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Following frequency distribution gives the weights of the students of a class.

$$\begin{array}{cccccccccc}Weight\left(inkg\right)& 31-35& 36-40& 41-45& 46-50& 51-55& 56-60& 61-65& 66-70& 71-75\\ Numberofstudents& 3& 6& 13& 9& 11& 7& 4& 2& 1\end{array}$$

Find the probability of

(i) choosing a student at random whose weight is atmost 40kg

(ii) choosing a student at random whose weight is greater than 40kg but less than 60kg

(iii) choosing a student at random whose weight is greater than 60kg [3 MARKS]

$\Delta DEF$ and $\Delta LMN$ are congruent in the correspondence $EDF\leftrightarrow LMN$. Write the pairs of congruent sides and congruent angles in the correspondence.

If we start at (0,0) on a rectangular coordinate system and move right 2 and down 2, where are we?

Question 100
Solve the following, select the rational numbers from the list which are also the integers.
$\frac{9}{4},\frac{8}{4},\frac{7}{4},\frac{6}{4},\frac{9}{3},\frac{8}{3},\frac{7}{3},\frac{6}{3},\frac{5}{2},\frac{4}{2},\frac{3}{1},\frac{3}{2},\frac{1}{1},\frac{0}{1},\frac{-1}{1},\frac{-2}{2},\frac{-3}{2},\frac{-4}{2},\frac{-5}{2},\frac{-6}{2}$

Question 1 (iii)

What will be the unit digit of the squares of the following number:

799

The table below shows the percentage of expenditure on various items for two families. Represent them by a bar graph.

Factorize the following:

$10m^3{n}^2+15m^{4}n-20m^2{n}^3$

The cost of 12 identical articles is ₹1,080. How many articles can one buy for ₹1,620?

Four alternative options are given for each of the following statements.

Select the correct option.

Nine percent of Rs 700 is:

A. Rs 63

B. Rs 630

C. Rs 6.3

D. Rs 0.63

The volume of a cube is 343 cm'. Its total surface area is

(a) $196c{m}^2$

(b) $49c{m}^2$

(c) $294c{m}^2$

(d) $147c{m}^2$

The lengths of the parallel sides of a trapezium are 19 cm and 13 cm and its area is 128 $c{m}^2$. The distance between the parallel sides is
(a) 9 cm (b) 7 cm
(c) 8 cm (d) 12.5 cm

Question 2(iv)

Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:

675

A closed box is 40 cm long, 50 cm wide and 60 cm deep. Find the area of the foil needed for covering it.

For the given diagram what is A ∩ B and B ∩ C.

If the HCF of 657 and 963 is expressible in the form 657 x + 963 $\times (-15)$ find x?

Which figure given below is a closed curve as well as a polygon?

Question 3: Draw rough diagrams of two angles such that they have:

(a) One ray in common.

Find the cube-roots of :

(i) $700\times 2\times 49\times 5$ (ii) $-216\times 1728$ (iii) $-64\times -125$

(iv) $-\frac{27}{343}$ (v) $\frac{729}{-1331}$ (vi) 250.047 (vii) -175616

Find the cost of $8kg$ of rice, if the cost of $10kg$ is $Rs.325$.

ABCD is a trapezium. P is the midpoint of BC. AB = 14 cm, DC = 6 cm. The distance between AB and CD is 8 cm. Find the area of the triangle AQD.

In the figure, $l||m||n$. Then, the value of $y$ is:

The average value of a group of observations is 25. If the observations are 29, 32, 16, 7, x and x+4, then find the value of x.

The same rectangular flag with dimensions given is arranged in different orientations. The options have different base and corresponding height combinations. Pick the option in which all of the combinations are correct.

Squares of which of the following numbers will have 1 (one) at their unit's place:

(i) 57 (ii) 81

(iii) 139 (iv) 73

(v) 64

Solve using appropriate proper properties

$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}$

Question 7 (i)
Without adding, find the sum:

1 +3 + 5+7 + 9

Anshul took a paper and put down his pencil on it. But as soon as he put the pencil on the paper, he was called for some work. The pencil left a small mark on the paper which looked like the figure shown below. What is that mark usually called?

To construct the following rectangle inside a circle, the 2 diametres we consider must be ___.

Question 9

For calculation of interest compounded half-yearly, keeping the principal same, which one of the following is true?

(a) Double the given annual rate and half the given number of years

(b) Double the given annual rate as well as the given number of years

(c) Half the given annual rate as well as the given number of years

(d) Half the given annual rate and double the given number of years

Without adding find the
sum

(i) 1 + 3 + 5 + 7 + 9

(ii) 1 + 3 + 5 + 7 + 9
+ 11 + 13 + 15 + 17 + 19

(iii) 1 + 3 + 5 + 7 + 9
+ 11 + 13 + 15 + 17 + 19 + 21 + 23