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Questions >> Olympiad-Math

Olympiad-Math

For what value of x will the points $(x,-1) ,(2,1)$ and $(4,5)$ are collinear ?

asked Oct 29, 2014 by meena.p

1 answer

Two vertices of a triangle are $(3.-5)$ and $(-7,4)$ .If its centroid is $(2,-1)$ then its third vertex is ___________

asked Oct 29, 2014 by meena.p

1 answer

The coordinates of one end of a diameter of a circle are $(4,-1)$ and the coordinate of the center of the circle are $(1,-3)$ . The coordinate of the other end of the diameter are _______

asked Oct 29, 2014 by meena.p

1 answer

The coordinates of A and B are $(1,4)$ and $B(5,2)$ respectively, then the coordinate of P if $AP: PB$ is $3:4$ are ____

asked Oct 29, 2014 by meena.p

1 answer

The ratio in which the point $(-6,5)$ divides the join of $A(-3,1)$ and $B(-8,9)$ is ______

asked Oct 29, 2014 by meena.p

1 answer

The coordinate of the centroid of a triangle whose vertices are $(0,6), (8,12)$ and $(8,0)$ is _______

asked Oct 29, 2014 by meena.p

1 answer

If $D,E$ and $F$ are the mid point of sides $BC,CA$ and $AB$ respectively of a $\Delta ABC$ , then $\large\frac{area\;of\;\Delta DEF}{area\;of\;\Delta ABC}$ =______

asked Oct 29, 2014 by meena.p

1 answer

The vertices of a triangle ABC are $A(4,6),B(1,5)$ and $C(7,2)$ . A line is drawn to intersect the sides AB and AC at D and E respectively. Such that $\large\frac{AD}{AB} =\frac{AE}{AC}=\frac{1}{4}$ . Then the ratio of $\large\frac{\Delta ADE}{\Delta ABC}$ is _________

asked Oct 29, 2014 by meena.p

1 answer

Two vertices of a triangle having coordinates $(8,7)$ and $(9,4)$ and the centroid is at the origin, then the coordinates of the third vertex is ________

asked Oct 29, 2014 by meena.p

1 answer

The value of 'a' such that the point $(3,a)$ lies on the line represented by $2x-3y+5=0$ is _____

asked Oct 29, 2014 by meena.p

1 answer

The ratio in which the line segment giving the points $A(3,-6)$ and $B(5,3)$ being divided by x-axis is______

asked Oct 29, 2014 by meena.p

1 answer

The mid point of the line segment joining the points $A(x,y+1)$ and $B(x+1,y+2)$ is $C\bigg(\large\frac{3}{2},\frac{5}{2}\bigg)$ then the value of x and y are _______

asked Oct 29, 2014 by meena.p

1 answer

The perimeter of a triangle formed by the points $(0,0),(1,0)$ and $(0,1)$ is

asked Oct 29, 2014 by meena.p

1 answer

If the points $(k,2k),(3k,3k)$ and $(3,1)$ are collinear,then the value of k is ______

asked Oct 29, 2014 by meena.p

1 answer

A line segment is of length 10 units . If the coordinates of its one end are $(2,-3)$ and the abscissa of the other end is 10, then its ordinate is _______

asked Oct 29, 2014 by meena.p

1 answer

The difference between the two sides of a right angled triangle is $2$ cm and the length of its hypotenuse is $10$ cm.The measurement of the two sides are ________

asked Oct 29, 2014 by sreemathi.v

1 answer

A segment $AB$ of 2 m length is divided internally by $C$ into two parts such that $AC^2=AB\times AC$ .The length of the part $CB$ is _____

asked Oct 29, 2014 by sreemathi.v

1 answer

The area of a triangle is $18\;cm^2$ and the sum of its base and altitude is $12$ cm.The measurements of the base and altitude is _____

asked Oct 29, 2014 by sreemathi.v

1 answer

The longest rod that can be placed flat on the bottom of a box is $45$ cm.The box is $9$ cm longer than its width.The dimensions of the bottom of the box are ______

asked Oct 29, 2014 by sreemathi.v

1 answer

The sum of first $n$ natural numbers is given by the relation $S=\large\frac{n(n+1)}{2}$ .If their sum is $276$ ,then the value of $n$ is _______

asked Oct 29, 2014 by sreemathi.v

1 answer

If the centroid of a triangle in $(1,4)$ and two of its vertices are $(4,-3)$ and $(-9,7)$ , then the area of the triangle is

asked Oct 29, 2014 by meena.p

1 answer

If we divide $12$ into two parts such that the sum of their squares is $74$ ,then the two parts are _____

asked Oct 29, 2014 by sreemathi.v

1 answer

The sum of the squares of two consecutive odd numbers is $202$ ,then the numbers are ______

asked Oct 29, 2014 by sreemathi.v

1 answer

The sum of two natural numbers is $8$ .If the sum of the reciprocals is $\large\frac{8}{15}$ ,then the numbers are _________

