Recent questions in Real Numbers

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

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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