Recent questions tagged sec-c

Three numbers are selected at random (with out replacement ) from first six positive integers. If X denotes the smallest of the three numbers obtained , find the probability distribution of X.Also find the mean and variance of the distribution .

asked May 30, 2016 by meena.p

1 answer

A diet is to contain at least 80 units of vitamin A and 100 units of minerals. Two foods $ F_1 \: and F_2$ are available . Food $ F_1 $ costs Rs. 4 perunit and $ F_2$ costs Rs. 6 per unit. One unit of food $ F_1 $ contains 3 units of vitamin A and 4 units of minerals. One unit of food $ F_2 $ contains 6 units of vitamin A and 3 units of minerals. Formulate this as a linear programming problem and find graphically the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.

asked May 30, 2016 by meena.p

1 answer

Find the equation of the plane containg two parallel lines $ \large\frac{x-1}{2} = \frac{y+1}{-1} = \frac{z}{3} $ and $\large\frac{x}{4} = \frac{y-2}{-2} =\frac{z+1}{6}$ . Also find the plane thus obtained contains the line $ \large\frac{x-2}{3} =\frac{y-1}{1} =\frac{z-2}{5}$ or not .

asked May 30, 2016 by meena.p

1 answer

Using integration find the area of the region $f(x,y): y^2 \leq 6ax$ and $ x^2+y^2 \leq 16a^2$

asked May 30, 2016 by meena.p

1 answer

Find the maximum and minimum values of $f(x)=\sec x + \log \cos ^2x, 0 < x < 2 \pi$

asked May 30, 2016 by meena.p

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Determine the intervals in which the function $f(x)=x^4 -8x^3+22x^2-24 x +21$ is strictly increasing or strictly decreasing.

asked May 30, 2016 by meena.p

1 answer

Using of elementary row operations, find the inverse of the following matrix : $\begin{bmatrix} 2 & -1 & 3\\ -5 & 3 & 1\\-3 & 2 & 3\end{bmatrix}$

asked May 30, 2016 by meena.p

1 answer

Using properties of determinant prove that : $\begin{bmatrix}(b+c)^2 & a^2 & bc \\ (c+a)^2 & b^2 & ca \\ (a+b)^2 & c^2 & ab \end{bmatrix}$ $=(a-b)(b-c)(c-a) (a+b+c)(a^2+b^2+c^2)$

asked May 30, 2016 by meena.p

1 answer

A cross section of a light pipe made of a glass fibre of refractive index 1.68 . The outer covering of the pipe is made of material of refractive index 1.44 . What is the range of the angles of incident rays with the axis of pipe for which the total reflection inside the pipe takes place .

asked May 13, 2016 by meena.p

1 answer

A person with a normal near point $(25 cm)$ using a compound microscope with an objective of focal length 8.0 mm and an eye piece of focal length 2.5 cm can bring an object placed 9.0 mm from the objective in sharp focus. what is the separation between the two lenses ? calculate the magnifying power of the microscope ?

asked Mar 3, 2016 by meena.p

1 answer

A compound microscope consists of an objective less of focal length $2.0\;cm$ and an eye -piece of focal legth $6.25\;cm$ , separated by a distance of 15 cm . How far from the objective should an object be placed in order to obtain the final image at the least distance of distinct vision (25 cm) . What is the magnifying power

asked Mar 3, 2016 by meena.p

1 answer

A prism is made of glass of unknown refractive index. A parallel beam of light is incident on a face of the prism. By rotating the prism the minimum angle of deviation is measured to be $40 ^{\circ}$ The refractive angle of the prism is $60^{\circ}$ If the prism is placed in water (refractive index 1.33) predict the new minimum angle of deviation of a parallel beam of light

asked Feb 17, 2016 by meena.p

1 answer

What is the amount of chlorine evolved when 2 ampere of current is passed for $30$ minutes in an aqueous solution of $Nacl$

asked Sep 21, 2015 by meena.p

1 answer

An electron and a positron are released $(0,0,0)$ and $(0,01.5 \;R)$ respectively , in a uniform magnetic field $\overrightarrow{B} =B_0 \hat i$, each with an equal momentum of magnitude $P= eBR$ Under what condition on the direction of momentum will the orbit be non- intersecting circles.

asked Jul 31, 2015 by meena.p

1 answer

A rectangular conducting loop consists of two wires on two opposite sides of length l joined together by rod of length d. The wires are each of the same material but with cross - section differing by a factor of 2. The thicker wire has a resistance R and the rods of low resistance , Which in turn are connected to a constant voltage source $V_0$ the loop is placed in uniform magnetic field B at 45 to its plane . Find the $T$ the torque exerted by the magnetic field on the loop about an axis through the centers of rods.