asked Oct 29, 2014 by sreemathi.v

1 answer

Four points $A(6,3),B(-3,5),C(4,-2)$ and $D(x,3x)$ are given in such a way that $\large\frac{\Delta DBC}{\Delta ABC}=\frac{1}{2}$ , then the value of x is _______

asked Oct 29, 2014 by meena.p

1 answer

One side of a rectangle exceeds its other side by $2$ cm.If its area is $195$ $cm^2$ ,then the sides of the rectangle is ______

asked Oct 29, 2014 by sreemathi.v

1 answer

The area of the triangle whose vertices are $A(2,7),B(3,-1)$ and $(-5,6)$ are

asked Oct 29, 2014 by meena.p

1 answer

The sum of the squares of two consecutive positive integers is $545$ .Then the integers are

asked Oct 29, 2014 by sreemathi.v

1 answer

The vertices of a triangle are $(1,k),(4,-3)$ and $(-9,7)$ and its area is 15 sq.units , then the value of k is

asked Oct 29, 2014 by meena.p

1 answer

The dimensions of a room whose length is $3$ m more than its breadth,if the area of the room is $70$ sq.m.The quadratic equation to find the dimensions of the room is _____

asked Oct 29, 2014 by sreemathi.v

1 answer

The hypotenuse of a right angled triangle is $6$ meters more than twice of the shortest side.The third side is two meters less than the hypotenuse.The quadratic equation to find the sides is ______

asked Oct 29, 2014 by sreemathi.v

1 answer

Two consecutive positive even integers,the sum of whose squares is $340$ .The quadratic equation to find the integers,is ______

asked Oct 29, 2014 by sreemathi.v

1 answer

The product of two consecutive positive integers is $306$ .The quadratic equation to find the integers,if $x$ is the smallest integer is _____

asked Oct 29, 2014 by sreemathi.v

1 answer

The product of two consecutive positive integers is $240$ .The quadratic equation whose roots of these integers is _____

asked Oct 29, 2014 by sreemathi.v

1 answer

If $x=2$ and $x=3$ are the roots are the equations $3x^2-2px+2q=0$ ,then the value of $p$ and $q$ are ______

asked Oct 29, 2014 by sreemathi.v

1 answer

Say True or False : <br> $3$ is a root of the equation <br> $\sqrt{x^2-4x+3}+\sqrt{x^2-9}=\sqrt{4x^2-14x+16}$

asked Oct 29, 2014 by sreemathi.v

1 answer

If $x=\large\frac{2}{3}$ and $x=-3$ are the roots of the equation $ax^2+7x+b=0$ ,then the values of $a$ and $b$ are _______

asked Oct 29, 2014 by sreemathi.v

1 answer

If one root of the quadratic equation $2x^2+kx-6=0$ is $2$ ,then the value of $k$ is _____

asked Oct 29, 2014 by sreemathi.v

1 answer

The value of $k$ if $x=-a$ is a solution of the equation $x^2+2ax-k=0$ is _______

asked Oct 29, 2014 by sreemathi.v

1 answer

The factors for $x=\large\frac{1}{2-\Large\frac{1}{2-\Large\frac{1}{2-x}}}$ , $x\neq 2$ are

asked Oct 29, 2014 by sreemathi.v

1 answer

The factors of the quadratic equation $9x^2-9(a+b)x+(2a^2+5ab+2b^2)=0$ are _____

asked Oct 29, 2014 by sreemathi.v

1 answer

The roots of the quadratic equation $a^2b^2x^2+b^2x-a^2x-1=0$ are ______

asked Oct 29, 2014 by sreemathi.v

1 answer

The factors for the quadratic equation $(x-3)(x-4)=\large\frac{34}{33^2}$ are _______

asked Oct 29, 2014 by sreemathi.v

1 answer

The roots of the quadratic equation $\large\frac{x+3}{x-2}-\frac{(1-2)}{x}=\frac{17}{4}$ are _______

asked Oct 29, 2014 by sreemathi.v

1 answer

The points $(a, b+c) , (b, c+a)$ and $(c,a+b)$ ________

asked Oct 28, 2014 by meena.p

1 answer

If the Points $(1,4), (3,y)$ and $(-3,16)$ are collinear , then the value of y is

asked Oct 28, 2014 by meena.p

1 answer

If the Points $(-3,12), (7,6)$ and $(x,9)$ are collinear , then the value of x is

asked Oct 28, 2014 by meena.p

1 answer

If the Points $(1,5), (k,1)$ and $(4,11)$ are collinear , then the value of k is

asked Oct 28, 2014 by meena.p

1 answer

The points $(-1,1), (5,7)$ and $(8,10)$ ______

asked Oct 28, 2014 by meena.p

1 answer

The two opposite angular points of a square are $(3,4)$ and $(1,-1)$ the coordinates of the remaining angular points are ________

asked Oct 28, 2014 by meena.p

1 answer

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