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Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the length(in cm) of the smallest part.

1. 2.9

Factorise:
$3a^{3}b-243a{b}^3$

In a camp, there is enough flour for 300 persons for 42 days. How long will the flour last, if 20 more persons join the camp?

The diagonals of a parallelogram ABCD intersect at O. If $BOC={90}^{\circ }and\angle BDC={50}^{\circ }$ then $\angle OAB=$

$\sqrt[4]{4\sqrt[3]{32^2}}$ equals to

A.) $2^{\frac{-1}{6}}$
B.) $2^{-6}$
C.) $2^{\frac{1}{6}}$
D.) $2^6$

An infinite G.P. has first term 'x' and sum '5', then x belongs to

$$\begin{array}{ccccc}Outcome& 2& 3& 5& 6\\ Frequency& 10& 14& 16& 20\end{array}$$

A dice was thrown 80 times and the frequency of occurrence of 2, 3, 5 and 6 is given in the table. What is the probability of occurrence of 1 or 4?

The mean of 5 observations is 17. If the mean of the first 3 observations is 15, then find the mean of the other two.

$(256{)}^{0.16}\times (256{)}^{0.09}$

The cost of a toy horse is same as the cost of three balls .

Express the statement in linear equation in two variables.

A and B are finite sets such that n(A) = 17 and n(B) = 29. If A is a subset of B, then, $n\left(\right(A\cup B)-(A\cap B\left)\right)$= ___ .

Factorization of $64a^3–343b^3$ is:

What is Inradius?

If the object is solid, the space occupied by such an object is called volume and if the object is hollow, the space that can be filled is called ___

For representing the root 5 on the number line we should take only two units are we can take other units also

Give possible expression for the length and breadth of the rectangle having 35y^2+13y-12 as its area.

Which of the following are new numbers obtained while constructing the Spiral of Theodorus?

Anita has only 20 paise & 25 paise coins in her purse. She has 50 coins in all totaling to Rs.11.25. The linear equation representing the situations is

If two ratios are equal, then we say that they are ___.

27x cube + y cube - z cube + 9xyz

An exterior angle of a triangle is 110^o; and one of the interior opposite angles is 30^o, then the other two angles of the triangle are

Find the value of $si{n}^2\theta +co{s}^2\theta at\theta ={30}^{\circ }\&{60}^{\circ }$ respectively.

The bisectors of the base angles of an isosceles triangle ABC, with AB = AC, meet at O.

If $\angle B=\angle C={50}^{\circ }$. What is the measure of angle O ?

The distance between the graphs of the equations y = - 1 and y = 3 is

If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are

If X^2+1/X^2=7, then find the value of X^3-1/X^3

On the number line $\sqrt{17}$ lies between

With reference to the figure, ABCD is a parallelogram. AE and CF are angle bisectors of ∠DAC and ∠ACB respectively. What can you say about lines AE and CF?

The supplement of an acute angles, is ___.

ABCD us a quadrilateral. Prove that

AB+BC+CD+DA>AC+BD

Factorize: $7a^2+14+\frac{7}{a^2}$

Factorize: $5x{y}^2+35xy$

Given one line and one circle that you can arrange in any way you like, the minimum number of points where they intersect is

Simplify: $\left(i\right){\left(\frac{x^{a+b}}{x^c}\right)}^{a-b}{\left(\frac{x^{b+c}}{x^a}\right)}^{b-c}{\left(\frac{x^{c+a}}{x^b}\right)}^{c-a}\left(ii\right)\sqrt[lm]{lm\frac{x^l}{x^m}}\times \sqrt[mn]{mn\frac{x^m}{x^n}}\times \sqrt[nl]{nl\frac{x^n}{x^l}}$

1. 4

If a + b + c = 9, and $a^2+b^2+c^2=35$, find the value of $a^3+b^3+c^3-3abc.$

A circus is cylindrical to a height of 3 metres and conical above it. If its diameter is 105 m and the slat height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent.

$\text{The area of an equilateral triangle is}81\sqrt{3}c{m}^2.\text{Its height is}\left(a\right)9\sqrt{3}cm\left(b\right)6\sqrt{3}cm\left(c\right)18\sqrt{3}cm\left(d\right)9cm$

Question 4(b)

Find the product using suitable properties:

$854\times 102$

ABCD is a parallelogram, G is the point on AB such that AG = 2 GB, E is a point of DC such that CE = 2 DE and F is the point of BC such that BF = 2 FC. Prove that:
$\left(i\right)ar\left(ADEG\right)=ar\left(GBCE\right)\left(ii\right)ar\left(△EGB\right)-\frac{1}{6}ar\left(ABCD\right)\left(iii\right)ar\left(△EFC\right)=\frac{1}{2}ar\left(△EBF\right)\left(iv\right)ar\left(△EGB\right)=\frac{3}{2}ar\left(△EFC\right)$
(v) Find what portion of the ara of parallelogram is the area of $△EFG.$

Question 142

The paper clip below has the indicated length. What is the length in standard form.

Question 7(c)

In the following pair of numbers, state which whole number is on the left of the other number on the number line? Also write them with the appropriate sign (>, <) between them.
98765, 56789

Question 14(ii)
50 students enter for a school javelin throw competition. The distance (in metres) thrown are recorded below :

$\begin{array}{cccccc}Distance\left(inm\right)& 0-20& 20-40& 40-60& 60-80& 80-100\\ Numberofstudents& 6& 11& 17& 12& 4\end{array}$


(ii) Draw a cumulative frequency curve (less than type) and calculate the median distance thrown by using this curve.