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Questions >> Olympiad-Math >> Class 9

Class 9

Logical Reasoning

Coordinate Geometry

Euclid Geometry

Linear Equations

Lines and Angles

Triangles, circles and quadrilaterals

Surface Areas and Volumes

Statistics and Probability

Logical and Analytical Reasoning

Everyday Mathematics

In a $\Delta ABC$ ,AD is a median .X is a point on AD such that AX : XD = 2 : 3.Ray BX intersects AC in Y.Then BX=______ XY.

asked Jan 5, 2015 by sreemathi.v

1 answer

A point D is on the side BC of an equilateral triangle ABC such that $DC=\large\frac{1}{4}$ $BC$ .Then $AD^2$ =____ $CD^2$

asked Jan 5, 2015 by sreemathi.v

1 answer

ABC is a right angled triangle at A.BL and CM are its two medians,then $4(BL^2+CM^2)=$ _______

asked Jan 5, 2015 by sreemathi.v

1 answer

If one diagonal of a trapezium divides the other diagonal in the ratio 1 : 2,then one of the parallel sides is ______ the other.

asked Jan 3, 2015 by sreemathi.v

1 answer

The perpendicular AD on the base BC of a $\Delta ABC$ intersects BC at D such that DB=3CD.Then $2(AB^2-AC^2)=$ ______

asked Jan 3, 2015 by sreemathi.v

1 answer

In $\Delta ABC$ .the bisector of $\angle A$ intersects BC in D.If AB=18 cm,AC=15 cm and BC=22 cm then BD=_____

asked Jan 3, 2015 by sreemathi.v

1 answer

In $\Delta ABC$ ,P and Q are points on sides AB and AC respectively such that $PQ\parallel BC$ .If AP=4 cm,PB=6 cm and PQ=3 cm,then BC is ____

asked Jan 3, 2015 by sreemathi.v

1 answer

$\Delta ABC$ and $\Delta DBC$ are on the same base BC.Then $\large\frac{ar\;\Delta ABC}{ar\;\Delta DBC}$ =______

asked Jan 3, 2015 by sreemathi.v

1 answer

In a $\Delta ABC,\angle BCA=90^{\large\circ}$ and Q is the midpoint of BC.Then $AB^2+3AC^2=$ ______

asked Jan 3, 2015 by sreemathi.v

1 answer

ABCD is a rectangle in which BC=2AB.A point E lies on ray CD such that CE=2BC.Then BE is _____ AC.

asked Jan 3, 2015 by sreemathi.v

1 answer

In $\Delta PQR$ ,M and N are points on sides PQ and PR respectively such that PM=15 cm and NR=8 cm .If PQ=25 cm and PQ=20 cm ,then MN is ______ QR.

asked Jan 3, 2015 by sreemathi.v

1 answer

The corresponding sides of two similar triangles are in the ratio 1 : 3.If the area of the smaller triangle is $40\;cm^2$ ,then the area of the larger triangle is ________

asked Jan 3, 2015 by sreemathi.v

1 answer

The value of $x$ in the adjacent figure if $DE\parallel AB$ is ______

asked Jan 3, 2015 by sreemathi.v

1 answer

An aeroplane leaves an airport and flies due north at a speed of $1000$ km/hr.At the same time,another aeroplane leaves the same airport and flies due west at a speed of $1200$ km/hr.How far apart will be the two planes after $1\large\frac{1}{2}$ hours?

asked Jan 3, 2015 by sreemathi.v

1 answer

The vertices of a triangle ABC are A(a-1)an B $(2\sqrt a)$ an C(a+1)an is ________ triangle.

asked Jan 3, 2015 by sreemathi.v

1 answer

In a quadrilateral ABCD, $\angle B=90^{\large\circ}$ and $AD^2=AB^2+BC^2+CD^2$ ,then $\angle ACD=$ ______

asked Jan 2, 2015 by sreemathi.v

1 answer

A wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end.How far from the base of the poles should the stake be driven so that the wire will be taut?

asked Jan 2, 2015 by sreemathi.v

1 answer

In $\Delta PQR$ ,M and N are points on sides PQ and PR respectively such that PM=15 cm and NR=8 cm.If PQ=25 cm and PR=20 cm,then MR is ________ QR

asked Jan 2, 2015 by sreemathi.v

1 answer

ABCD is a trapezium in which $AB\parallel DC$ . $P$ and $Q$ are points on sides AD and BC such that $PQ\parallel AB$ .If $PD=18,BQ=35$ and $QC=15$ ,then $AD$ =______

asked Jan 2, 2015 by sreemathi.v

1 answer

A staircase is as shown in the figure.Measurements of the steps are marked in the figure.Find the distance between AB.

asked Jan 2, 2015 by sreemathi.v

1 answer

$\Delta ABC$ is an isosceles triangle in which $\angle C=90^{\large\circ}$ .If $AC=6$ cm,then $AB=$ _____

asked Jan 2, 2015 by sreemathi.v

1 answer

In an isosceles triangle ABC if AC=BC,and $AB^2=2AC^2$ ,then $\angle C$ =___

asked Jan 2, 2015 by sreemathi.v

1 answer

ABCD is a trapezium such that $BC\parallel AD$ and $AB=4$ cm.If the diagonals AC and BD intersect at O,such that $\large\frac{AO}{OC}=\frac{DO}{OB}=\frac{1}{2}$ ,then $BC$ =

asked Jan 2, 2015 by sreemathi.v

1 answer

$\Delta ABC$ is a right triangle,right-angled at A and $AD\perp BC$ .Then $\large\frac{BD}{DC}$ =____

asked Jan 2, 2015 by sreemathi.v

1 answer

In a $\Delta ABC,AD$ is the bisector of $\angle BAC$ .If $AB=6$ cm, $AC=5$ cm,and $BD=3$ cm,then $DC$ =

asked Jan 2, 2015 by sreemathi.v

1 answer

A man goes $24$ m due west and then $7$ m due north.How far is he from the starting point?