asked Jul 31, 2015 by meena.p

1 answer

A 100 turn rectangular coil $ABCD$ is hung from one arm of a balance(as shown in the figure) . A mass 500 g is added to the other arm to balance the weight of the coil . A current $4.9\;A$ passes through the coil and a constant magnetic field of $0.2 \;T$ acting inward (in xz plane) is switched on such that only arm CDof length 1 cm lies in the field . Hoe much additional mass 'm' must be added to regain the balance ?

asked Jul 31, 2015 by meena.p

1 answer

A multi range voltmeter can be constructed by using a galvanometer circuit as shown in the figure. We want to construct a voltmeter that can measure $2V,20V$ and $200\;V$ using a galvanometer of resistance $10\Omega$ and that produces maximum deflection for current of $1mA$ Find $R_1,R_2$ and $R_3$ that have to be used

asked Jul 31, 2015 by meena.p

1 answer

A short bar magnet placed in a horizontal plane has its axis aligned along the magnet north - south direction . Null points are found on the axis of the of the magnet at $14\;cm$ from the center of the magnet . The earth magnetic field at the place is $0.36\;G$ and the cycle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the null - point (14 cm) from the centre of the magnet?

asked Jul 13, 2015 by meena.p

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Determine the current drawn from a 12 v supply with internal resistance $0.5 \Omega$ by the infinite network shown in the figure . Each resistor has $\Omega$ resistance

asked Jul 7, 2015 by meena.p

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A paisa coin is made up of Al-my alloy and weights $0.75\;g$ It has a square shape and its diagonal measures $17\;mm$ It is electrically neutral and contains equal amounts of positive and negative charges. Treating the paisa coins made up only $Al$, find the magnitude of equal number of positive and negative charges. What conclusion do you draw from this magnitude ?

asked Apr 29, 2015 by meena.p

1 answer

A hollow charged conductor has a tiny hole cut into its surface . show that the electric field in the hole is $ \bigg( \large\frac{\sigma}{2 \in_0}\bigg)$$\hat n$, where $\hat n$ is the unit vector in the outward normal direction and $\sigma$ is the surface change density near the hole.

asked Apr 28, 2015 by meena.p

1 answer

In a certain region of space , electric field is along the z- direction throughout. The magnitude of electric field is, however not constant but increases uniformly along the positive z- direction, at the rate of $10^5 N/c-m$. What are the force and torque experienced by a system having a total dipole moment equal to $10^{-7}c-m$ in the negative z- direction ?

asked Apr 28, 2015 by meena.p

1 answer

A dietician wants to develop a special diet using two foods X and Y. Each packet (contains 30g) of food X contains 12 units of calcium , 4 units of iron, 6 units of cholesterol and $6 \;units$ of vitamin A. Each packet of the same quantity of food Y contains 3 units of calcium, 20 units of iron , 4 units of cholesterol and 3 units of vitamin A. The diet requires at least 240 units of calcium , at least 460 units of iron and at most 300 units of cholesterol. Make an LPP to find how many packets of each food should be used to minimise the amount of vitamin A in the diet, and solve it graphically.

asked Mar 23, 2015 by meena.p

1 answer

A dealer deals in two items only - item A and item B . He has $Rs. 50,000$ to inverst and a space to store at most 60 items. An item A cost $Rs. 2500$ and item B costs $Rs. 500$. A net profit to him on item A is $Rs. 500$ and on item B is $Rs. 150$. If he can sell all the items that he purchases , how should he inverst his amount to have maximum profit ? Formulate an LPP and solve is graphically .

asked Mar 23, 2015 by meena.p

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Assume that the chances of a patient having a heart attack is $40\%$ . It is also assumed that a meditation and yoga course reduces the risk of heart attack by $30\%$ and the prescription of a certain drug reduces its chance by $25\%$ . At a time a patient can choose any one of the two options with equal probabilities . Its given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of mediation and yoga.

asked Mar 23, 2015 by meena.p

1 answer

Find the vector and cartesian equation of the plane passing through the intersection of the planes $\overrightarrow {r} . (\hat i +\hat j+ \hat k)=6$ and $\overrightarrow {r} . (2\hat i +3\hat j+ 4 \hat k)=-5$ and the point $(1,1,1)$

asked Mar 23, 2015 by meena.p

1 answer

Solve the following differential equation , given that $y=0$ , then $ x= \large\frac{\pi}{4}: $$ \sin 2x \large\frac{dy}{dx}$$-y =\tan x$

asked Mar 23, 2015 by meena.p

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Find the general Solution of the differential equation $\large\frac{dy}{dx}=\frac{y^2}{xy-x^2}$

asked Mar 23, 2015 by meena.p

1 answer

Find the point on the curve $y= \large\frac{x}{1+x^2} $, Where the tangent to the curve has the greatest slope.

