Recent questions tagged sec-c

Using matrix solve the following system of linear equations : $ 2x+y+z=3 ; 3x-y+z=0 ;x-2y+3z = -6$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the largest possible area of the right-angled triangle whose hypotenuse is 5 cm.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Prove that the radius of the right circular cylinder of the greatest curved surface that can be inscribed in a given cone is half of the radius of the cone.

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the region included between the parabola $ y^2=x $ & the line $ x+y=2.$

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the shortest distance between the lines : $\overrightarrow r = (1+2\lambda ) \hat i + (2+3\lambda)\hat j + (3+4\lambda)\hat k $ and $ \overrightarrow r = (2+3\mu ) \hat i + 4(1+\mu)\hat j + 5(1+\mu)\hat k $

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Find the angle between the planes $ 4x+8y+z-8=0 \: and \: y+z-4=0. $

asked Jan 11, 2013 by thanvigandhi_1

0 answers

Using matrix solve the following system of linear equations : $ x+y+z=4;2x-y+z=-1;2x+y-3z = -9$

asked Jan 10, 2013 by thanvigandhi_1

0 answers

If $ A = \begin{bmatrix} 3 & 1 \\ 7 & 5 \end{bmatrix} $, find x and y that $ A^2+x1 = yA.$ Hence find $ A^{-1} $.

asked Jan 10, 2013 by thanvigandhi_1

0 answers

Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is $ \large\frac{1}{3}h.$

asked Jan 10, 2013 by thanvigandhi_1

0 answers

Find the area of the smaller part of the circle $ x^2+y^2=a^2$ cut off by the line $ x=\large\frac{a}{\sqrt 2}$

asked Jan 10, 2013 by thanvigandhi_1

2 answers

Form the differential equation of the family of circles in the first quadrant which touch the coordinates axes.

asked Jan 10, 2013 by thanvigandhi_1

0 answers

Find the equation of plane passing through the (-1, -1, 2) and $ \bot $ to each of the following planes : $ 2x+3y-3z=2 \: and \: 5x-4y+z=6 $.

asked Jan 10, 2013 by thanvigandhi_1

0 answers

A farmer has a supply of chemical fertilizer of type I which contains 10% nitrogen and 6% phosphoric acid and type II fertilizer which contains 5% of nitrogen and 10% phosphoric acid. After testing the soil conditions of a field, it is found that atleast 14kg of nitrogen and 14 kg of phosphoric acid is required for a good crop. The fertilizer type I costs Rs.2/kg and the type II costs Rs. 3/kg. How many kilograms of each fertilizer should be used to meet the requirement and the cost be minimum?

asked Jan 10, 2013 by thanvigandhi_1

0 answers

A can hit a target 4 times in 5 shots, B 3 times in 4 shots and C 2 times in 3 shots. Calculate the probability that \[\begin{array}{1 1} ((i) \: A,B,C\: all \: may \: hit. \\ (ii)\: Any\: two \: of \: A,B\: and \: C\: will\: hit \ the \: target. \\ (iii)\: None \: of\: them \: will \: hit \: the \: target.\\(iv)None \:of\:hem\:will\:hit\:the\:target. \end{array} \]

asked Jan 10, 2013 by thanvigandhi_1

0 answers

The probability distribution of a random variable x is given as under:\[P(X=x)=\left \{\begin{array}{1 1}kx^2 & for\;x=1,2,3\\2kx & for\;x=4,5,6\\0 & otherwise\end{array}\right.\]Where k is a constant.Calculate\[(i)\;E(X)\quad(ii)\;E(3X^2)\quad(iii)\;P(X\geq 4)\]

asked Jan 9, 2013 by sreemathi.v

1 answer

Let X be a discrete random variable whose probability distribution is defined as follows:\[P(X=x)=\left \{\begin{array}{1 1}k(x+1) & for\;x=1,2,3,4\\2kx & for\;x=5,6,7\\0 & otherwise\end{array} \right.\]where k is a constant. Calculate\[(i)\;the\;value\;of\;k\quad(ii)\;E(X)\quad(iii)\;standard\;deviation\;of\;X\]

asked Jan 9, 2013 by sreemathi.v

1 answer

A shop keeper sells three types of flower seeds $A_1,A_2 and\;A_3$.They are sold as a mixture where the proportions arev4:4:2 respectively.The germination rates of the three types of seeds are 45%,60% and 35%.Calculate the probability\[\begin{array}{1 1}(i)\;of\;a\;randomly\;chosen\;seed\;to\;germinate\\(ii)\;that\;it\;will\;not\;germinate\;given\;that\;seed\;is\;of\;type\;A_3\\(iii)\;that\;it\;is\;of\;the\;type\;A_2\;given\;that\;a\;randomly\;chosen\;seed\;does\;not\;germinate\end{array}\]

asked Jan 9, 2013 by sreemathi.v

1 answer