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A bag contains $4$ red, $3$ green and $5$ blue balls. In how many ways, $2$ red, $1$ green and $3$ blue balls can be drawn from the bag?

Three metal cubes whose edges measure 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find (i) side-length (ii) total surface area of the new cube. What is the difference between the total surface area of the new cube and the sum of total surface areas of the original three cubes?

Solve the following questions:



i) What is the percentage of people in the height range of 149.5 -159.5cm?

ii) What is the percentage difference between height group 159.5 - 169.5cm and 169.5 - 179.5cm?

What will happen to the volume of a cuboid if its :
(i) Length is doubled, height is same and breadth is halved?
(ii) Length is doubled, height is doubled and breadth is same?

In a triangle ABC, D is the midpoint of AB and E is the midpoint of AC. If DE = 7.5 cm, then BC = ____.

Find the curved surface area and the total surface area of a right circular cylinder whose height is 15 cm and the diameter of the cross-section is 14 cm.

If $x\text{and}y$ are inversly related, then, find $l,m\text{and}n$.

Romesh borrowed a sum of $Rs.245760$ at $12.5\%$ per annum compounded annually. On the same day, he lent out his money to Ramu at the same rate of interest but compounded semi-annually. Find his gain after $2$ years.

Select the pair which contains the same common factor.

The formula for finding the total surface area of a cuboid is __________.

Anubhav, a student of class VII, was asked to construct an Isosceles right triangle ABC with hypotenuse AC = 13 cm. Which of the following conclusions can help him to construct the triangle?

Question 59

The area of cultivated land and the crop harvested is a case of direct proportion.

The adjacent figure shows 3 different views of a three – dimensional figure made from cubes. Which could be a drawing of the figure?

Draw the figure for pentagonal prism and write the number of faces, edges and vertices. [2 MARKS]

A student has obtained 35% marks in a test . If the student scored 24.5 marks, find the maximum marks

Suppose 3^k × b² = 6⁴ for some positive integers k, b. Find all possible values of k + b.

Question 95(ii)

The weights (in kg) of 30 students of a class are as follows :
39, 38, 36, 38, 40, 42, 43, 44, 33, 33, 31, 45, 46, 38, 37,
31, 30, 39, 41, 41, 46, 36, 35, 34, 39, 43, 32, 37, 29, 26
Prepare a frequency distribution table using one class interval as (30-35), 35 not included.
Which class has the maximum frequency ?

Question 1
Construct the square READ with RE = 5.1 cm.

In a school of $720$ students, the ratio of the no. of boys to the no. of girls is $3:5.$ If $18$ new girls are admitted in the school, then find how many new boys may be admitted so that the ratio of the no. of boys to the no. of girls may change to $2:3.$

Solve each of the following equations and also verify your solution :

$\frac{(3x+1)}{16}+\frac{(2x-3)}{7}=\frac{(x+3)}{8}+\frac{(3x-1)}{14}$

Question 4 (iii)
Name the quadrilateral whose diagonals:

(iii) Are equal.

Choose the option with the correct punctuation.

Manisha accountant said “If Ramesh human resource manager doesn’t intimate me about the meeting, I will complain to the authorities”.

Find the mean of the marks obtained by 20 students in a classroom.

$\begin{array}{cc}\text{Marks}& \text{Frequency}\\ 87& 2\\ 78& 3\\ 53& 1\\ 98& 2\\ 92& 2\\ 97& 1\\ 81& 2\\ 65& 2\\ 98& 3\\ 76& 2\end{array}$

Which of the following holds true?

The number of apples sold by a shop is given in the table below:

$$\begin{array}{cc}\text{Day}& \text{No. of apples sold}\\ \text{Monday}& 60\\ \text{Tuesday}& 35\\ \text{Wednesday}& 50\\ \text{Thursday}& 55\end{array}$$

If the picture of an apple represents 10 apples, then draw a pictograph for the above data.

The cost of a refrigerator is ₹9000. Its value depriciates at the rat of 5% every year . find the total depreciation in its value at the end of 2 years

Question 19



The following is the map of a town. Based on it answer the question.



The number of hospitals in the town is

(a) 1

(b) 2

(c) 3

(d) 4

Find the 14-th and 15-th triangular numbers, and find their sum. Verify the Statement 8 for this sum.

Find the value of 'a', if $x+2$ is a factor of $4x^4+2x^3-3x^2+8x+5a$.

Find the two consecutive positive integers, such that the sum of their squares is 365.

The difference between two selling prices of a shirt at profits of 4% and 5% is ₹6.Find

(a) cost price of the shirt

(b) the two selling prices of the shirt

Question 2(ii)
Simplify and express the result in power notation with positive exponent:

${\left(\frac{1}{2^3}\right)}^2$

The dimensional formula of capacitance is



$[$0.77 Mark$]$

In the given figure, ABCD is a kite with AC and BD as diagonals and $\angle ABC$ = ${30}^{\circ }$. Find $x$.

The difference between selling a coat at a profit of 4% and that of 6% is Rs. 3. What are the two selling prices?

Calculate the compound interest on $Rs.15000$ in $3$ years; if the rates of interest for successive years be $6\%$, $8\%$ and $10\%$ respectively.