Recent questions tagged sec-c

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

asked Feb 19, 2015 by meena.p

0 answers

Solve by the method of completing the squares: $3x^2 + 2x-1=0$

asked Feb 19, 2015 by meena.p

1 answer

The sum of three numbers in an $A.P.$ is $-3,$ and their product is $8$. Find the numbers [ ans: -4,-1,2 or 2,-1,-4]

asked Feb 19, 2015 by meena.p

2 answers

From a thin metallic piece, in the shape of a trapezium $ABCD,$ in which $AB$ is parallel to $CD$ and $\angle BCD = 90^{\circ}$, a quarter circle $BEFC$ is removed. Given $AB = BC = 3.5\;cm$ and $DE = 2cm,$ calculate the area of the remaining piece of the metal sheet.

asked Feb 19, 2015 by meena.p

1 answer

The cost of painting the total outside surface of a closed cylindrical oil tank at $50\;paise$ per sqdm is $Rs. 275$. The height of the tank is $5$ times the radius of the base of the tank. Find its volume .

asked Feb 19, 2015 by meena.p

1 answer

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

asked Feb 10, 2015 by meena.p

1 answer

Evaluate : $\int \large\frac{1}{1+ 3 \sin ^2 x +8 \cos ^2 x}$$dx$

asked Feb 10, 2015 by meena.p

1 answer

An amount of $Rs. 5000$ is put into three investments at the rate of interest of $6\%,7\%$ and $8\%$ per annum respectively . The total annual income is $Rs. 385$ If the combined income from the first two investments is $Rs. 70$ more than the income from the third , find the amount of each investment by matrix method.

asked Feb 10, 2015 by meena.p

1 answer

If a machine is correctly setup, it produces $90\%$ acceptable items. If it is incorrectly setup, it produces only $40 \% $ acceptable items . past experience shows that $80\%$ of the setups are correctly done . If after a certain setup, the machine produces 2 acceptable items, find the probability that machine is correctly setup.

asked Feb 10, 2015 by meena.p

0 answers

Let the point $(2,3,4)$ lie on the top of Tajmahal. Find the perpendicular distance of the point $(2,3,4)$ from the line $\large\frac{(4x)}{2}=\frac{y}{6} =\frac{(1-z)}{3}$.Also find the coordinates of the perpendicular. Do you think that heritage is important is important for the country and its people ?

asked Feb 10, 2015 by meena.p

0 answers

If the length of the three sides of a trapezium other than the base are equal to 10 cm , then find the area of the trapezium when it is maximum .

asked Feb 10, 2015 by meena.p

1 answer

Find the area bounded by the curve $y= 2x-x^2$ and the straight line $y=-x$

asked Feb 10, 2015 by meena.p

1 answer

Compute the area bounded by the lines $x+2y =2 ; y-x =1$ and $2x+y=7$

asked Feb 10, 2015 by meena.p

1 answer

A small manufacturer has employed 5 skilled men 10 semi - skilled men and makes an article in two qualities deluxe model and an ordinary model. The making of a deluxe model requires 2 hrs work bt skilled man and 2 hrs work by a semi skilled man. The ordinary model requires 1 hr by a skilled man and 3 hrs by a semi skilled man. By union rules no mam may work more than 8 hrs per day. The manufactures clear profit on deluxe model is Rs.15 and an orsinary model is Rs. 10. How many of each type should be made in order to maximize his total daily profit.

asked Feb 10, 2015 by meena.p

1 answer

Evaluate $I= \int \limits _0^{\large\frac{\pi}{2}} \large\frac{x}{\sin x +\cos x}$$dx$

asked Jan 23, 2015 by meena.p

1 answer

A wire of length $36\;cm$ is cut into two pieces. One of the pieces is turned in the form of a square and the other in the form of an equilateral triangle. Find the length of each piece so that the sum of the areas of the two be minimum.

asked Jan 23, 2015 by meena.p

1 answer

Make a rough sketch of the region given below and find its area using the method of integration $\{(x,y): 0 \leq y \leq x^2 +3, 0 \leq y \leq 2x+3,0 \leq x \leq 3 \}$

asked Jan 23, 2015 by meena.p

1 answer

Using integration find the area of the triangular region whose sides have the equation $y = 2x+1, y=3x+1,x=4$

asked Jan 23, 2015 by meena.p

1 answer

Show that the differential equation $(x-y) \large\frac{dy}{dx}$$ = x+2y$ is homogenous and solve it

asked Jan 23, 2015 by meena.p

1 answer

Using matrix method , solve the following system of linear equations: $5x+y-z=7, 4x-2y-3z=5, 7x+2y+2z=7.$

asked Jan 23, 2015 by meena.p

1 answer

A company produces two types of goods $A$ and $B$ that require gold and silver. Each unit of type $A$ requires $1\; gm$ of silver and $2 \;gm$ of gold. Type $B$ requires(each unit) $2\; gm$ of silver and $1\;gm$ of gold. The company has only $80\; gm$ of gold. Each unit of type A brings profit of $Rs. 500$ and each unit of type $B$ brings profit of $Rs. 400.$ Find the no of units of each type the company should produce to maximize the profit.

