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Question 5(i)

Show that:

$(3x+7{)}^2-84x=(3x-7{)}^2$

What must be subtracted from $(x^3-3x^2+5x-1)$ to get $(2x^3+x^2-4x+2)$ ?

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

Represent sixth root of 8 in decimal form. [4 MARKS]

Which of the following numbers are notperfect cubes?

(i) 216

(ii) 128

(iii) 1000

(iv) 100

(v) 46656

Question 15

In the following question out of the four options only one is correct, write the correct answer.

The sum of three consecutive multilpes of 7 is 357. Find the smallest multiple.

(a) 112

(b) 126

(c) 119

(d) 116

Question 25

A graph showing two sets of data simultaneously is known as:

(a) Pictograph

(b) Histogram

(c) Pie chart

(d) Double bar graph

Vasudevan invested $Rs.60000$ at an interest rate of $12\%$ per annum compounded half-yearly. What amount would he get

(i) after $6$ months?

(ii) after $1$ year?

The following items are purchased from the showroom

T-Shirt worth Rs. 1200
Jeans worth Rs. 1000
2 skirts worth Rs. 1350 each.
What will these items cost to Shikha if the sales tax is 7%?

A six-faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice, the probability that the sum of two numbers thrown is even :

Splitting the middle term, what do we get as the factors of x² - 2√3x + 3?

In the inequation x represents the amount of gas present in the gas cylinder. So, the value of x is .

In a college there are 10 periods per day each of 40 minutes. The students were protesting to reduce the number of periods but the Principal did not want to reduce the working hours. What should be the working hours of each period if Principal reduces the number of periods to 8?

If $A$ is a $2\times 2$ matrix such that $A^{2021}+A^{2020}=I,$ where $|A+I|$ is non-singular, then ${\left(A^{2020}\right)}^{-1}$is equal to

Question 18

Write the correct answer from the given four options.

Which of the following numbers is not a perfect cube?

a) 216

b) 567

c) 125

d) 343

Factorisation of $81x^3-x{y}^2$ gives

Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is Rs 1,600, find the marked price.

An annual function was held at a school. The following data represents the number of participants in different items.





What will be the mean of this data without an outlier?

Simplify and write in exponential form: $4^3\times 4^{-2}\times {16}^2$

Which of the following mapped diagram satisfies given function.

$y=x^2$

Domain:$\{1,2,-1,-2,3,-3\}$

Range:$\{1,4,9\}$

Given that $x\in \text{Domain}\&y\in \text{Range}$

Which one of the following solids can be formed using the net given?

Question 1

A park, in the shape of a quadrilateral ABCD, has $\angle C={90}^{\circ },\text{AB}=9m,\text{BC}=12m,\text{CD}=5m\text{and AD}=8m$. How much area does it occupy?

In a quadrilateral MIST, MI = 3.5 cm, IS = 6.5 cm, Angle M = ${75}^{\circ }$, Angle I = ${105}^{\circ }$ and Angle S = ${120}^{\circ }$. Which line segment should be drawn first?

The area of a rectangle is 100 square metres. What could be its dimensions?

Question 34

A coin is tossed three times. The number of possible outcomes is
(a) 3
(b) 4
(c) 6
(d) 8

In an election between two candidates, one, candidate secured 58% of the votes polled and won the election by 18,336 votes. Find the total number of votes polled and the votes secured by each candidate.

Which of these numbers is the largest?

For constructing $\Delta$LMN exactly identical to $\Delta$ABC, choose from the options, the measurements required.

Question 6 (iii)

For the following number, find the smallest whole number by which it should be divided so as to get a perfect square. Also, find the square root of the square number so obtained:

396

A car travelled 60 km towards the north direction from a point A. From there, it travelled 100 km in the south direction. How far is the car from point A now?

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

The exponential form of a × a × a is:

A. 3a

B. 3 + a

C. a³

D. 3 − a

On Sunday, 845 people went to a Zoo. On Monday, only 169 people went. What is the percent decrease in the people visiting the Zoo on Monday? [2 MARKS]

A sheet of paper of length 10 cm and breadth 5 cm is rolled along its length to form a cylinder, Find the volume of the cylinder. Take $\pi$ = 3.14.

If ${\left[{\left\{{\left(\frac{1}{7^2}\right)}^{-2}\right\}}^{-\frac{1}{3}}\right]}^{\frac{1}{4}}=7^m$ then find the value of $m$.

The cost price of 20 articles is same as the selling price of 16 articles. Find the gain percent.