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Two parallel lines touch a circle at points A and B respectively. If the area of the circle is 25 $\pi$ ${cm}^2$, then AB is____________.

Simplify the following:

(1) Subtract (−5) from 5.

(2) How much should be subtracted from (+5) to get −7?

(3) By how much (−10) exceeds (−20).

(4) From what number should (+10) be subtracted to get −15?

(5) What must be added to +7 to get −10?

(6) What should be added to +10 to get −4?

(7) If then, fill up the gap.

(8) If then fill up the gap.

(9) . Find the difference and show the operation by drawing a number line.

(10) Subtract −100 from the sum of −30 and +30.

What letters of the English alphabet have reflectional symmetry
(i.e., symmetry related to mirror reflection) about.

(a) a vertical mirror

(b) a horizontal mirror

(c) both horizontal and vertical mirrors

The entry to a fair costs Rs 20 and each game at the fair costs Rs 5 to play. If Shalini went to the fair and the number of games she played is x, write an expression for the total money spent.

Rita read $\frac{3}{8}th$ of the book on Monday and $\frac{4}{5}th$ of remaining on Tuesday. If there were $30$ pages unread, how many pages does the book contains.

The location of co-ordinates A and B in the form (x, y) are (___,___) and (___,___) respectively.

Rani had Rs 18.50. She bought one ice-cream for Rs 11.75. How much money does she have now?

In the below given figure of parallelogram, AF and BE are angle bisectors of $\angle A$ and $\angle B$ respectively. Find the measure of $x$.

Solve the following problems.

An agent receives an amount of Rs. 2,400 as commission by selling chemical fertilizers. If the rate of commission is 2%, find the cost of chemicals sold by him.

Let $n^3$. A list of numbers $x_1,x_2.....x_n$ has mean $m$ and standard deviation $s$. A new list of numbers $y_1,y_2....y_n$ is made as follows : $y_1=\frac{x_1+x_2}{2},y_2=\frac{x_1+x_2}{2}$ and $y_j=x$ for $j=3,4,.......$. The mean and the standard deviation of the list are $\hat{\mu }$ and $\hat{\sigma }$ . Then which of the following is necessarily true?

If the area of a room is $\frac{226}{4}$ m² and its breadth is $\frac{57}{16}$ meters, then what is its length?

What is the base and exponent in 7³?

A man travelled $60$ km by car and $240$ km by train. Find what percent of the total journey did he travel by car and what percent by train?

Solve the following problems.

A certain sum of money is deposited by your father in Sahara India in the form of cumulative deposit. Your father gets an amount of Rs. 10,000 after 6 years. If Rs. 2,800 is the interest included in the amount find the sum deposited by your father.

Virat and Samrat together invested $Rs.5000$ and $Rs.120000$ to start a business. They suffered a loss of $20\%$. How much loss did each of them incur.

Question 94

State whether the statement is True or False.

If the areas of two rectangles are same, they are congruent.

Question 172

Mass of Mars = $6.42\times {10}^{29}kg$ and Mass of the Sun = $1.99\times {10}^{30}kg$. What is the total mass ?

A coin is tossed and a die is rolled one after the other. Find the probability of flipping a tail and seeing a 4.

Solve:

(i) $2-\frac{3}{5}$

(ii) $4+\frac{7}{8}$

(iii) $\frac{3}{5}+\frac{2}{7}$

(iv) $\frac{9}{11}-\frac{4}{15}$

(v) $\frac{7}{10}+\frac{2}{5}+\frac{3}{2}$

(vi) $2\frac{2}{3}+3\frac{1}{2}$

(vii) $8\frac{1}{2}-3\frac{5}{8}$

$\sqrt[4]{42}$ can also be written as

In $\Delta ABC,\angle B={90}^{\circ }$. Find the sides of the triangle, if AB = (x + 2) cm, BC = (x + 4) cm and AC = (x + 6) cm.

Which congruence criterion is used in the following:

Given: $\angle$ MLN = $\angle$ FGH , $\angle$ NML= $\angle$ HFG and LM = HF. So $△$ LMN ≅ $△$ GFH.

If $y=\left(f\right(f\left(x\right)){)}^3,f(0)=0$ and $f^{\prime }\left(0\right)=2,$ then ${\left(\frac{dy}{dx}\right)}_{x=0}$ is equal to

The standard notation of 1650000 is given by .

The product of two numbers is $15\frac{5}{6}$.

If one number is $6\frac{2}{3}$, what will be the other number?

Give first
the step you will use to separate the variable and then solve the
equation:

(a) 3l
= 42 (b) (c)

(d) 4x
= 25 (e) 8y = 36 (f)

(g)
(h) 20t
= − 10

Question 9 (i)

100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

$\begin{array}{cc}\text{Number of letters}& \text{Number of surnames}\\ 1-4& 6\\ 4-6& 30\\ 6-8& 44\\ 8-12& 16\\ 12-20& 4\end{array}$

(i) Draw a histogram to depict the given information.

Factorise:$x^3{y}^2-z{x}^{2}y+x^4{y}^3$

If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes.)

Write down the rational number whose numerator is the smallest four digit number and denominator is the largest five digit number.