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$(\frac{a^m}{a^{-n}}{)}^{m-n}\times (\frac{a^n}{a^{-l}}{)}^{n-l}\times (\frac{a^l}{a^{-m}}{)}^{l-m}$

If $x=2+\sqrt{3}$, then $x^3+\frac{1}{x^3}$ = __.

The volume of the cylinder having base area as $20c{m}^2$ and height as 4 cm is equal to

By how much is $5a^2{b}^2-18a{b}^2-10a^{2}b$ greater than $-5a^2+6a^{2}b-7ab$?

__ is defined as the line segment joining the opposite vertices of a quadrilateral.

If $\sqrt{5^n}=125,then{5}^{n\sqrt{64}}$ =

I have a certain number of chocolates. My friend has $4$ more than twice the number of chocolates I have. Which of the following equations depicts the relation between the number of chocolates I have with the chocolates my friend has?
($x$ - no. of chocolates I have, and $y$ - no. of chocolates my friend has)

If l and m is interesting line and l parallel to p and m is parallel to q show that p and also intersect

Can we draw a quadrilateral ABCD with following specifications; AB = 3 cm, BC = 5 cm, AD = 4 cm, CD = 7 cm and BD = 8 cm?

In a mixture of 42 litres, the ratio of sugar solution to salt solution is 3:4. Find the amount of sugar solution to be added to convert the ratio to 4 :3.

The highest exponent among the terms in a polynomial is called the __ of the polynomial.

Which of the following statement is not correct?

If $A=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right],$ then which one of the following statements is not correct ?

The tops of two poles of height 20m and 14m are connected by a wire. If the wire makes an angle of 30 degree with horizontal, then the length of the wire is:

In the figure given below identify interior angles.

Area of the right-angled triangle given in the figure below is .

Which of the following fractions is equal to $\frac{1}{\sqrt{3}-\sqrt{5}}$?

The weights of three objects X, Y and Z measured on three celestial bodies are listed in the box. (g on the Moon, Jupiter and Mercury are 1.7 $m{s}^{-2}$, 25.4 $m{s}^{-2}$ and 3.8 $m{s}^{-2}$ respectively)

Which of the following sequences show X, Y and Z in ascending order of their masses?

If $a{x}^n$ is a zero degree polynomial in $x$, what can be said about $a$?

It is given that the probability of winning a game is 0.7. What is the probability of losing the game?

(a) 0.8

(b) 0.3

(c) 0.35

(d) 0.15

In the figure, AB and CD are parallel lines and transversal EF intersects them at P and Q respectively. If $\angle APR={25}^{\circ },\angle RQC={30}^{\circ }$ and $\angle CQF={65}^{\circ },$ then

The decimal representation of a rational number is

(a) always terminating (b) either terminating or repeating

(c) either terminating or nonrepeating (d) neither terminating nor-repeating

If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.

The expression $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$ when simplified reduces to $a-b\sqrt{15}$

Then a + b is

In the given figure,ABCD is a ||gm in which AB=CD=5 cm and $BD\perp DC$ such that BD=6.8 cm.Then,the area of ABCD=?

(a) $17c{m}^2$

(b) $25c{m}^2$

(c) $34c{m}^2$

(d) $68c{m}^2$

$ABCD$ is a rhombus with $\angle ABC={56}^{\circ }$. Determine $\angle ACD$.

Prove that the medians corresponding to equal sides of an isosceles triangle are equal.

Sir,

Please give the answer for this question

If x2+5x+6 is a factor of p(x) then __________is 0

The square plot given below has a green portion which is $0.25$ of the total plot. So, the fractional representation of this part is .

How can we represent 100grams in kilograms?

Which point on the number line best represents the number 2.83?

Are the following points P (1, 3), Q (3, –1), R (–5, –5) are the vertices of a right angled triangle.

Factorise: $(a+b{)}^2-2(a^2-b^2)+(a-b{)}^2$

Find two irrational numbers between 0.16 and 0.17.

For any two finite sets A and B

1) If the polynomial az³+4z²+3z-4 and z³-4z+a leave the same remainder when divided by z-3 m. Find the value of a?

Simplify :

(x-y) ³ + (y-z) ³ + (z-x) ³

A unique solution for a pair of linear equations is obtained if

S1 : the graphs of the equations have only one point of intersection.

S2 : The ratio of coefficients of the two variables are equal.

In a regular polygon each interior angle is 120 degree grater than each exterior angle. Calculate the number of side of the polygon.

In triangle, $\angle B={90}^{\circ }$, $AB=(2x+1)$ cm and $BC=(x+1)$ cm . If the area of the triangle ABC is $60c{m}^2$ ,find its perimeter .

Find the value of (x-a)³+(x-b)+(x-c)³-3(x-a)(x-b)(x-c) , if a+b+c=3x

For what value of $a$ is the line $y=ax$ parallel to the line $\frac{2}{3}y-6x=3$ ?

How can we factorise a² + 2ab + b² -9

If the abscissa of a point is y and the ordinate is x then the coordinates of the point are ........

In the figure, $\frac{AO}{OC}=\frac{BO}{OD}=\frac{1}{2}andAB=5cm$. Find the value of CD .

Figure 2.

Division of a fraction “A” by a whole number “p” is the same as multiplying the fraction with ___.

Given two rational numbers lying between 0.232332333233332... and 0.212112111211112.