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In figure given below, find the value of $\angle$1 + $\angle$2.

Question 1(j)

State whether the given expression is an equation or not.Give reason for your answer.Identify the variable in the given expression.

$7=(11\times 2)+p$

Construct
an equilateral triangle of side 5.5 cm.

Represent the inequality $x+7\ge 7$ on the number line.



Note: In a number line, a closed circle on the number gets included in the solution, while an open circle on the number will not get included in the solution.

A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:

$\begin{array}{cccccccc}2.6& 3.0& 3.7& 3.2& 2.2& 4.1& 3.5& 4.5\\ 3.5& 2.3& 3.2& 3.4& 3.8& 3.2& 4.6& 3.7\\ 2.5& 4.4& 3.4& 3.3& 2.9& 3.0& 4.3& 2.8\\ 3.5& 3.2& 3.9& 3.2& 3.2& 3.1& 3.7& 3.4\\ 4.6& 3.8& 3.2& 2.6& 3.5& 4.2& 2.9& 3.6\end{array}$

Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5. Calculate the number of batteries having a life of 3.5-4.0 years.

Burst the angles that can be drawn using set squares?

Question 5(a)

Add :p ( p - q ), q (q - r ) and r (r - p ).

In the given figure, ∠ABC = ${90}^{\circ }$, BM is a median, AB = 8 cm and BC = 15 cm. Find the value of CM.

A circle has a radius of $7cm.$ What is the nature of the value of its circumference?

In the figure below, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of $\angle$ POS and $\angle$ SOQ respectively. If $\angle$ POS = $x$, then find $\angle$ ROT.

Question 84 (d)

Simplify and express each fo the following exponential form.
$\left(\frac{a^6}{a^4}\right)\times a^5\times a^0$

Express the following fractions as percentage.

At 4 am, the temperature in Eastbourne was $-5^{\circ }C$. By 1 pm, it had increased by $4^{\circ }C$. The temperature in Eastbourne at 1 pm is .

If the sides of a triangle $ABC$ are $6,8,10$ units, then the radius of its circumcircle is

Question 34

State whether the following statement is true (T) or false (F).

Shika's present age is p years. Reemu's present age is 4 times the present age of Shikha. After 5 years, Reemu's age will be 15p years.

Question 3

Draw a $\Delta$ABC in which BC= 6cm, CA = 5 cm and AB= 4 cm .Construct a triangle similar to it and of scale factor = $\frac{5}{3}$.

Thinking process

Here, scale factor = $\frac{m}{n}=\frac{5}{3}$ i.e m > n then the triangle to be construction is larger than the given through use this concept and then constant the required triangle.

Question 94 (f)

Taking $x=\frac{-4}{9},y=\frac{5}{12}$ and $z=\frac{7}{18}$, find
The sum of reciprocals of x and y

Fill in the blanks.

Look at the given measure of sides and angles of the triangles, which of the following triangle cannot be constructed?

Find the value of $(5{)}^6\times (7{)}^6$.

Express the following ratios in fractions.

In the given figure, ABC is a triangle in which ∠ABC> 90° and AD ⊥ CB produced. Prove that AC² = AB² + BC² + 2BC.BD.

${\left(\frac{5}{7}\right)}^{-5}$ is equal to :

$(-374)÷(-17)=$ ______.

How many points do three parallel lines intersect at?

The sum of a number and its half is five less than twice the number. Which of the following equations represents given statement mathematically?

Ratio of two angle of a linear pair is 7:5.Find the angles

In a right-angled triangle, the measure of ____________ angle/angles is 90^o.

Which of the following is/are obtuse angled triangle(s)?