Recent questions tagged sec-b

Solve the following differential equation : $ xdy-(y-x^3)dx=0 $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Find the equation of the plane passing through the points (1,-1,2) and (2,-2,2) and perpendicular to the plane 6x-2y+2z = 9.

asked Feb 5, 2013 by meena.p

1 answer

Using vector method, show that the diagonals of a Rhombus bisect each other at right angles.

asked Feb 5, 2013 by meena.p

1 answer

Using vector method, prove that if two medians of a triangle are equal, then it is an isosceles.

asked Feb 5, 2013 by meena.p

1 answer

Using vector method, prove that if the diagonals of a parallelogram are equal in length, then it is a rectangle.

asked Feb 5, 2013 by meena.p

1 answer

Prove that the perpendicular bisectors of a triangle are concurrent.

asked Feb 5, 2013 by meena.p

1 answer

Prove that the altitudes of a triangle are concurrent.

asked Feb 5, 2013 by meena.p

1 answer

Using vector method, find the angle between two diagonals of a cube?

asked Feb 5, 2013 by meena.p

1 answer

Using vector method prove that : $a)\;\sin (A+B)=\sin A\cos B+\cos A\sin B$

asked Feb 5, 2013 by meena.p

1 answer

In a triangle ABC, prove that $\Large\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

asked Feb 5, 2013 by meena.p

1 answer

A binary operation * on the set (0,1,2,3,4,5} is defined as : $ f(x) = \left\{ \begin{array}{l l}a+b, & \quad if { a+b < 6} \\ a+b-6, & \quad if { a+b \geq 6} \end{array} \right. $ Show that zero is the identity for this operation and each element 'a' of the set is invertible with 6-a, being the inverse of 'a'.

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Using properties of determinants, solve the following for x : $ \begin{vmatrix} x-2 & 2x-3 & 3x-4 \\ x-4 & 2x-9 & 3x-16 \\ x-8 & 2x-27 & 3x-64 \end{vmatrix} = 0 $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Find the relationship between 'a' and 'b' so that the function 'f' defined by $ f(x) = \left\{ \begin{array}{l l}ax+1, & \quad if { x \leq 3} \\ bx+3, & \quad if { x > 3} \end{array} \right. $ is continuous at x = 3.

asked Feb 5, 2013 by thanvigandhi_1

1 answer

If $ x^y=e^{x-y}$, show that $ \large\frac{dy}{dx}=\frac{logx}{\{log(xe)\}^2} $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

If $ x=\tan\bigg(\large\frac{1}{a}$$\ log \: y \bigg) $ show that $ (1+x^2)\large\frac{d^2y}{dx^2}$$+(2x-a)\large\frac{dy}{dx}=0 $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Evaluate : $\int_0^{\large\frac{\pi}{2}} \large\frac{x+sinx}{1+cosx}$$dx $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Solve the following differential equations : $ xdy-ydx=\sqrt{x^2+y^2}dx $

asked Feb 5, 2013 by thanvigandhi_1

1 answer

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

asked Feb 5, 2013 by thanvigandhi_1

1 answer

Find the shortest distance between the following lines whose vector equations are $ \overrightarrow r = (1-t)\hat i +(t-2)\hat j + (3-2t)\hat k \: and \: \overrightarrow r = (s+1)\hat i +(2s-1)\hat j - (2s+1)\hat k .$

asked Feb 5, 2013 by thanvigandhi_1

0 answers

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

asked Feb 5, 2013 by thanvigandhi_1

0 answers

A random variable X has the following probability distribution : Determine : \begin{bmatrix} (i)\: K & (ii) \: P(X<3) & (iii)\: P(X>6) & (iv)\: P(0<X<3) \end{bmatrix}

asked Feb 5, 2013 by thanvigandhi_1

0 answers

If $\Large\frac{1}{a},\frac{1}{b},\frac{1}{c}$are the $\large p^{th},q^{th}and\;r^{th}\;$ terms of an AP and $ \bar{u}=(q-r)\bar{i}+(r-p)\bar{j}+(p-q)\bar{k}\;and\;\bar{v}=\large\frac{1}{a}\bar{i}+\frac{1}{b}\bar{j}+\frac{1}{c}\bar{k}$ then prove that $\bar{u}\; and\;\bar{v}$ are orthogonal vectors.

asked Feb 4, 2013 by meena.p

1 answer

Prove that the area of a paralellogram with diagonals $\bar{a}\;and\;\bar{b}\;is\;\frac{1}{2}|\bar{a} \times \bar{b}|$

asked Feb 4, 2013 by meena.p

1 answer

Let $ \bar{a},\bar{b},\;and\;\bar{c}$ be three vectors such that $|\bar{a}|=3,|\bar{b}|=4,|\bar{c}|=5$ and each one of them being perpendicular to sum of the other two, find $ |\bar{a}+\bar{b}+\bar{c}|$

asked Feb 4, 2013 by meena.p

1 answer

L and M are the mid-points of sides BC & DC of a paralellogram ABCD. Prove that $ \overline{AL}+\overline{AM}=\frac{3}{2}\overline{AC}$

asked Feb 4, 2013 by meena.p

1 answer

Vectors $ 2\bar{i}-\bar{j}+2\bar{k}\;and\;\bar{i}+\bar{j}-3\bar{k}$ act along two adjacent sides of a parallelogram. Find the angle between the diagonals of the parallelogram.

