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Simplify
and solve the linear equation

The surface areas of six faces of a cuboid are 12, 12, 36, 36, 48, 48, (all in cm²). The volume of the solid in cm³, is ____.

The following are the expenses of a household.



$\begin{array}{cc}\text{Items}& \text{Expenditure (in}₹)\\ \text{Food}& 4000\\ \text{Clothing}& 2000\\ \text{Rent}& 1500\\ \text{Education}& 1500\\ \text{Miscellaneous}& 1000\end{array}$



When drawing a pie – chart, the central angle for money spent on education will be ____ .

Given below is a pie chart showing the time spend by a group of 350 children in different games. Observe it and answer the questions that follow.

How many children spend atleast one our in playing games ?

The fraction of the shaded part, in step 3 of the given process is

Find the ${15}^{th}$ term from the end in the expansion of $(4x+\frac{1}{16x^2}{)}^{21}$

Find the total number of diagonals in a triangle.

Let $A(5,4,6),B(1,-1,3)$ and $C(4,3,2)$ form $\Delta ABC.$ If the internal bisector of angle $A$ meets $BC$ in $D$, then the length of $AD$ is:

Match the following:
$\begin{array}{cc}\text{Column A}& \text{Column B}\\ 1.\{1,2,4,8\}& \text{A.{x: x is a natural even number less than 10}}\\ 2.\left\{2\right\}& \text{B.{x: x is a prime number and a divisor of 8}}\\ 3.\{2,4,6,8\}& \text{C.{x: x is a divisor of 8}}\\ 4.\{4,6,8,9\}& \text{D.{x: x is a composite number less than 10}}\end{array}$

Question 73

Find two numbers, whose sum is 100 and whose ratio is 9 : 16.

Let PQRS be a rhombus, with PR = 15 cm and QS = 8 cm. Find the area of the rhombus.

Find the least number that must be added to 3325 so as to get a perfect square.(Use long division method)

Question 6

$(1^0+2^0+3^0)$ is equal to
(a) 0
(b) 1
(c) 3
(d) 6

Which of the following is a rational number?

Surabhi borrowed a sum of Rs. 12,000 from a finance company to purchase a refrigerator. If the rate of interst is $5\%$ per annum compounded annually, calculate the compound interest that Surabhi has to pay to the company after 3 years.

Determine
n if

(i) (ii)

What is the degree of the polynomial $y^2(y^5{)}^2$ ?

ABCD is a parallelogram in which $\angle ={110}^{\circ }$. Find the measure of each of the angles $\angle B,\angle Cand\angle D$.

The parallel sides of a trapezium measure 14 cm and 18 cm and the distance between them is 9 cm. The area of the trapezium is
(a) $96c{m}^2$ (b) $144c{m}^2$
(c) $189c{m}^2$ (d) $207c{m}^2$

The list below gives the daily wages earned by 30 labourers in the Anantapuri village. Prepare a frequency table of these.

Now can you answer these questions?

(i) What is the daily wages of most labourers?

(ii) How many get 220 rupees a day?

(iii) How many get more than 150 rupees a day?

(iv) How many get the least amount of wages?

Draw a bar graph to represent this data.

The train is moving at a uniform speed of 80 kmph. How far will it go in 15 minutes?

Rajan buys a toy for Rs. 75 and sells it for Rs. 100 gain percent is

(a) $25\%$

(b) $20\%$

(c) $33\frac{1}{3}\%$

(d) $37\frac{1}{2}\%$

Tick the correct answer in each of the following:

The compound interest on Rs 10000 at $12\%$ per annum for $1\frac{1}{2}$ years, compounded annually, is

(a) Rs 1872 (b) Rs 1720 (c) Rs 1910.16 (d) Rs 1782

The probability of getting a prime number when a die is rolled is .

Factorize $8x^3+y^3+12x^{2}y+6x{y}^2$

Find the angle x in the given figure.

What percentage of the Indian population consists of Adivasis?

Question 26

___ is charged on the sale of an item by the government and is added to the bill amount.

In fig, if line PQ and RS intersect at point T, such that $\angle PRT={40}^{\circ }$ , $\angle RPT={95}^{\circ }$ and $\angle TSQ={75}^{\circ }$, find $\angle SQT$.

Give an example for the following axioms from your experience:

(a) If equals are added to equals, the wholes are equal.

(b) The whole is greater than the part.