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Two manufacturers Ram and Shyam manufacture only three wooden items; bed, table and sofa. The sales (in rupees) of these three items by both of manufacturers in month of June and July are given by the following matrices $A$ and $B$ respectively.



Sale in June

$\begin{array}{ccccccc}& & & \text{Bed}& \text{Table}& \text{Sofa}& \end{array}A=\left[\begin{array}{ccc}5000& 10000& 15000\\ 25000& 15000& 5000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$



Sale in July

$\begin{array}{ccccccc}& & & \text{Bed}& \text{Table}& \text{Sofa}& \end{array}B=\left[\begin{array}{ccc}2500& 5000& 3000\\ 10000& 5000& 5000\end{array}\right]\begin{array}{c}\text{Ram}\\ \text{Shyam}\end{array}$



The decrease in sale from June to July is given by



[1 mark]

Johny was asked to count the number of studens in the classroom. He saw that there are a total of $5$ students sitting on each bench. How many students do class have if there are $20$ benches in the classrooms?

Prove that:
(i) $\frac{1}{3+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{3}+1}=1$
(ii) $\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}=2$

In the given figure two parallel lines l,m are intersected by a tranversal. If $\angle 2={65}^{\circ }$ then $\angle 7$ and $\angle 6$ are

If Ajay earns ₹3000 in 10 days then he earns ₹ ___ in 25 days.

David draws a card from a well-suffled pack of $52$ cards. What is the probability that David draws a red numbered card?

Simplify using brackets: $245\times 235–235\times 255$.

Q58. What will come in place of (?) in the following number series?

9 17 33 65 ?

Question 45

In the following question, fill in the blanks to make the statements true.

$[2^{-1}+3^{-1}+4^{-1}{]}^0=$ ___

Which of the following conversions are correct?

What is the value of below figure in the tally chart?

Question 1(iii)

Identify the terms, their coefficients for the following expression:

$4x^2{y}^2-4x^2{y}^2{z}^2+z^2$

The identity for the addition of whole numbers is

Find the square root of i.

Or

Solve the quadratic equation $x^2+x+\frac{1}{\sqrt{2}}=0$

Two squares of area $9m^2$ are placed adjacent to each other, what would be dimensions of the new rectangle formed ?

Suppose you have to walk for 4.87 km to attend a party at your friend's home. If you have already walked for 1500 m twice, how many more kilometres do you have to go?

It seemed like a forever journey for Jack as he was moving towards Cottage city. He remembered that his famous work on time travel was criticized everywhere. Maybe people in future now are making fun of him. For his work, he was nominated for the “Excellence Award”. He then checked the status of the number of votes he got.

Find the frequency of people voting for Jack.

Write one and two tenths as decimal?

Question 12
If the sum of two angles is equal to an obtuse angle, then which of the following is not possible?
a) One obtuse angle and one acute angle
b) One right angle and one acute angle
c) Two acute angles
d) Two right angles

The perimeter of a regular hexagon is

In a 12-sided polygon, the external angles are all equal. How much is each external angle? And each angle of the polygon.

Write the cardinal value of the following set:

$A=\left\{\text{Numbers less than}15\text{divisible by}4\right\}$

What is the volume of a large block if it is made up of 34 cubes, each of side 1 cm ?

Which of these group(s) of numbers is/ are are co-prime numbers?

You start from your home at point A and run 100 m in West direction to reach point B. After that, you run 50 m in East direction to reach point C. Then you run 100 m in a South direction and reach point D. Which of the following is true?

Rashmi has ₹5555.50 in her wallet. She bought a saree for ₹555.5 and bought an umbrella for ₹55.50. She paid ₹5.50 as auto fare. What will be the total amount of money left with her?

Which of the following do not have two lines of symmetry?

Which option gives proper fraction?

Question 1(iv)

Find the rule, which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule

A pattern of letter V as

Question 4

A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in all?

In order to be admitted into the United States Army, a person's height must be greater than or equal to 60 inches and less than 80 inches. Which graph represents these conditions?



Note: In a number line, a closed circle on the number gets included in the solution, while an open circle on the number will not get included in the solution.

Convert 1.25 to fraction which is in its simplest form.

If 3/4 of a pound of strawberries is divided equally into 3 bags, each bag will contain pounds of strawberries.

Which of the following is the smallest?
$\frac{1}{4},\frac{1}{5},\frac{3}{4}$ and $\frac{2}{5}$

The prime factorisation of 272 is .