asked Feb 4, 2013 by meena.p

1 answer

What is the area of the parallelogram having diagonals $ 3\bar{i}+\bar{j}-2\bar{k}\;and\;\bar{i}-3\bar{j}+4\bar{k}$?

asked Feb 4, 2013 by meena.p

1 answer

If $ \hat{a}\;and\;\hat{b}$ are unit vectors inclined at an angle $\theta$,then prove that\[(a)\;\cos \frac{\theta}{2}=\frac{1}{2}|\hat{a}+\hat{b}|\qquad(b)\;\tan \frac{\theta}{2}=\frac {|\hat{a}-\hat{b}|}{|\hat{a}+\hat{b}|}\]

asked Feb 4, 2013 by meena.p

1 answer

Prove that angle in a semi-circle is a right angle.

asked Feb 4, 2013 by meena.p

1 answer

If $ \bar{a}\;and\;\bar{b}$ are vectors,prove that $ |\bar{a} \times \bar{b}|^2+(\bar{a}.\bar{b})^2=|\bar{a}|^2.|\bar{b}|^2$

asked Feb 4, 2013 by meena.p

1 answer

Prove the triangle inequality $\bigg|\overrightarrow{a}+\overrightarrow{b}\bigg|\leq\bigg|\overrightarrow{a}\bigg|+\bigg|\overrightarrow{b}\bigg|$

asked Feb 4, 2013 by meena.p

1 answer

If $ \overrightarrow {a}+ \overrightarrow {b}+ \overrightarrow {c}=\overrightarrow 0$ show that $ \overrightarrow {a} \times \overrightarrow {b}=\overrightarrow {b} \times \overrightarrow {c}=\overrightarrow {c} \times \overrightarrow {a}$

asked Feb 4, 2013 by meena.p

1 answer

If $\bar{\alpha}=3\bar{i}-\bar{j}\;and\;\bar{\beta}=2\bar{i}+\bar{j}-\bar{k}.$ Express $ \bar{\beta}$ as a sum of two vectors $ \bar{\beta_1}\;and\;\bar{\beta_2},\;where \; \bar{\beta_1}$ is parallel to $ \bar{\alpha}\;and\; \bar{\beta_2}$ is prependicular to $ \bar{\alpha}$

asked Feb 4, 2013 by meena.p

1 answer

A curve passing through the point (1,1) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of p from the x-axis. Determine the equation of the curve.

asked Feb 4, 2013 by meena.p

0 answers

A wet porous substance in the open air losses its moisture at a rate proportional to the moisture content. If a sheet hung in the wind loses half of its moisture during the first hour, when will it have lost 95% moisture, weather conditions remaining the same.

asked Feb 4, 2013 by meena.p

0 answers

A population grows at the rate of 8% per year. How long does it take for the population to double?

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[(x^3-3xy^2)dx=(y^3-3x^2y)dy\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[\frac{dy}{dx}=\frac{y^2+y+1}{x^2+x+1}=0.\]

asked Feb 4, 2013 by meena.p

0 answers

Solve the differential equation :\[(x^2y+y^2x)dy=(x^3+y^3)dx\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[\sqrt{1-y^2}dx=[\sin^{-1}y-x]dy\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[(x^3-3xy^2)dx=(y^3-3x^2y)dx\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[(x^3y^3+xy)\frac{dy}{dx}=1\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[\frac{dy}{dx}=\cos ^3x\sin^4x+x\sqrt {2x+1}\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[\bigg[x\sqrt {x^2+y^2}-y^2\bigg]dx+xydy=0\]

asked Feb 4, 2013 by meena.p

0 answers

Solve:\[ydx-(x+2y)^2dy=0\]

asked Feb 4, 2013 by meena.p

1 answer

Using properties of determinants, prove the following : $\begin{vmatrix} x+4 & 2x & 2x \\ 2x & x+4 & 2x \\ 2x & 2x & x+4 \end{vmatrix}=(5x+4)(4-x)^2 $

asked Feb 4, 2013 by thanvigandhi_1

1 answer

Find the value of a and b such that the following function f(x) is a continuous functions : $ f(x) = \left\{ \begin{array}{l l}5, & \quad { x \leq 2} \\ ax+b, & \quad { 2 < x < 10} \\ 21, & \quad { x \geq 10 } \end{array} \right. $

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Solve:\[x\frac{dy}{dx}=y(log y-log x+1)\]

asked Feb 4, 2013 by meena.p

0 answers

Solve the following differential equation: $ (1+y^2)(1+\log x)dx+xdy=0$

asked Feb 4, 2013 by thanvigandhi_1

0 answers

If two vectors $ \overrightarrow a \: and \: \overrightarrow b$ are such that $ |\overrightarrow a|=2,|\overrightarrow b|=1\: and \: \overrightarrow a.\overrightarrow b=1$, then find the value of $ (3\overrightarrow a-5\overrightarrow b).(2\overrightarrow a+7\overrightarrow b).$

asked Feb 4, 2013 by thanvigandhi_1

0 answers

Ask Questions, Get Answers