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Represent the following numbers as integers with appropriate signs.

A deposit of rupees two hundred.

Three cubes of side $4cm$ each, are joined end to end. Then, the total surface area of the resultant cuboid is

Find the probability of getting an ace from a well-shuffled deck of 52 playing cards?

In the trapezium ABCD shown below, AB and CD are parallel. Using the given measurements (in centimetres), find its area:

A circular primary clarifier processes an average flow of 5005 $m^3/d$ of municipal waste water. The overflow rate is 35 $m^3/m^2/d$. The diameter of clarifier shall be

The sum of the digits of a two-digit number is 12. If the new number formed by reversing the digits is greater than the orginal number by 54, find the orginal number.

Dear mentor,

An almirah is sold at rs. 5225 after allowing a discount of 5%. Find it's marked price.

Solution:

According to the information given,

x>5225

5225= 5% of x

5225= 0.95 x

x= 5500

I didn't understand the bolded step.

Please explain clearly.

Thankyou 👦👦👦

Question 3

Construct a rectangle with adjacent sides of length 5cm and 4cm.

Convert the given statement into an equation in x.



“When a number ‘$x$’ is added to $3$ and the sum is divided by $2$, the result is the number ‘$x$’ itself.”

$x$ is defined as 30% of 30. If $y=x^2+4x+7$, find the value of y.

Is "4a + 3b = 3b + 6" a linear equation.

Give reasons for the same.

Question 1 (i)

Find the squares of the following numbers:

32

Explain the properties of a kite with appropriate diagram.

Subtract $7p(3q+7p)$ from $8p(2p-7q)$.

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

The difference between highest and lowest score of a distribution gives:

A. class interval

B. class width

C. range

D. class limit

Extending the same logic you’ve seen in the video so far, find out the sum of the first 10 natural numbers.
(You can use $S_{10}=1+2+3+\dots +10$ and proceed)

Consider the figure:

If $\angle$A = ${70}^{\circ }$​, $\angle$ACD = ${120}^{\circ }$​, then the value of $\angle$B (in degrees) is
___

Quadrilaterals with four right angles are __________ and ______ .

Match the following quantities with their values for a cone having base diameter as 6 cm and height as 4 cm.

It is given that $(\frac{x}{y}{)}^z=(\frac{y}{x}{)}^{-5}$. Find the value of $z$.

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 identify the correct pictograph for the above data.

The time spent for sessions of various subjects is given in the line plot. The fraction of time for the Math session is

There were 7 friends in a birthday party. If 3 friends ate $\frac{5}{8}$ of the cake, 2 others ate $\frac{1}{8}$ of the cake, then what fraction of the cake was left over for the remaining 2 friends?

Question 37

The curved surface area of a cylinder which exactly fits in a cube of side b is ___

A steel box has dimensions of 2 m, 3 m and 0.5 m. It has to be gold plated through electrolysis. If each square metre of gold plating costs ₹100 , then gold plating the outer surface of the box costs :

Question 49

Which ratio is larger 10 : 21 and 21 : 93?

At what rate percent per annum will a sum of Rs. 4000 yield compound interest of Rs. 410 in 2 years?

What will be the diameter of the sphere whose surface area is $616{\text{cm}}^2$?

If the side of a cube is $x$, then its volume is ___.

Each interior angle of a regular decagon (a) 60${}^{\circ }$ (b) 120${}^{\circ }$ (c) 144 ${}^{\circ }$ (d) 180 ${}^{\circ }$

If $\frac{x+c}{x+1}=c+1$. Express $x$ in terms of $c$.
Given c is a constant, $c\ne 0$, $c\ne -1$ and $x\ne -1$.

Find the values of the letters in the following and give reasons for
the steps involved.

How to find the under root of any possible number for eg: root 947