5,-1).$

asked Jan 17, 2013 by sreemathi.v

1 answer

If the function $ f(x) = \left\{ \begin{array}{l l} x^2+3x+a, & \quad { x \leq 1}\\ bx+2, & \quad { x > 1} \end{array}. \right. $ is differentiable for all x. Find a and b.

asked Jan 17, 2013 by thanvigandhi_1

0 answers

If $A,B,C,D$ are the points with position vectors $\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},2\overrightarrow{i}+\overrightarrow{j}+3\overrightarrow{k},2\overrightarrow{i}-3\overrightarrow{k},3\overrightarrow{i}+2\overrightarrow{i}+\overrightarrow{k},$ respectively ,find the projection of $\overrightarrow{AB}$ along $\overrightarrow{CD}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

Differentiate : $\large \frac{x}{a} $$\sqrt {x^2-a^2}+\large\frac{a^2}{2}$$\sin^{-1}\large\frac{x}{a}$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Find the sine of the angle between the vectors $\overrightarrow{a}=3\hat i+\hat j+2\hat k$ and $\overrightarrow{b}=-2\hat i+2\hat j+4\hat k.$

asked Jan 17, 2013 by sreemathi.v

1 answer

FInd a vector of magnitude 6 ,which is perpendicular to both the vectors $2\hat i-\hat j+2\hat k$ and $4\hat i-\hat j+3\hat k.$

asked Jan 17, 2013 by sreemathi.v

1 answer

A vector $\overrightarrow{r}$ has magnitude 14 and direction ratios 2,3,-6.Find the direction cosines and components of $\overrightarrow{r}$,given that $\overrightarrow{r}$ makes an acute angle with x-axis.

asked Jan 17, 2013 by sreemathi.v

1 answer

If $ y=x^{x^{x....^{\infty}}} $, then prove that $ \large\frac{dy}{dx}=\frac{y^2}{x(1-ylog\: x )}$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

A vector $\overrightarrow{r}$ is inclined at equal angles to the three axes.If the magnitude of $\overrightarrow{r}$ is $2\sqrt 3$ units,find $\overrightarrow{r}.$

asked Jan 17, 2013 by sreemathi.v

1 answer

Show that $ y = \log (1+x)-\large\frac{2x}{2+x}$ is an increasing function of x for all value of x > -1.

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Show that the line $ \large\frac{x}{a}+\frac{y}{b}$$=1$ touches the curve $y=be^{\large\frac{-x}{a}}$ at the point where it crosses the y - axis.

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Using vectors,find the value of k such that the points $(k,-10,3),(1,-1,3)$ and $(3,5.3)$ are collinear.

asked Jan 17, 2013 by sreemathi.v

1 answer

Evaluate : $ \int \large\frac{2x+1}{\sqrt {x^2+4x+3}}$$dx$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

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

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Solve the differential equation $ 2xy+y^2-2x^2\large\frac{dy}{dx}$$=0 : y(1)=2.$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are the position vectors of $A$ and $B$,respectively,find the position vector of a point $C$ in $BA$ produced such that $BC=1.5BA$.

asked Jan 17, 2013 by sreemathi.v

1 answer

Solve the differential equation $ (y+x)\large\frac{dy}{dx}$$=y-x. $

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Let $ \overrightarrow a = 2\hat i + \hat k, \overrightarrow b = \hat i + \hat j + \hat k$ and $ \overrightarrow c = 4\hat i - 3\hat j + 7\hat k$ be three vectors. Find a vector $ \overrightarrow r $ which satisfies $ \overrightarrow r$ x $ \overrightarrow b = \overrightarrow c $ x $ \overrightarrow b$ and $ \overrightarrow r. \overrightarrow a =0.$

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Find the shortest distance between the lines $\large\frac{x-3}{1} = \frac{y-5}{-2} = \frac{z-7}{1}$$ \: and \: \large\frac{x+1}{7} = \frac{y+1}{-6} = \frac{z+1}{1}. $

asked Jan 17, 2013 by thanvigandhi_1

0 answers

Assume that each child born is equally likely to be a boy or girl. If a family has two children, what is the conditional probability that both are girls given that (a) the eldest is a girl (b) at least one is a girl (c) pre-natal * determination is a crime. What will you do if you come to know that some of your known is indulging in pre-natal * determination?

asked Jan 17, 2013 by thanvigandhi_1

0 answers

The area of the region bounded by the curve $x=2y+3$ and the y-lines $y=1$ and $y=-1$ is \[(A)\;4 sq.units\quad(B)\;\frac{3}{2} sq. units\quad(C)\;6 sq.units\quad(D)8 sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $y=x+1$ and the lines $x=2$ and $x=3$ is \[(A)\frac{7}{2} sq.units\quad(B)\;\frac{9}{2}sq. units\quad(C)\frac{11} {2}sq.units\quad(D)\frac{13}{2} sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the circle $x^2+y^2=1$ is \[(A)\;2\pi sq.units\quad(B)\;\pi sq. units\quad(C)\;3\pi sq.units\quad(D)4\pi sq.units\]

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the ellipse $\large\frac{x^2}{25}+\frac{y^2}{16}=1$ is \begin{array}{1 1}(A)\;2 \pi sq.units & (B)\;20{\pi}^2 sq.units\\(C)\;16{\pi}^2 sq.units & (D)\;25\pi sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $y=sin x$ between the ordinates $x=0$ and $x=\large\frac{\pi}{2}$ and the x-axis is

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by parabola $y^2=x$ and the straight line $2y=x$ is \begin{array}{1 1}(A)\;\frac{4}{3} sq.units & (B)\;1 sq.units\\(C)\;\frac{2}{3} sq.units & (D)\;\frac{1}{3}sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $y=\cos x$ between $x=0$ and $x=\pi$ is \begin{array}{1 1}(A)\;2 sq.units & (B)\;4 sq.units\\(C)\;3 sq.units & (D)\;1sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region in the first quadrant enclosed by the x-axis,the line y=x and the circle $x^2+y^2=32$ is \begin{array}{1 1}(A)\;16\pi\; sq.units & (B)\;4\pi \;sq.units\\(C)\;32\pi\; sq.units & (D)\;24\pi\;sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

2 answers

'' is a binary operation defined on Q. Find which of the following binary oprations are associative and which are commutative : $(i) ab=a-b\: for \: a,b \in Q (ii) a*b = \large\frac{ab}{4}$$\: for \: a,b \in Q.$

asked Jan 16, 2013 by thanvigandhi_1

0 answers

The area of the region bounded by the curve $y=\sqrt {16-x^2}$ and x-axis is \begin{array}{1 1}(A)\;8\pi \;sq.units & (B)\;20\pi\; sq.units\\(C)\;16\pi\; sq.units & (D)\;256\pi\; sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

The area of the region bounded by the curve $x^2=4y$ and the straight line $x=4y-2$ is \begin{array}{1 1}(A)\;\frac{3}{8}sq.units & (B)\;\frac{5}{8}sq.units\\(C)\;\frac{7}{8}sq.units & (D)\;\frac{9}{8} sq.units \end{array}

asked Jan 16, 2013 by sreemathi.v

1 answer

Show that the relation in the set $ A = { x : x \in W, o \leq x \leq 12} $ given by R = {(a, b) : a-b is a multiple of 4} is an equivalence relation.

asked Jan 16, 2013 by thanvigandhi_1

0 answers

Ask Questions, Get Answers