Recent questions tagged 65-2-3

Two schools $P$ and $Q$ want to award their selected students on the values of Tolerance,Kindness and Leadership. The school $P$ wants to award $Rs.x,\:Rs.y\:and\:\:Rs.z$ each for the three respective values to $3,2\:and\:1$ students respectively with a total award money of $ Rs.2,200.$ School $Q$ wants to spend $Rs.3,100$ to award its 4,1 and 3 students on the respective values (by giving the same award money to the three values as school $P$). If the total amount of award for one prize on each value is $Rs.1,200,$ using matrices, find the award money for each value.

asked Mar 23, 2014 by rvidyagovindarajan_1

1 answer

If $x=a\:cos\theta+b\:sin\theta$ and $y=a\:sin\theta-b\:cos\theta$, then show that $y^2.\large\frac{d^2y}{dx^2}$$-x\large\frac{dy}{dx}$$+y=0$

asked Mar 23, 2014 by rvidyagovindarajan_1

1 answer

Three cards are drawn at random (without replacement) from a well shuffled pack of 52 playing cards. Find the probability distribution of number of red cards. Hence find the mean of the distribution.

asked Mar 23, 2014 by rvidyagovindarajan_1

1 answer

Show that $cot^{-1}7+cos^{-1}8+cot^{-1}18=cot^{-1}3$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Solve: $cos(tan^{-1}x)=sin(cot^{-1}(\large\frac{3}{4}))$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Integrate the function $(3x-2)\sqrt{x^2+x+1}$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Solve the differential equation $(x^2-yx^2)dy+(y^2+x^2y^2)dx=0$ Given $y=1$ when $x=1$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Find a unit vector perpendicular to each of the vector $ \overrightarrow a + \overrightarrow b$ and $ \overrightarrow a - \overrightarrow b$, where $ \overrightarrow a = \hat i + \hat j + \hat k$ and $ \overrightarrow b = \hat i + 2\hat j +3\hat k$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Find the distance of the point $P(-1,-5,-10)$ from the point of intersection of the line joining the points $A(2,-1,2)$ and $B(5,3,4)$with the plane $x-y+z=5$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Find the equation of the plane that contains the point $(1,-1,2)$ and is $\perp$ to the planes $2x+3y-2z=5$ and $x+2y-3z=8$. Hence find the distance of the point $(-2,5,5)$ from the plane obtained above.

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Find the distance between the two lines $l_1$ and $l_2$ where $l_1: \overrightarrow r=(\hat i+2\hat j-4\hat k)+\lambda(2\hat i+3\hat j+6\hat k)$ and $l_2: \overrightarrow r=(3\hat i+3\hat j-5\hat k)+\mu(4\hat i+6\hat j+12\hat k)$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} a^2&bc&ac+c^2 \\ a^2+ab&b^2&ac \\ ab&b^2+bc&c^2 \end{vmatrix} = 4a^2b^2c^2\]

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Find the value of $\hat i\times (\hat j+\hat k)+\hat j\times (\hat k+\hat i)+\hat k\times (\hat i+\hat j)$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Find the value of $a-2b$ if $\begin{bmatrix}a+4 & 3b\\8 & -6\end{bmatrix}=\begin{bmatrix}2a+2 & b+2\\8 & a-8b\end{bmatrix}\qquad$

asked Mar 21, 2014 by rvidyagovindarajan_1

1 answer

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are diamodns? (ii) only 3 cards are diamonds? (iii) none is a diamonds?

asked Mar 20, 2014 by balaji.thirumalai

1 answer

Evlauate$ \Large \int_0^{\pi/4}$$ \large \frac{\sin x+\cos x}{9+16\sin 2x}$$dx$

asked Mar 20, 2014 by balaji.thirumalai

1 answer

Find the projection of the vector $ \hat i + \hat j + \hat k$ on the vector $\hat j$.

asked Mar 20, 2014 by rvidyagovindarajan_1

1 answer

Find the value of the following:\[cos^{-1} \big(- \frac {1} {2} \big)+2 sin^{-1}\frac {1} {2} \]

asked Mar 20, 2014 by rvidyagovindarajan_1

1 answer

Let $R=\{(a,a^3):\:a\: is\: a\: prime\:number\: less\: than\: 5\}$ be a relation. Find the Range of $R$.

