Recent questions tagged sec-b

Find the points on the curve $4x^2+9y^2=14$, where the tangents are perpendicular to the line $2y +x =0$

asked Feb 9, 2015 by meena.p

1 answer

Use differentials to find the approximate value of $\sqrt {0.037}$

asked Feb 9, 2015 by meena.p

1 answer

If $x^{my^n}=(x+y)^{m+n}$, prove that $\large\frac{dy}{dx}=\frac{y}{x}$

asked Feb 9, 2015 by meena.p

1 answer

If $x^y =e^{(x-y)}$, prove that $\large\frac{dy}{dx}= \large\frac{\log x}{(1+\log x)^2}$

asked Feb 9, 2015 by meena.p

0 answers

Using the properties of determinants prove the following : $\begin{vmatrix}3a & -a+b & -a+c \\ a-b & 3b & c-b \\ a-c & b-c & 3c \end{vmatrix}$$=3( a+b+c)(ab+bc+ca)$

asked Feb 9, 2015 by meena.p

0 answers

Find the differential equation of the family of curves given by $y^2-2ky +x^2=k^2$

asked Feb 9, 2015 by meena.p

1 answer

Evaluate $\int \limits ^{\pi/4} _{-\pi/4} |\sin x |dx$

asked Feb 9, 2015 by meena.p

0 answers

Solve : $\int \large\frac{2 \sin x + 3 \cos x}{3 \sin x +4 \cos x }$$dx$

asked Feb 9, 2015 by meena.p

1 answer

Solve :$\int \large\frac{\sin \theta \cos \theta}{\cos ^2 \theta - \cos \theta -2}$$d \theta$

asked Feb 9, 2015 by meena.p

0 answers

A water tank has a shape of an inverted right circular cone with its axis vertical and vertex lower most. Its semi vertical angle is $\tan^{-1} (0.5)$.Water is poured into it at a constant rate of 5 cubic meter per hour. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is $4\; m$

asked Feb 9, 2015 by meena.p

2 answers

Verify Rolle's theorem for the function $f(x)= \sin x + \cos x , x \in [0,\pi/2]$

asked Feb 9, 2015 by meena.p

0 answers

Differentiate w.r.t x $y= e^{\sin x } +(\tan x) ^x $

asked Jan 23, 2015 by meena.p

1 answer

Show that the lines $\overrightarrow{r} = (\overrightarrow{i} +\overrightarrow{j} - \overrightarrow{k} ) + \lambda (4 \overrightarrow{i} -\overrightarrow{k})+ \mu ( 2 \overrightarrow{i} +3 \overrightarrow{k}) $ intersect. Find their point of intersection.

asked Jan 23, 2015 by meena.p

1 answer

Prove that $tan^{-1} \large\frac{3}{4} $$ + tan^{-1}\large\frac{3}{5} $$+ tan^{-1} \large\frac{8}{19} = \frac{\pi}{4}$

asked Jan 23, 2015 by meena.p

0 answers

Use this to evaluate $\int \limits_0^2 x \sqrt {2-x} dx$

asked Jan 23, 2015 by meena.p

1 answer

Prove that $\int \limits_0^a f(x)dx =\int \limits_0^a f(a-x)dx$

asked Jan 23, 2015 by meena.p

0 answers

Find the equation of the two planes through the points $(4,2,1),(2,1,-1)$ and making angles of $\large\frac{\pi}{4}$ with the plane $x-4y+z-9=0$

asked Jan 23, 2015 by meena.p

1 answer

Find the coordinates of the point where the line passing through the points $(3,4,1)$ and $(5,1,6)$ crosses the xy plane

asked Jan 23, 2015 by meena.p

1 answer

Evaluate $\int \cos 2x \log \sin x dx $

asked Jan 23, 2015 by meena.p

1 answer

Evaluate $\int \large\frac{1+\tan x}{x+ lo \sec x}$

asked Jan 23, 2015 by meena.p

1 answer

Find the angle of intersection of the curves $x^2+4y^2=8$ and $x^2-2y^2=4$

asked Jan 23, 2015 by meena.p

1 answer

Find the equation of the normal to the point of the curve $x^2+2y^2-4x-6y+8=0$ at the point whose abscissa is $2$

asked Jan 23, 2015 by meena.p

1 answer

$f(x) = \left\{ \begin{array} {1 1} 5, & \quad\text{ if x_1 \leq x \leq \sqrt 2 } \\ ax+b ,& \quad \text{if $2x$ < 10 }\\ 21 ,& \quad \text{if $x$ \geq 10 } \end{array} \right. $ Find the values of a and b

asked Jan 23, 2015 by meena.p

1 answer

If $ y = \large\frac {\sqrt{1- \sin x}}{\sqrt{1+\sin x} }$ then show that $ \large\frac{dy}{dx} $$+ \sec^2 \bigg( \large\frac{\pi}{4} $$-x \bigg)=0$

asked Jan 23, 2015 by meena.p

0 answers

Using Rolle’s theorem, find the points on the curve $Y= x^2, x\in [-2,2]$ where the tangent is parallel to the x-axis.

asked Jan 23, 2015 by meena.p

1 answer

A binary operation is defined by $ab = 2^{ab}.$ Determine whether $$ is commutative or associative?

