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Evaluate : ( 8a³ - 27b³ ) / ( 64x³ + y³ ) , where ( 64x³ + y³ ) ≠ 0

Question 4 (viii)
Find the square roots of the following numbers by the Prime Factorizationmethod:
9216

A food stock can feed 800 children for 60 days. If 400 more children arrive, how long will the stock last?

Given the line of symmetry, find the other hole.

Question 1 (v)
What will be the unit digit of the squares of the following number:

1234

Difference of a two digit number and the number obtained after reversing the digits is always divisible by:

Simplify:

(2xy + 4yz + 9) - (3yz - 3xy - 1)

Find the quotient when 73 - 37 is divided by

(i) 9 (ii) 4

The standard notation of 1000a + 100b + c is

Find the cube root of $\frac{-512}{343}$?

Sam's cubicle is exactly in the shape of a cube of side 6 m. It is a closed cubicle from all the 6 surfaces. The total surface area of the cubicle ignoring the thickness is ___$m^2$

Find the solution of 2x – 3 = 7. [1 MARK]

The value of 0.0000987 in standard form is

Jane is wrapping a can of paint to gift a friend. If the can is 11 inches high and has a diameter of 7 inches, then how many square inches of wrapping paper will she use for covering the can?

Two numbers are in the ratio of 8 : 3. If they differ by 15, then find the numbers.

Factorise : $x^2-(a-3)x-3a$

When we start constructing a quadrilateral whose 2 diagonals and 3 sides known, in how many ways can the construction be started.

Find the probability of getting the number 9 in a throw of a die

$75\%$of what number is $15$

Question 76

Find the area of the following field. All dimensions are in metres.

64800 can be expressed in the form of exponents as

Question 3

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

If 8x-3=25+17x, then x is:

(a) a fraction

(b) an integer

(c) a rational number

(d) cannot be solved

The sum of exterior angles of a polygon is one-third of the sum of interior angles. Find the number of sides in the polygon.

Fill in the blanks :

(i) The product of a rational number and its reciprocal is........

(ii) Zero has..... reciprocal.

(iii) The numbers....... and ....... are their own reciprocals.

(iv) Zero is...... the reciprocal of any number.

(v) The reciprocal of a, where $a\ne 0,$ is....

(vi) The reciprocal of $\frac{1}{a}$, where $a\ne 0$, is.....

(vii) The reciprocal of a positive rational number is........

(viii) The reciprocal of a negative rational number is..........

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

$\frac{5x}{3}+\frac{2}{5}=1$

Factorise:
$p^2-10p+25$

Question 17

What is the area of the rhombus ABCD below if AC = 6 cm and BE = 4 cm?

(a) $36c{m}^2$ (b) $16c{m}^2$ (c) $24c{m}^2$ (d) $13c{m}^2$

Find out which part of the sentence has an error:

$\frac{Theydid{n}^{\prime }t}{a}\frac{workhard}{b}\frac{togetgoodmarks}{c}\frac{Did{n}^{\prime }tthey?}{d}$

Using $a^2-b^2=(a+b)(a-b),$ find
${51}^2-{49}^2$.

The product of $\frac{-26}{35}$ and $\frac{-28}{39}$ is

In $△$ ABC and $△$ DEF, $\angle$A = $\angle$E = ${40}^{\circ }$ and $\frac{AB}{ED}$ = $\frac{AC}{EF}$. Find $\angle$B if $\angle$F is ${65}^{\circ }$.

Factorize $3x^2-(3\sqrt{3}-1)x-\sqrt{3}$ and verify relationship between the zeroes and the coefficients. [2 MARKS]

Explain how abc is represented as a 3 digit number. [1 MARK]

How many polygons exist, the number of whose sides is less than that of a decagon?

A watch dealer pays $10\%$ customs duty on a watch which costs $Rs.500$ abroad. For how much should he mark it, if he desires to make a profit of $20\%$ after giving a discount of $25\%$ to the buyer?

What should be added to $x^2+3x-8$ to get $x^2+x+6$?

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find :

(i) A - B (ii) A - C (iii) A - D

(iv) B - A (v) C - A (vi) D - A

(vii) B - C (viii) B - D (ix) C - B

(x) D - B (xi) C - D (xii) D - C

From his observations, he tried to draw conclusions. Something about the “Dodo” birds was not alright. But what was it? He took out his tablet having an encyclopedia which had everything in it. He searched “Dodo”. In the results, it was given that “These birds live around Mauritius”. There was also a table, which gave the number of Dodo birds in different years. The table was as follows:

$\begin{array}{cc}\text{Year}& \text{No. of Dodo birds}\\ 1665& 1500\\ 1675& 300\\ 1681& 1\\ 1685& \text{Extinct}\end{array}$

Looking at the table and analyzing the data, he derived the conclusion that:

If S is the set of distinct values of b for which the folowing system of linear equations
$x+y+z=1$,
$x+ay+z=1$
and $ax+by+z=0$ has no solution, then S is

Andy’s friend Sandy also got his land restructured. In his case, the land was rectangular before. Keeping the same base and same parallels, LandGrabbers restructured it into a parallelogram-shaped land as shown in the figure. Sandy spent ₹ 400 on fencing and ₹ 500 on ploughing earlier. If AE is twice of AD, find the extra amount he has to spent now on fencing and ploughing respectively in terms of ‘x’ and ‘y’.

The value of a machinery is Rs. 10000, which is depreciating at the rate of 15% annually. The value of the machinery after 2 years in rupees ___

Let,$f\left(x\right)=x^{2}andg\left(x\right)=3x+4$.Find the value of $\frac{(f+g)\left(x\right)}{(f-g)\left(x\right)}$ when x = 1

If the suffix ‘-some’ is added to ‘whole’, ‘meddle’ and quarrel, the resultant words will be