asked Mar 20, 2014 by rvidyagovindarajan_1

1 answer

If $A$ is a $3\times 3$ matrix, and $ |A|\neq0$ and $|3A|=k.|A|,$ then write the value of $k$

asked Mar 20, 2014 by rvidyagovindarajan_1

1 answer

Find the angle between the pairs of lines: $ \overrightarrow r = 2\hat i -5 \hat j +\hat k + \lambda (3\hat i +2 \hat j +6\hat k)\: and \: \overrightarrow r = 7\hat i - 6\hat k + \mu (\hat i +2\hat j +2\hat k) $

asked Mar 20, 2014 by rvidyagovindarajan_1

1 answer

Use elementary column operation $C_2\rightarrow C_2-2C_1$ in the matrix equation $\begin{bmatrix}4 & 2\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 2\\0 & 3\end{bmatrix}\:\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}$

asked Mar 20, 2014 by rvidyagovindarajan_1

1 answer

Evaluate $\int\large\frac{dx}{sin^2x\:cos^2x}$

asked Mar 20, 2014 by rvidyagovindarajan_1

1 answer

A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?

asked Nov 16, 2012 by fingeazy

1 answer

Ask Questions, Get Answers

If $x=a\:cos\theta+b\:sin\theta$ and $y=a\:sin\theta-b\:cos\theta$, then show that $y^2.\large\frac{d^2y}{dx^2}$$-x\large\frac{dy}{dx}$$+y=0$

Three cards are drawn at random (without replacement) from a well shuffled pack of 52 playing cards. Find the probability distribution of number of red cards. Hence find the mean of the distribution.

Show that $cot^{-1}7+cos^{-1}8+cot^{-1}18=cot^{-1}3$

Solve: $cos(tan^{-1}x)=sin(cot^{-1}(\large\frac{3}{4}))$

Integrate the function $(3x-2)\sqrt{x^2+x+1}$

Solve the differential equation $(x^2-yx^2)dy+(y^2+x^2y^2)dx=0$ Given $y=1$ when $x=1$

Find a unit vector perpendicular to each of the vector \( \overrightarrow a + \overrightarrow b\) and \( \overrightarrow a - \overrightarrow b\), where \( \overrightarrow a = \hat i + \hat j + \hat k\) and \( \overrightarrow b = \hat i + 2\hat j +3\hat k\)

Find the distance of the point $P(-1,-5,-10)$ from the point of intersection of the line joining the points $A(2,-1,2)$ and $B(5,3,4)$with the plane $x-y+z=5$

Find the equation of the plane that contains the point $(1,-1,2)$ and is $\perp$ to the planes $2x+3y-2z=5$ and $x+2y-3z=8$. Hence find the distance of the point $(-2,5,5)$ from the plane obtained above.

Find the distance between the two lines $l_1$ and $l_2$ where $l_1: \overrightarrow r=(\hat i+2\hat j-4\hat k)+\lambda(2\hat i+3\hat j+6\hat k)$ and $l_2: \overrightarrow r=(3\hat i+3\hat j-5\hat k)+\mu(4\hat i+6\hat j+12\hat k)$

Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} a^2&bc&ac+c^2 \\ a^2+ab&b^2&ac \\ ab&b^2+bc&c^2 \end{vmatrix} = 4a^2b^2c^2\]

Find the value of $\hat i\times (\hat j+\hat k)+\hat j\times (\hat k+\hat i)+\hat k\times (\hat i+\hat j)$

Find the value of $a-2b$ if $\begin{bmatrix}a+4 & 3b\\8 & -6\end{bmatrix}=\begin{bmatrix}2a+2 & b+2\\8 & a-8b\end{bmatrix}\qquad$

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are diamodns? (ii) only 3 cards are diamonds? (iii) none is a diamonds?

Evlauate$ \Large \int_0^{\pi/4}$$ \large \frac{\sin x+\cos x}{9+16\sin 2x}$$dx$

Find the projection of the vector \( \hat i + \hat j + \hat k\) on the vector $\hat j$.

Find the value of the following:\[cos^{-1} \big(- \frac {1} {2} \big)+2 sin^{-1}\frac {1} {2} \]

Let $R=\{(a,a^3):\:a\: is\: a\: prime\:number\: less\: than\: 5\}$ be a relation. Find the Range of $R$.

If $A$ is a $3\times 3$ matrix, and $ |A|\neq0$ and $|3A|=k.|A|,$ then write the value of $k$

Find the angle between the pairs of lines: $ \overrightarrow r = 2\hat i -5 \hat j +\hat k + \lambda (3\hat i +2 \hat j +6\hat k)\: and \: \overrightarrow r = 7\hat i - 6\hat k + \mu (\hat i +2\hat j +2\hat k) $

Use elementary column operation $C_2\rightarrow C_2-2C_1$ in the matrix equation $\begin{bmatrix}4 & 2\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 2\\0 & 3\end{bmatrix}\:\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}$

Evaluate $\int\large\frac{dx}{sin^2x\:cos^2x}$