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Recent questions tagged 65-2-3
Questions
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.
cbse
class12
modelpaper-2014
65-2-3
sec-c
q25
math
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$
cbse
class12
modelpaper-2014
65-2-3
sec-b
q17
math
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.
cbse
class12
modelpaper-2014
65-2-3
sec-b
q16
math
asked
Mar 23, 2014
by
rvidyagovindarajan_1
1
answer
Show that $cot^{-1}7+cos^{-1}8+cot^{-1}18=cot^{-1}3$
cbse
class12
modelpaper-2014
65-2-3
sec-b
q14-b
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Solve: $cos(tan^{-1}x)=sin(cot^{-1}(\large\frac{3}{4}))$
cbse
class12
modelpaper-2014
65-2-3
sec-b
q14-a
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Integrate the function $(3x-2)\sqrt{x^2+x+1}$
cbse
class12
modelpaper-2014
65-2-3
q18-b
math
sec-b
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 $x=1$
cbse
class12
modelpaper-2014
65-2-3
sec-b
q13
math
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 \( \overrightarrow b = \hat i + 2\hat j +3\hat k\)
cbse
class12
modelpaper-2014
65-2-3
sec-b
q11-b
math
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 $x-y+z=5$
cbse
class12
modelpaper-2014
65-2-3
sec-c
q24-b
math
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.
cbse
class12
modelpaper-2014
65-2-3
sec-c
q24-a
math
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 $l_2: \overrightarrow r=(3\hat i+3\hat j-5\hat k)+\mu(4\hat i+6\hat j+12\hat k)$
cbse
class12
modelpaper-2014
65-2-3
sec-b
q19
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} a^2&bc&ac+c^2 \\ a^2+ab&b^2&ac \\ ab&b^2+bc&c^2 \end{vmatrix} = 4a^2b^2c^2\]
cbse
class12
modelpaper-2014
65-2-3
sec-b
q22
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Find the value of $\hat i\times (\hat j+\hat k)+\hat j\times (\hat k+\hat i)+\hat k\times (\hat i+\hat j)$
cbse
class12
modelpaper-2014
65-2-3
sec-a
q9
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Find the value of $a-2b$ if $\begin{bmatrix}a+4 & 3b\\8 & -6\end{bmatrix}=\begin{bmatrix}2a+2 & b+2\\8 & a-8b\end{bmatrix}\qquad$
cbse
class12
modelpaper-2014
65-2-3
sec-a
q8
math
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?
cbse
class12
modelpaper-2014
65-2-3
sec-c
q26-1
math
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$
cbse
class12
ch7
modelpaper-2014
65-2-3
sec-c
q29
math
asked
Mar 20, 2014
by
balaji.thirumalai
1
answer
Find the projection of the vector \( \hat i + \hat j + \hat k\) on the vector $\hat j$.
cbse
class12
modelpaper-2014
65-2-3
sec-a
q7
math
asked
Mar 20, 2014
by
rvidyagovindarajan_1
1
answer
Find the value of the following:\[cos^{-1} \big(- \frac {1} {2} \big)+2 sin^{-1}\frac {1} {2} \]
cbse
modelpaper-2014
65-2-3
sec-a
q6
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 $R$.
cbse
modelpaper-2014
65-2-3
sec-a
q5
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 $k$
cbse
modelpaper-2014
65-2-3
sec-a
q4
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) $
cbse
modelpaper-2014
65-2-3
sec-a
q3
asked
Mar 20, 2014
by
rvidyagovindarajan_1
1
answer
Use elementary column operation $C_2\rightarrow C_2-2C_1$ in the matrix equation $\begin{bmatrix}4 & 2\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 2\\0 & 3\end{bmatrix}\:\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}$
cbse
modelpaper-2014
65-2-3
sec-a
q2
asked
Mar 20, 2014
by
rvidyagovindarajan_1
1
answer
Evaluate $\int\large\frac{dx}{sin^2x\:cos^2x}$
cbse
modelpaper-2014
65-2-3
sec-a
q1
easy
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?
cbse
class12
bookproblem
ch12
sec2
q6
p520
sec-c
medium
math
modelpaper-2012
modelpaper-2014
65-2-3
q23
asked
Nov 16, 2012
by
fingeazy
1
answer
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