asked Jan 23, 2015 by meena.p

0 answers

There are $80$ workers in a publication house. Out of which $20$ are hardworking and honest. Three workers are selected at random out of them. Write the probability distribution for the selected workers who are hardworking and honest. Also find the mean of the distribution. Write the importance of hardworking and honesty in one’s life.

asked Jan 23, 2015 by meena.p

1 answer

An urn contains 10 white and 3 black balls. Another urn contains 3 white and 5 black balls. Two balls are drawn from the first urn and put into the second urn and then a ball is drawn from the second urn. Find the probability that it is a white ball.

asked Jan 23, 2015 by meena.p

1 answer

Find the length and foot of the perpendicular from the point $(1,1,2)$ to the plane $\overrightarrow{r}(\hat i - 2 \hat j + 4 \hat k) +5=0$

asked Jan 21, 2015 by meena.p

1 answer

A dealer wishes to purchase a number of fans and radio. He has only $\$5760$ to invest and has a space for atmost 20 items. A fan costs him $\$360$ and a radio $\$240$. His expectation is this he can sell a fan at a profit of $\$22$ and a radio at a profit of $\$18$ . Assuming that he can sell all the items that he buys, how should be invert his money for maximum profit? Translate the problem as LPP and solve it graphically . What is the importance of electricity in our life .

asked Jan 21, 2015 by meena.p

1 answer

By examining the chest X-ray , the probability that TB is detected when a person is actually suffering is $0.99$ . The probability of an healthy person diagnosed to have TB is $0.001$ . In a certain city, 1 in 1000 people suffer from TB. A person selected at random and is diagnosed to have TB. What is the probability that be action has TB?

asked Jan 21, 2015 by meena.p

1 answer

Find the area enclosed by the curve $y=1x$ and $y= -|x-1|+1$

asked Jan 21, 2015 by meena.p

1 answer

find the area bounded by the lines $y= 4x+5,y=5-x$ and $4y= x+5$

asked Jan 21, 2015 by meena.p

1 answer

Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm

asked Jan 21, 2015 by meena.p

1 answer

Evaluate $\int\limits_0^{\pi/2} \large\frac{\cos x}{1+ \cos x+ \sin x}$$dx$

asked Jan 21, 2015 by meena.p

1 answer

Evaluate $\int\limits_0^{\pi} \large\frac{x}{1- \cos \alpha \sin x}$$dx$

asked Jan 21, 2015 by meena.p

1 answer

The cost of $4kg$ Onion,$3kg$ wheat and $2kg$ rice is $\$60$. The cost of $2\;kg$ onion,$4\;kg$ wheat and $6\;kg$ rice is $\$90$. The cost of $6\;kg$ onion, $2\;kg$ wheat and $3\;kg$ rice is $\$70$. Find the cost of each item per kg by matrix method.

asked Jan 21, 2015 by meena.p

1 answer

The equation of the circle circumscribing the triangle whose sides are the lines $y=x+2,3y=4x,2y=3x$ is _____________

asked Oct 15, 2014 by sreemathi.v

1 answer

Find the equation of a circle passing through the point $(7,3)$ having radius $3$ units and whose centre lies on the line $y=x-1$.

asked Oct 14, 2014 by sreemathi.v

1 answer

Find the equation of the circle which passes through the points $(2,3)$ and $(4,5)$ and the centre lies on the straight line $y-4x+3=0$.

asked Oct 13, 2014 by sreemathi.v

1 answer

If the lines $2x-3y=5$ and $3x-4y=7$ are the diameters of a circle of area 154 square units,then obtain the equation of the circle.

asked Oct 13, 2014 by sreemathi.v

1 answer

Calculate the mole fraction of ethylene glycol $(C_2H_6O_2)$ in a solution containing 20% of $C_2H_6O_2$ by mass.

asked Aug 8, 2014 by sreemathi.v

1 answer

0.5g KCl was dissolved in 100g water and the solution originally at $20^{\large\circ}C$,froze at $-0.24^{\large\circ}C$.Calculate the percentage ionization of salt.$(K_f$ per 1000g of water =1.86K)

asked Aug 8, 2014 by sreemathi.v

1 answer

The freezing point of 0.02 mole fraction solution of acetic acid in benzene is 277.4K.Assuming molality equal to molarity,calculate $K_c$ for the equilibrium reaction $2CH_3COOH\;\;\leftrightharpoons\;\;(CH_3COOH)_2$.Given : $T_f$(benzene) =$278.4$ and $K_f$(benzene)=5.0K kg $mol^{-1}$.

asked Aug 8, 2014 by sreemathi.v

1 answer

The boiling point elevation of 0.30g acetic acid in 100g benzene is 0.0633K.Calculate the molar mass of acetic acid from this data?What conclusion can you draw about the molecular state of the solute in the solution?[Given $K_b$ for benzene = $2.53\;K kgmol^{-1}]$

asked Aug 7, 2014 by sreemathi.v

1 answer

If boiling point of an aqueous solution is $100.1^{\large\circ}$C.What is its freezing point?Given,latent heat of fusion and vaporisation of water as 80 cal $g^{-1}$ and 540 cal $g^{-1}$ respectively.

asked Aug 7, 2014 by sreemathi.v

1 answer