asked Jan 23, 2015 by meena.p

0 answers

Using the properties of determinants prove that $\begin{vmatrix} x+y & x & x \\ 5x+4y & 4x & 2x \\10x+8y & 8x & 3x \end{vmatrix}=x^3$

asked Jan 23, 2015 by meena.p

0 answers

If $x \sqrt {1+y} +y\sqrt {1+x}=0$. Then prove that $(1+x)^2 \large\frac{dy}{dx}$$+1=0$

asked Jan 21, 2015 by meena.p

0 answers

A coin is biased , so that head is 3 times as to occur as tail. If the coin is tossed twice. Find the probability distribution of number of tails.

asked Jan 21, 2015 by meena.p

1 answer

In a die game , a player pays a stake of $\$1$ for each throw of a die. She receives $\$5$, if the die shows a 3, $\$2$ if the die shows 1 or 6 and nothing otherwise. What is the player expected profit per throw over a long series of throws?

asked Jan 21, 2015 by meena.p

1 answer

The volume of a cube is increasing at a rate of $9\;cm^2/s$ . How fast is the surface area increasing . When the length of the edge is $10\;cm$

asked Jan 21, 2015 by meena.p

1 answer

Find the value of $\tan \bigg[\sin^{-1}\bigg(\large\frac{2x}{1+x^2}\bigg)+$$\cos^{-1} \bigg( \large\frac{1-y^2}{1+y^2}\bigg)\bigg]$

asked Jan 21, 2015 by meena.p

1 answer

Find the value of $\sin (2 \tan ^{-1} \large\frac{1}{3})$$+ \cos(\tan^{-1} 2 \sqrt 2)$

asked Jan 21, 2015 by meena.p

0 answers

Find the inverse of $A = \begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}$ by elementary transformation and hence solve the following system of linear equation : $2x+y=3; 4x+2y=6$

asked Jan 21, 2015 by meena.p

1 answer

If $f(x) = \left\{ \begin{array} {1 1} 1 & \quad, \text{ if $ x \leq$ 3 }\\ ax+b & \quad, \text{if $3 < x < 5$ } \\ 7 & \quad, \text{ if $ 5 \leq x $ } \end{array} \right.$ Determine the values if a and b so that $f(x)$ is continuous?

asked Jan 21, 2015 by meena.p

1 answer

If $ f(x) = \left\{ \begin{array} {1 1} \large\frac{ 2^{x+2}-16}{4^x-16}, & \quad\text{ if $x \neq 2$ } \end{array} \right. $ is a continuous at $x=2,$ then find k ?

asked Jan 21, 2015 by meena.p

1 answer

$\begin{align} \int \limits_{\large\frac{\pi}{3}}^{\large\frac{\pi}{2}}\frac{\sqrt {1+\cos x}}{(1- \cos x)^{5/2}}dx \end{align}$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate : $ \int \large\frac{dx}{(x-1)\sqrt {2x+3}}$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate = $\int \large\frac{x^2}{(x \sin x +\cos x)^2}$

asked Jan 21, 2015 by meena.p

1 answer

Solve the differential equation : $(x+2y^2) \large\frac{dy}{dx}$$=y$, given that when $x=2$ and $y=1$. If x devotes the percentage of who are intelligent and y denotes the percentage of people who are work holic, find x when $y=2 \%$ workoholics are always preferable. Do you agree ?

asked Jan 21, 2015 by meena.p

1 answer

Find the equation of the plane containing the line intersection of the plane $x+y+z-6=0$ and $2x+3y+4z+5=0$ and Passing through the pay $(1,1,1)$

asked Jan 21, 2015 by meena.p

1 answer

Find the shortest distance between the lines whose vector equations are : $\overrightarrow{r}= (\hat i+2 \hat j+3 \hat k)+ \lambda (2 \hat i+ 3 \hat j +4 \hat k)$ and $\overrightarrow{r}= (2 \hat i+4 \hat j+5 \hat k)+ (4 \hat i+ 6 \hat j +8 \hat k)$

asked Jan 21, 2015 by meena.p

1 answer

Using the properties of determines evaluate : $\begin{vmatrix} 1 & a & a^2-bc \\1 & b & b^2-ca \\1 & c & c^2-ab\end{vmatrix}$

asked Jan 21, 2015 by meena.p

1 answer

Let $f : N \to R$ be a function defined as $f(x)=4x^2+12x+15$. Show that $f: N \to R$ is invertible. Find the inverse of f

asked Jan 21, 2015 by meena.p

0 answers

Show that the point $(x,y)$ given by $x=\large\frac{2at}{1+t^2}$ and $y=\large\frac{a(1-t^2)}{1+t^2}$ lies on a circle for all real values of $t$ such that $-1\leq t \leq 1$ where $a$ is any given real numbers.

asked Oct 17, 2014 by sreemathi.v

1 answer

Find the equation of the hyperbola with foci $(0,\pm\sqrt{10})$,passing through $(2,3)$.

asked Oct 15, 2014 by sreemathi.v

1 answer

Find the equation of the hyperbola with vertices $(0,\pm 7),e=\large\frac{4}{3}$.

asked Oct 15, 2014 by sreemathi.v

1 answer

Find the equation of the hyperbola with vertices $(\pm 5,0)$,foci $(\pm 7,0)$.

asked Oct 15, 2014 by sreemathi.v

1 answer

Show that the set of all points such that the difference of their distances from $(4, 0)$ and $(-4, 0)$ is always equal to $2$ represent a hyperbola.

asked Oct 14, 2014 by sreemathi.v

1 answer

Find the equation of the set of all points whose distance from $(0, 4)$ are $\large\frac{2}{3}$ of their distance from the line $y = 9$.

asked Oct 14, 2014 by sreemathi.v

1 answer

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