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'To a number, add another and then subtract this sum from the first number' is algebraically written as

The data values:

2, 3, 3, 4, 6, 7 have mode = ______ .

BD is a perpendicular bisector of AC. Which statement can NOT always be proven?

A class is divided into 2 batches for a school picnic. One batch has boys and girls in the ratio 3 : 4 and the other batch has it in the ratio 2 : 3. There are 20 more students in the first batch than the second. Find the total number of girls in the first batch if the number of boys in the second batch are 20.

Question 144(ii)
Four friends had a competition to see how far could they hop on one foot. The table given shows the distance covered by each.
$\begin{array}{cc}\text{Name}& \text{Distance covered (in km)}\\ \text{Seema}& \frac{1}{25}\\ \text{Nancy}& \frac{1}{32}\\ \text{Megha}& \frac{1}{40}\\ \text{Soni}& \frac{1}{20}\end{array}$

What is the total distance covered by Seema and Megha?

Rahul can do 2/7 of a certain work in 6 days while Suresh can do 3/5 of the same work in 9 days. They started work together but after 7 days Tahul left the work. Find in how many days Suresh can complete the remaining work?

'Sum of a and 10' is written as

The complement of 72 degree 40 seconds

Find the area of the parallelogram ABCD (in sq. meters).

Question 55

$4^9$ is greater than ${16}^3.$

A company has 92 offices, and each office has 279 employees. They are all invited to a party. Estimate the number of people who will attend the party if the number of employees is rounded off to the nearest tens and number of offices to the nearest hundreds.

5/9 is not equivalent to

The weight of one packet of tea powder is 1/4 kg. The weight of 20 such packets is _________ kg.

Express each of the following rational numbers as a sum of an integer and rational number:

i) -22/5

A and B are points on a straight line. C and D are points on a different line. The points P and Q are common to both the lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$. Which of the following statements is false?

Coefficient of term $x{y}^2$ in expression $x^3-x^5+x{y}^2$

Given a polynomial p(x) = $x^5-9x^4+24x^3-52x+48$. The zeroes of the polynomial are $\sqrt{2},-\sqrt{2}$ and 2. Find the other 2 zeroes.

Question 72

State whether the statement is True or False.

The difference between the lengths of any two sides of a triangle is smaller than the length of third side.

Find the equivalent fraction of $\frac{14}{42}$ with denominator as 6.

A submarine is travelling at a speed of 220 mph at a depth of 1600 miles from sea level . To avoid detection, it further goes down 220 miles . Later when it reaches safe zone, it ascends 440 miles. Finally, what is the depth of submarine from the sea level?

The diameter of a circular park is 14 m. Find the perimeter ($\pi$= 22/7). (Select all that apply)

Question 17
The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour?
$(Take\pi =3.14)$

In the figure, AB || CD and $\angle 1:\angle 2=3:2$. The measure of $\angle 6$ is

Prove that the bisectors of the base angles of an isosceles triangle are equal.

Using the assumed - mean method, find the mean height of the plants from the following frequency-distribution table:

$\begin{array}{cccccc}{\text{Height (in cm) x}}_i& 60& 64& 68& 72& 76\\ {\text{Number of plants f}}_i& 5& 16& 40& 30& 9\end{array}$
[4 MARKS]

1. 18

How many edges are there in a cuboid?

Question 4(iv)
Identify the greater number, wherever possible, in each of the following:
(iv) ${100}^{2}or{2}^{100}$

'n' is an even number. What is the result of multiplication of odd numbers immediately preceded and followed by 'n'?

Question 86
State whether the statement is True or False.
After rotating a figure by ${120}^{\circ }$ about its centre, the figure coincides with its original position. This will happen again, if the figure is rotated at an angle of ${240}^{\circ }$.

Question 1(e):

Write the fraction representing the shaded portion:

Question 68 (b)

Express $\frac{3}{4}$ as a rational number with denominator -80.

Solve: $\frac{3x+3}{3}=7$

In a four sided field, the length of the longer diagonal is 128 m. The lengths of the perpendiculars from the opposite vertices on this diagonal are 22.7 m and 17.3 m. Find the area of the field. [4 MARKS]

Observe the given rectangle

How many minimum numbers of rows or columns we need to add to make it a square.

Which of the following correctly represent 588 as the product of its prime power.

Question 8(ii)
The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:
$\begin{array}{cccccccc}Day& Mon& Tue& Wed& Thurs& Fri& Sat& Sun\\ Rainfall\left(inmm\right)& 0.0& 12.2& 2.1& 0.0& 20.5& 5.5& 1.0\end{array}$
Find the mean rainfall for the week.

For a triangle ABC, the true statement is

A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight, and describes 88 metres when it traces ${72}^{\circ }$ at the centre, find the length of the rope.