Recent questions tagged sa-2

If $A(-2,-1), B(a,0), C(4,b)$ and $D(91,2)$ are the vertices of a parallelogram, find the values of a and b.

asked Feb 19, 2015 by meena.p

1 answer

Find the coordinates of the circumcentre of the triangle whose vertices are $(8,6),(8.2)$ and $(2,-2)$. Also find its circum-radius

asked Feb 19, 2015 by meena.p

1 answer

$ABC$ is a right angled triangle , right angled at A. Find the area of the shaded region if $AB = 6cm, BC = 10cm$ and $I$ is the centre of the incircle of $\Delta ABC.$

asked Feb 19, 2015 by meena.p

1 answer

Sonia buys a shop for $Rs. 1,20,000$. She pays half the amount in cash and agrees to pay the balance in $12$ annual installments of $Rs. 5000$ each. If the rate of interest is $12 \%$ and she pays with the installment due on the unpaid amount, find the total cost of the shop.

asked Feb 19, 2015 by meena.p

0 answers

Ramesh has got $24000/$ - as Puja Bonus. He donated ` 5000/'- to temple. He gave $`12000/-$ to his wife, ` $2000/-$ to his servant and gave rest of the amount to his daughter. a. What is the probability of wife's share? b. Calculate the probability of servant's share? c. What is the probability of daughter's share? d. Which value are depicted by Ramesh from the way the amount is distributed?

asked Feb 19, 2015 by meena.p

1 answer

A fast train takes 3 hrs less than the a slow train for a journey of $600\;km$. If the speed of the slow train is 10km/hr less than that of the fast train, find the speeds of the two trains

asked Feb 19, 2015 by meena.p

1 answer

If two tangents are drawn to a circle from an external point, then prove that, a)They subtend equal angles at the centre b) They are equally inclined to the segment, joining the centre to that point.

asked Feb 19, 2015 by meena.p

0 answers

Two circles with centres A and B of radii $3\;cm$ and $4\;cm$ respectively intersect at two points C and D such that AC and BC are tangents to the two circles. Find the length of the common chord

asked Feb 19, 2015 by meena.p

1 answer

An aeroplane flying horizontally $1\;km$ above the ground is observed at an angle of elevation of $60^{\circ}$. After 10 seconds, its elevation is observed to be $30^{\circ}$. Find the speed of the aeroplane in km/hr

asked Feb 19, 2015 by meena.p

1 answer

If the angle of elevation of a cloud from a point h meteres above a lake is a and the angle of depression of its reflection in the lake be b, prove that the distance of the cloud from the point of observation is $\large\frac{2hsec \alpha}{tan \beta -tan \alpha}.$

asked Feb 19, 2015 by meena.p

1 answer

A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainer is $\large\frac{8}{9}$ of the curved surface of the whole cone, find the ratio of the line-segment into which the cone’s altitude is divided by the plane.

asked Feb 19, 2015 by meena.p

1 answer

Water flows at the rate of $10\;m$ per minute through a cylindrical pipe having its diameter as $5\;mm$. How much time will it take to fill a conical vessel whose diameter of base is $40\;cm$ and depth $24\;cm$?

asked Feb 19, 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

0 answers

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

0 answers

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

$O$ 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

How many lead shots each having diameter $3\;cm$ can be made from a cuboidal lead solid of dimensions $9cm \times 11cm \times 12cm$

asked Feb 19, 2015 by meena.p

1 answer

IF $\Delta ABC$ is isosceles with $AB =AC$ and centre $(O,r)$ is the incircle of the $∆ABC$ touching $BC$ at $L$. Prove that $L$ bisects $BC.$

asked Feb 19, 2015 by meena.p

0 answers

A circus tent is cylindrical upto a height of $3m$ and conical above it. I the diameter of the base is $105\;m$ and the slant height of the conical part is $53\;m$, find the total canvas used in making the tent.

asked Feb 19, 2015 by meena.p

1 answer

In a musical chair game, the person playing the music has been advised to stop playing the music at any time within $2$ minutes after she startys playing. What is the probability that the music will stop within half a minute after starting?

asked Feb 19, 2015 by meena.p

1 answer

Prove that the points $(a,b+c),(b,c+a),(c,a+b)$ are collinear.

asked Feb 18, 2015 by meena.p

0 answers

Determine the ratio of the volume of a cube to that of a sphere which will exactly fir inside the cube.

asked Feb 18, 2015 by meena.p

1 answer

If a circle is inscribed in a parallelogram, how will the parallelogram change?

asked Feb 18, 2015 by meena.p

0 answers

What is the value of ‘t’, if the points $(t,2t),(-2,6)$ and $(3,1)$ are collinear?

asked Feb 18, 2015 by meena.p

1 answer

What is the diameter of the semicircular protractor whose perimeter is $36\;cm$?

asked Feb 18, 2015 by meena.p

1 answer

What is the maximum volume of a cone that can be carved out of a solid hemisphere of radius ‘r’ ?

asked Feb 18, 2015 by meena.p

1 answer

From the letter “Mathematics” a letter is selected. What is the probability that the selected letter is a vowel?

asked Feb 18, 2015 by meena.p

1 answer

What is the angle of elevation of the sun when the length of the shadow of a vertical pole is equal to the height?

asked Feb 18, 2015 by meena.p

1 answer

Find the value of $a_{30} – a_{10}$ for the A.P. $4,9,14,19… $

asked Feb 18, 2015 by meena.p

1 answer

For what value of $p,$ does the equation has real roots, $2px^2 – 8x +p=0$

asked Feb 18, 2015 by meena.p

1 answer

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