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A crystal (of an element 'X') has a bcc structure. It has an edge length of $4.3\stackrel{\circ }{A}$. The shortest distance between the atoms is:

The point of intersection of the lines x= -3 and y= -4 is___

1. 9

The perimeter of a rhombus is 164 cm and one of its diagonals is 80 cm. Find its area.

In the figure given below, P and Q are centres of two circles, intersecting at B and C, and ACD is a straight line.

If $\angle APB={150}^{\circ }\text{and}\angle BQD=x^{\circ }$, find the value of x.

If parallelogram ABCD and rectangle ABEM are of equal area, then:

Assertion: Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.

Reason: Angle in a semi-circle is a right angle.



Which of the following options is correct?

C is the mid-point of PQ if P is (4, x), C is (y, -1) and Q is (-2, 4), then x and y respectively are

Prove that in a quadrilateral the sum of all the sides is greater than the sum of its diagonals.

In a ΔABC, the line joining the mid points D and E of sides AB and AC respectively, is produced to meet at point F such that DE = EF. What can you say about the figure DFCB?

factorise

0.729a³+0.343b³

Evaluate the following:

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

Which of the following rational numbers is a non-terminating and repeating decimal?

If $x^a$+$\frac{1}{x^b}$ is a polynomial in one variable and if it is given that $a=b$, then this is a polynomial for $a=$ ___

How many zeroes do the polynomials
$P_1\left(x\right)=x^3+x^2+x+1$ and
$P_2\left(x\right)=x^2+1$
have in common?

How many rounds should Ben run in order to complete $8\text{km}$?

If the circumference of a circle is 528 cm, then its area is ______ $c{m}^2$.



$(\pi =\frac{22}{7})$

If an alphabet is picked from the word MISSIMMIPPI what is the probability that an alphabet 'M' is picked?

In a burglary at the godown of Bharat Goel on the night of 14th July, 2016 part of the stock was stolen.
From the following particulars, find out the estimated value of loss of stock by theft.

$\begin{array}{cc}& Rs.\\ \text{Stock on 1st April, 2016}& 1,20,000\\ \text{Purchases from 1st April to 14th July, 2016}& 8,20,000\\ \text{Sales from 1st April to 14th July, 2016}& 12,00,000\\ \text{Stock remaining after burglary}& 24,000\end{array}$

The normal rate of gross profit for his business is 30% of selling price.

Find the inverse of the given matrix
$\left[\begin{array}{ccc}1& 0& 0\\ 3& 3& 0\\ 5& 2& -1\end{array}\right]$

Assuming two lines AC and DE crossing each other at point B .
From the options given below select the combination of angles if four angles are formed by 2 lines crossing each other and the sum of 2 angles is ${100}^{\circ }$.

A bowl contains milk and chocos.

$\text{The fraction of milk in the bowl is}\frac{3}{7}.\text{When}$

$\text{we add chocos to it, it rises to}\frac{12}{14}\text{of the bowl.}$



Find the fraction of chocos added to the bowl.

In the given figure, PQRS is a parallelogram and ∠R is 100^o then ∠Q is

Respected Sir/Ma'am

I am having a problem in solving the following question ; can you please help me out :-

Factorise the following :-
x²/2 + 9x/2 + 10

Thank You

Find the sum and product of the zeroes polynomial $9x^2-6x+1$. [2 MARKS]