asked Jan 2, 2015 by sreemathi.v

1 answer

$\Delta ABC\sim \Delta DEF$ .If $BC=3$ cm, $EF=4$ cm and ar $(\Delta ABC)=54\; cm^2$ ,then ar $(\Delta DEF)$ =

asked Jan 2, 2015 by sreemathi.v

1 answer

$\Delta ABC \sim \Delta DEF$ ,ar $(\Delta ABC)=9 cm^2$ ,ar $(\Delta DEF)=16 cm^2$ .If $BC=2.1$ cm, then the measure of EF is

asked Jan 2, 2015 by sreemathi.v

1 answer

$\Delta ABC \sim \Delta DEF$ such that $DE=3$ cm, $EF=2$ cm, $DF=2.5$ cm, $BC=4$ cm,the perimeter of the $\Delta ABC$ is

asked Jan 2, 2015 by sreemathi.v

1 answer

In a $\Delta ABC$ which is an equilateral triangle such that $AD\perp BC$ ,then $AD^2$ =_____

asked Jan 2, 2015 by sreemathi.v

1 answer

In an equilateral triangle ABC,if $AD\perp BC$ ,then

asked Jan 2, 2015 by sreemathi.v

1 answer

ABCD is a trapezium such that $BC\parallel AD$ and $AB=4$ cm.If the diagonals AC and BD intersect at O such that $\large\frac{AO}{OC}=\frac{DO}{OB}=\frac{1}{2}$ ,then $BC$ =

asked Jan 2, 2015 by sreemathi.v

1 answer

If D,E,F are the mid-points of sides BC,CA and AB respectivelyof $\Delta ABC$ ,then the ratio of the areas of triangles DEF and ABC is

asked Jan 2, 2015 by sreemathi.v

1 answer

A vertical stick $12$ cm long casts a shadow $8$ cm long on the ground.At the same time a tower casts a shadow 40 m long on the ground.The height of the tower is _______

asked Jan 2, 2015 by sreemathi.v

1 answer

A ladder reaches a window which is 12 m above the ground on one side of the sheet,keeping its foot at the same point,the ladder is turned to the other side of the sheet to reach a window $9$ m high.The length of the ladder is $15$ m,then the width of the sheet is ______

asked Jan 2, 2015 by sreemathi.v

1 answer

The perimeters of two similar triangles are $30$ cm and $20$ cm respectively.If one side of the first triangle is $15$ cm,the corresponding side of the second triangle is _____

asked Jan 2, 2015 by sreemathi.v

1 answer

In the given figure $AB\parallel MN$ .If $PA=x-2,PM=x,PB=x-1$ and $PN=x+2$ ,find the value of $x$ .

asked Jan 2, 2015 by sreemathi.v

1 answer

In the given figure,AD is the bisector of $\angle BAC$ .If $BD=2$ cm, $DC=3$ cm and $AB=5$ cm,then $AC$ =______

asked Jan 2, 2015 by sreemathi.v

1 answer

Two poles of height $7$ m and $12$ m stand on a plane ground.If the distance between their feet is $12$ m,then the distance between their tips is __________

asked Jan 2, 2015 by sreemathi.v

1 answer

The area of a right angled triangle if its radius is $3$ cm and altitude drawn to the hypotenuse is $2$ cm is ______

asked Jan 2, 2015 by sreemathi.v

1 answer

In two similar triangles $ABC$ and $DEF,AC=10\;cm$ and $DF=8\; cm$ and $AB=6.5$ cm then $DE$ =______

asked Jan 2, 2015 by sreemathi.v

1 answer

In $\Delta$ ABC,DE $\parallel$ BC.If $AD=x,DB=x-2,AE=x+2$ and $EC=x-1$ ,then the value of $x$ is _____

asked Jan 2, 2015 by sreemathi.v

1 answer

The length of a diagonal of a rectangle whose adjacent sides are $8$ m and $6$ m long is _______

asked Jan 2, 2015 by sreemathi.v

1 answer

Triangles ABC and DEF are similar as shown in the figure.The area of $\Delta ABC$ is $16$ sq.cm and that of $\Delta DEF$ is $25$ sq.cm.If $BC=2.3$ cm then $EF$ is _______

asked Dec 31, 2014 by sreemathi.v

1 answer

In the given figure AD is the bisector of $\angle BAC, AB=6$ cm, $AC=5$ cm and $BD=3$ cm then $DC$ =_______

asked Dec 31, 2014 by sreemathi.v

1 answer

Two triangles ABC and DEF are similar to each other in which $AB=10$ cm and $DE=8$ cm,then the ratio of the areas of $\Delta ABC$ and $\Delta DEF$ is ________

asked Dec 31, 2014 by sreemathi.v

1 answer

If $(a+b)=13,(a-b)=11$ then $a^2+b^2$ =_____

asked Dec 31, 2014 by sreemathi.v

1 answer

The value of $(996)^2$ is ______

asked Dec 31, 2014 by sreemathi.v

1 answer

If $2x+y=3$ and $xy=1$ ,then the value of $8x^3+y^3$ is ______

asked Dec 31, 2014 by sreemathi.v

1 answer

If $(x-\large\frac{1}{x})$ $=5$ ,then $x^3-\large\frac{1}{x^3}$ =_____

asked Dec 31, 2014 by sreemathi.v

1 answer

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