Recent questions in Olympiad-Math

The height of the mountain if the elevation of its top at an unknown distance from the base is $30^{\circ}$ and at a distance $10\;km$ further off from the mountain along the same line whose where angle of elevation is $15^{\circ}$ is _____ $(\tan 15^{\circ} = 0.27)$

asked Nov 5, 2014 by meena.p

1 answer

The shadow of a vertical tower on level ground increases by $10\;cm$ The attitude of sun changes from the angle of elevation $45 ^{\circ}$ to $30^{circ}$ The height of the tower is _______

asked Nov 5, 2014 by meena.p

1 answer

At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is $\large\frac{5}{12}$ . On walking $192\;m$ towards the tower. the tangent of the angle of elevation is $\large\frac{3}{4}$ . The height of the tower is

asked Nov 5, 2014 by meena.p

1 answer

The angle of elevation of a jet plane from a point A on the ground is $60^{\circ}$ After a flight of $30$ seconds , the angle of elevation changes to $30^{\circ}$ . If the jet plane is flying at a constant height of $3600\sqrt 3\;m$ , then the speeds of the jet plane is _______

asked Nov 5, 2014 by meena.p

1 answer

The angles of depression of two ships from the tops of a light house are $45^{\circ}$ and $30^{\circ}$ towards east. If the ships are $100\;m$ apart, the height of the light house is _______

asked Nov 5, 2014 by meena.p

1 answer

The angle of elevation of a cloud from a point h meter above a lake is $\theta$ . The angle of of depression of the lake is $45^{\circ}4. The height of the cloud is

asked Nov 5, 2014 by meena.p

1 answer

If $x^a=c^b$ and $x^c=c^a$ then $a^2=$ _

asked Nov 5, 2014 by sreemathi.v

1 answer

The captain of an aeroplane who is flying at an alttitude of $1200\;m$ sights two ships at an angle of depression of $60^{\circ}$ and $30^{\circ}$ . The distance between the two ships is ________

asked Nov 5, 2014 by meena.p

1 answer

If $\big(\large\frac{a}{b}\big)^{x-1}=\big(\large\frac{b}{a}\big)^{x-3}$ ,then the value of $x$ is _____

asked Nov 5, 2014 by sreemathi.v

1 answer

From the top of a $50\;m$ high building , the angle of depression of a car on the road is $30^{\circ}$ . The distance between the car and the building is ________

asked Nov 5, 2014 by meena.p

1 answer

If $x=2^{2n}$ ,then the value of $8.x^{\Large\frac{3}{2n}}-8.x^{-\Large\frac{3}{2n}}$ is __

asked Nov 5, 2014 by sreemathi.v

1 answer

The value of $2\sqrt[3]{40}+3\sqrt[3]{625}-4\sqrt[3]{320}$ is _

asked Nov 5, 2014 by sreemathi.v

1 answer

The rational form of $18.\overline{48}$ is ____

asked Nov 5, 2014 by sreemathi.v

1 answer

$0$ is a ________ number

asked Nov 5, 2014 by sreemathi.v

1 answer

The rational form of $0.37\overline{81}$ is _____

asked Nov 5, 2014 by sreemathi.v

1 answer

If $\large\frac{5+2\sqrt 3}{7+4\sqrt 3}$ $=a+b\sqrt 3$ then the value of $a$ and $b$ is

asked Nov 5, 2014 by sreemathi.v

1 answer

If $x=\frac {\sqrt3 + 1}{2}$ then the value of $4x^3+2x^2-8x+7$

asked Nov 5, 2014 by sreemathi.v

1 answer

The simplest rationalising factor of $\sqrt[5]{a^2b^3c^4}$ is __

asked Nov 5, 2014 by sreemathi.v

1 answer

The value for $\sqrt{252}-5\sqrt 6+\sqrt{294}-3\sqrt{\large\frac{1}{6}}$ is ______

asked Nov 4, 2014 by sreemathi.v

1 answer

The angle of elevation of a cloud from a point $60\;m$ above a lake is $30^{\circ}$ and the angle of depression of the lake of the cloud in the lake is $60^{\circ}$ . The height of the cloud is

asked Nov 4, 2014 by meena.p

1 answer

What is the value of $\large\frac{1}{1+\sqrt 2}+\frac{1}{\sqrt 2+\sqrt 3}+\frac{1}{\sqrt 3+\sqrt 4}$ +...... 15 terms?

