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An iron rod of diameter 1cm and length 8cm is drawn into a wire of length 18m of uniform thickness. Find the thickness of the wire?

Question 5
You have studied in Class IX that a median of a triangle divides it into two triangles of equal areas. Verify this result for $\Delta$ ABC whose vertices are A (4, - 6), B (3, - 2) and C (5, 2).

The sum of series $1,\frac{1}{3},\frac{1}{9},\frac{1}{27},\frac{1}{81}.....$ is ___.

The value of $a$ if $(x-a)$ factor of $x^6-a{x}^5+x^4-a{x}^3+3x-a+2=0$ is

Prove that (√3 - √2)³ is irrational

In the adjoining figure O is the center of the circle. $\angle$AOD = ${120}^{\circ }$. If the radius of the circle be 'r', then find the sum of the areas of quadrilaterals AODP and OBQC:

Area of square ABCD with A(1,0) and B(4,0) is ___ square units.

A fan has 3 equally spaced blades. The central dial has an area of 3π cm². Length of each blade is (20-√3)cm. If a triangle is drawn from the tips of the blades, find its area.

In the given fig. PQ is tangent at point R of the circle with centre O. if $\angle$TRQ = ${30}^0$, find $\angle$PRS

The times (in seconds) taken by 150 atheletes to run a 110 m hurdle race are tabulated below

$\begin{array}{ccccccc}Class& 13.8-14& 14-14.2& 14.2-14.4& 14.4-14.6& 14.6-14.8& 14.8-15\\ Frequency& 2& 4& 5& 71& 48& 20\end{array}$

The number of atheletes who completed the race in less than 14.6 s is

Two pipes running together can fill a cistern in $\frac{12}{17}$ minutes. If one pipe takes 4 minutes more than the other to fill it, write the second degree equation from which we can find time taken by the pipe to fill the cistern.

In any three consecutive terms of an arithmetic sequence, the middle term is ___

Write the negation of the statement, for all positive integers n, $n^2$ + 41n + 41 is a prime number.

A circumcircle is drawn around an equilateral triangle. If the circum-radius r = 14 cm, find the area of the shaded region.

In △ ABC, D is a point on BC such that BD: DC = 1 : 2. If area △ ADC = 45 sq cm, then area of △ ABD = ____ sq cm.

There is a circle with centre O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

Prove that $(2\sqrt{3}-1)$ is an irrational number.

A chord 10 cm long is drawn in a circle whose radius is $5\sqrt{2}$ cm. Find the areas of both the segments.

$[Take\pi =\mathrm{3.14.}]$

$\begin{array}{cc}Assertion\left(A\right)& Reason\left(R\right)\\ Iftwotangentsaredrawntoacircle& Aparallelogramcircumscribinga\\ fromanexternalpointthenthey& circleisarhombus.\\ subtendequalanglesatthecentre.& \end{array}$

The correct answer is (a)/(b)/(c)/(d).

Find the value for k which each of the following systems of equations has a unique solution:

$4x+ky+8=0,x+y+1=0.$

If the 'less than type' ogive and 'more than type' ogive intersect each other at (20.5,15.5) then the median of the given data is

(a) 5.5 (b) 15.5 (c) 20.5 (d) 36.0

An equilateral triangle of side 9 cm is inscribed in a circle. The radius of the circle is

(a) 3 cm

(b) $3\sqrt{2}$ cm

(c) $3\sqrt{3}$ cm

(d) 6 cm

27 spherical iron balls of radius 5 cm each are melted and recasted into a big sphere.The radius of the single sphere is___.

In Fig. PSR, RTQ and PAQ are three semi-circles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region.

Solve the following quadratic equation by factorization.
$25x(x+1)=-4$

What is the relation between $\widehat{BC}$ and $\widehat{AD}$?

The sum of the first 20 term of the sqeuence 0.7, 0.77, 0.777,...., is
(IIT JEE Main 2013)

Points P, Q, R and S divide the line segment joining the points A (1, 2) and B (6, 7) in 5 equal parts. Find the coordinates of the points P, Q and R.

The angle of elevation of a stationery cloud from a point 2500 m above a lake is ${15}^{\circ }$ and the angle of depression of its reflection in the lake is ${45}^{\circ }$. What is the height of the cloud above the lake level? (Use tan ${15}^{\circ }$ = 0.268)

In the equation 2x+3y =6, if x=3, find the value of y

Rubix cube has a total surface area of 54 ${cm}^2$. The area occupied by a single red tile on Rubik's cube is

An event whose probability of occurrence is 1, is called as a ___ event.

Determine the nature of the roots of the following quadratic equations:
$\left(i\right)2x^2-3x+5=0\left(ii\right)3x^2-6x+3=0\left(iii\right)\frac{3}{5}{x}^2-\frac{2}{3}x+1=0\left(iv\right)3x^2-4\sqrt{3}x+4=0\left(v\right)3x^2-2\sqrt{6}x+2=0$

Solve each of the following quadratic equations:
$x^2+12x+35=0$

The length, breadth and height of a cuboid are 2 m, 5 m and 4m respectively.
1) What is the difference between total surface area and curved surface area ?
2) If a cube of side measuring 100cm is placed inside the cuboid, what is amount of void space in the cuboid? [4 MARKS]

What is the area of the shaded part in the figure, if its given that the side of square ABCD is 90 m and the side of square PQRS is 100 m?

In the adjoining figure, AB = 10 cm, BC =15 cm AD : DC = 2 : 3, then find the value of$\angle$ABC.

The tangent to a circle from a point outside the circle measures 15cm. The distance of the point from the centre is 12cm. The radius of the circle is

The radius and height of a right cone are in the ratio 3:4. The ratio of the total surface area to the curved surface of the cone is:

Write the following cubes in expanded form:
$\left(i\right)(2x+1{)}^3$
$\left(ii\right)(2a-3b{)}^3$
$\left(iii\right){[\frac{3}{2}x+1]}^3$
$\left(iv\right){[x-\frac{2}{3}y]}^3$

Five years ago Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

In fig., If PQ $\parallel$ BC and PR $\parallel$CD. Prove that $\frac{AR}{AD}$= $\frac{AQ}{AB}$. [4 MARKS]