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Write ${\left(\frac{1}{9}\right)}^{\frac{-1}{2}}\times (64{)}^{\frac{-1}{3}}$ as a rationalnumber.

Comment on the nature of the roots of the equation $2x^2–6x+8=0$

In an event there are two possible outcomes, the probability of occurrence of one outcome is 1. The probability of occurrence of the other outcome is:

The painter charged ₹ 5 per $m^2$ to paint the wall, as shown in the figure. Calculate the area to be painted and the money to be paid to the painter,

if the dimensions of the door is $3m\times 2m$ and that of the wall is $8m\times 8m$.

If the interest is compounded half-yearly, calculate the amount when the principal is Rs. 7,400; the rate of interest is 5% per annum and the duration is one year.

Given are three cylindrical buckets X, Y, Z whose circular bases are of radii 1, 2, 3 units, respectively, Initially, water is filled in these buckets up to the same height. Some water is then transferred from Z to X so that they both have the same volume of water. Some water is then transferred between X and Y so that they both have the same volume of water. If h${}_y$, h${}_z$ denote the heights of water at this stage in the buckets Y,Z, respectively, then the ratio $\frac{h_y}{h_z}$ equals.

${\left[\right(B^{\prime }\cup (B^{\prime }-A)\left)\right]}^{\prime }$ =___

An isosceles triangle has sides 4a, b and b. Find the length of the perpendicular dropped onto the unequal side from the vertex opposite to this side.

What is the remainder obtained when the polynomial P(x) = $x^7+9x^5+5x^3+x-1$ is divided by $x–1$?

If $5\tan \theta =4,$ then the value of $\frac{(5\sin \theta -4\cos \theta )}{(5\sin \theta +4\cos \theta )}$ is

Determine the ratio of the lateral surface area to total surface area of a cube.

Name all the properties of surds with examples?

If $P$ is a $3\times 3$ matrix such that $P^T=2P+I$, where $P^T$ is the transpose of $P$ and $I$ is the $3\times 3$ identity matrix, then there exists a column matrix $X=\left[\begin{array}{c}x\\ y\\ z\end{array}\right]\ne \left[\begin{array}{c}0\\ 0\\ 0\end{array}\right]$ such that

At which
point does the SMC curve intersect SAC curve? Give reason in support
of your answer.

Any pair of supplementary angles sum up to _____

YA is the bisector of $\angle$XYZ. O is any point on YA. If OP is parallel to YZ, then $△$YPO is _____.

Pentagon is a polygon with ___ sides.

Question 20
A recent survey found that ages of workers in a factory as follows:

$\begin{array}{cccccc}\text{Age(in years)}& 20-29& 30-39& 40-49& 50-59& 60\text{and above}\\ \text{Number of}& 38& 27& 86& 46& 3\\ \text{workers}& & & & & \end{array}$

If a person is selected at random, find the probability that the person is:
(i) 40 years or more.
(ii) Under 40 years.
(iii) Having age from 30 - 39 years.
(iv) Under 60 but over 39 years.

In the given figure, ABC is a triangle and FD is a median of $\Delta FBC.IfDE||BF,AB||DFandareaof\Delta ABC=48c{m}^2,thenar\left(\Delta ADF\right)+ar\left(\Delta BDE\right)is$

By inspection, 9 (2a - 3b)² - 12 (2a - 3b) gives

Find all the interior angles of the cyclic quadrilateral ABCD.

Factorise:
$10x^2-9x-7$

An equation of the type ------------- represents a line passing through the origin.

What is 40% of 20?

Question 2

A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? $(1m^3=1000l)$

If the points $P(2a+3,b-3)$ and$Q(5a-3,1-3b)$

are coincident, then the distance of the point $P$ from the origin is

Two points A & B are marked on the number line as shown in the figure. B = 7 and the distance between them is 20 units. Point A is