asked Nov 4, 2014 by sreemathi.v

1 answer

A kite is flying attached to a thread which is $165\;m$ long. The thread makes an angle of $30^{\circ}$ with the ground. The height of the kite from the ground is ________

asked Nov 4, 2014 by meena.p

1 answer

If $x=\sqrt{\large\frac{5+2\sqrt 6}{5-2\sqrt 6}}$ ,then the value of $x^2(x-10)^2$ is ____

asked Nov 4, 2014 by sreemathi.v

1 answer

If $2 cosec^2 30^{\circ} + x \sin^2 60^{\circ}- \large\frac{3}{4}$ $\tan^2 30 =10$ then the value of x is ________

asked Nov 4, 2014 by meena.p

1 answer

If $a=2+\sqrt 3$ ,then the value of $a^3+\large\frac{1}{a^3}$ is _____

asked Nov 4, 2014 by sreemathi.v

1 answer

The value of $\sin (70^{\circ}+ \theta) - \cos (20^{\circ}- \theta )$ =________

asked Nov 4, 2014 by meena.p

1 answer

If $g=t^{\large\frac{2}{3}}+4t^{\large\frac{-1}{2}}$ ,then the value of $g$ when $t=64$ is ____

asked Nov 4, 2014 by sreemathi.v

1 answer

If $x=\large\frac{\sqrt 5+\sqrt 3}{\sqrt 5-\sqrt 3}$ and $y=\large\frac{\sqrt 5-\sqrt 3}{\sqrt 5+\sqrt 3}$ then the value of $x+y+xy$ is _____

asked Nov 4, 2014 by sreemathi.v

1 answer

If A and B are angle and $\sin A = \cos B$ , then $A+B$ =______

asked Nov 4, 2014 by meena.p

1 answer

If $\large\frac{\sqrt 3-1}{\sqrt 3+1}=$ $a-b\sqrt 3$ then the value of $a$ and $b$ are __

asked Nov 4, 2014 by sreemathi.v

1 answer

If $\sin \theta + \cos \theta =1$ then $\cos \theta - \sin \theta=$ ______

asked Nov 4, 2014 by meena.p

1 answer

If $x+\sqrt{15}=4$ ,then $x+\large\frac{1}{x}$ is _____

asked Nov 4, 2014 by sreemathi.v

1 answer

If $\sec \theta + \tan \theta =m$ and $\sec \theta - \tan \theta =n$ then $mn$ =______

asked Nov 4, 2014 by meena.p

1 answer

The value of $\sqrt{5+2\sqrt 6}$ is _______

asked Nov 4, 2014 by sreemathi.v

1 answer

If $3 \sin \theta +5 \cos \theta =5$ , then $5\sin \theta -3 \cos \theta$ =_____

asked Nov 4, 2014 by meena.p

1 answer

If $\sqrt{14-b\sqrt{3}}=\sqrt 8+\sqrt 6$ ,then the value of $b$ is _____

asked Nov 4, 2014 by sreemathi.v

1 answer

If $a \cos \theta- b \sin \theta =c$ then $(a \cos \theta)$ =________

asked Nov 4, 2014 by meena.p

1 answer

If $x=3-2\sqrt 2$ ,then the value of $x^2+\large\frac{1}{x^2}$ is ___

asked Nov 4, 2014 by sreemathi.v

1 answer

If $x=2+\sqrt 3$ ,then the value of $x^2+\large\frac{1}{x^2}$ is ____

asked Nov 4, 2014 by sreemathi.v

1 answer

If $x=\large\frac{1}{2-\sqrt 3}$ then the value of $x^3-2x^2-7x+5$ ____

asked Nov 4, 2014 by sreemathi.v

1 answer

The value of $a^2+ab+b^2$ if $a=\large\frac{\sqrt 2+1}{\sqrt 2-1}$ and $b=\large\frac{\sqrt 2-1}{\sqrt 2+1}$ is ______

asked Nov 4, 2014 by sreemathi.v

1 answer

The value of $(cosec^2 \theta -1) \tan ^2 \theta =$ _____

asked Nov 4, 2014 by meena.p

1 answer

The value of $\sin ^2 32+ \sin ^2 58$ is ________

asked Nov 4, 2014 by meena.p

1 answer

If $\sqrt{13-a\sqrt{10}}=\sqrt8+\sqrt 5$ ,then the value of $'a'$ are __

asked Nov 4, 2014 by sreemathi.v

1 answer

If $x= r \sin \theta \cos \phi , y = \sin \theta \sin \phi$ , and $z= r \cos \theta ,$ then

asked Nov 4, 2014 by meena.p

1 answer

The HCF of the smallest composite number are the smallest prime number is ________

asked Nov 4, 2014 by sreemathi.v

1 answer

If $a \cot \theta + b\; cosec \theta =p$ and $b \cot \theta + a\; cosec \theta =q ,$ then $p^2-q^2=$

asked Nov 4, 2014 by meena.p

1 answer

$\cos ^4 A - \sin ^4 A =$

asked Nov 4, 2014 by meena.p

1 answer

The sum of the exponents of the prime factors in the prime factorization of $196$ is ____

asked Nov 4, 2014 by sreemathi.v

1 answer

If $\large\frac{\sin \theta}{1+\cos \theta}=$

asked Nov 4, 2014 by meena.p

1 answer

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