asked Mar 23, 2015 by meena.p

1 answer

Using integration , find the area bounded by the curve $y= |x-1|$ and $y= 3-|x|$

asked Mar 23, 2015 by meena.p

1 answer

Show that the relation R in the set $A= [1,2,3,4,5]$ given by $R= [(a,b):|a-b|] $ is divisible by 2. It is an equivalence relation . Show that all the elements of $[1,3,5]$ are related to each other and all the elements of $[2,4]$ are related to each other , but no element of ${1,3,5}$ is related to any element of $[2,4]$

asked Mar 22, 2015 by meena.p

1 answer

The 13th term of an A.P is four times its 3rd term . If its fifth term is 16, then find the sum of its first ten terms

asked Mar 18, 2015 by meena.p

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Find the value of 'k' so that the area of the triangle with vertices $(k+1,1)(4,-3)$ and $(7,-k)$ is $6 \;sq.units$

asked Mar 17, 2015 by meena.p

1 answer

A bus travels at a certain average speed for a distance of $75\;km$ and then travels a distance of $90\;km$ of an average speed of $10 km /hr$ more then the first speed. If it takes 3 hours to completed the total journey, find its first speed.

asked Mar 17, 2015 by meena.p

1 answer

If the 20th term of an AP is five times its third term . If its 10th term is 41, then find the sum of its first fifteen term

asked Mar 17, 2015 by meena.p

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Solve for $x : 2x^2+6 \sqrt 3 x -60 =0$

asked Mar 17, 2015 by meena.p

1 answer

All vertices of a rhombus be on a circle. Find the area of the rhombus , if the area of the circle is $1256\;cm^2$ $(\pi= 3.14)$

asked Mar 17, 2015 by meena.p

1 answer

Find the 60th term of the AP $8,10,12....,$ if it has a total of 60 terms and hence find the sum of its last 10 terms .

asked Mar 17, 2015 by meena.p

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$504$ cones , each of diameter $3.5\;cm$ and height 3 cm, are melted and recast into a metallic sphere. find the diameter of the sphere and hence find its surface [use $\pi =\large\frac{22}{7}$ ]

asked Mar 17, 2015 by meena.p

1 answer

A cubical block of side 10 cm is surmounted by a hemisphere . What is the largest diameter that the hemisphere can have ? Find the cost of painting the total surface area of the solid so formed, at the rate of $5$ per $100 \;sq\;cm$ [Use $\pi = 3.14$]

asked Mar 17, 2015 by meena.p

1 answer

A hemispherical bowl of internal diameter $36\;cm$ contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm Find the height of the each bottle. If $10 \%$ liquid is wasted in this transfer .

asked Mar 17, 2015 by meena.p

1 answer

If the coordinates of points A and B are $(-2,-2)$ and $(2,-4)$respectively, find the coordinates of P such that $AP=\large\frac{3}{7} $$AB$, where P lies on the line segment AB.

asked Mar 17, 2015 by meena.p

1 answer

The angle of elevation of an aeroplane from a point A on the ground is $60^{\circ}$. After a flight of 15 seconds the angle of elevation changes to $30^{\circ}$. If the aeroplane is flying at a constant height of $1500 \sqrt 3\;m$ find the speed of the palne in km/hr

asked Mar 17, 2015 by meena.p

1 answer

Solve for x$ \sqrt 3 x^2 -2 \sqrt 2 x -2 \sqrt 3 =0$

asked Mar 17, 2015 by meena.p

1 answer

The 14th term of an AP is twice its 8th term . If its 6th term is $-8$ , then find the sum of its first 20 terms

asked Mar 17, 2015 by meena.p

1 answer

Draw a circle of radius $6\;cm$. From a point $10\;cm$ away from its centre, construct the pair of tangents to the circle and measure their lengths.

asked Feb 19, 2015 by meena.p

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How many numbers of two digits are divisible by 7?

asked Feb 19, 2015 by meena.p

1 answer

$O$ is the centre of the circle and $BCD$ is tangent to it at $C.$ Prove that $\angle BAC + \angle AC = 90^{\circ}$

asked Feb 19, 2015 by meena.p

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Find the value of ‘k’, if the points $A(8,1), B(3,-4)$ and $C(2,k)$ are collinear

asked Feb 19, 2015 by meena.p

1 answer

How many terms of the series $54,51,48…$ is taken so that their sum is $513?$ Explain the double answer.

asked Feb 19, 2015 by meena.p

1 answer

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