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The outcome of 120 throws of a die is as shown below

$$\begin{array}{ccccccc}Outcome& 1& 2& 3& 4& 5& 6\\ Frequency& 15& 20& 22& 18& 24& 21\end{array}$$

(i) What is the probability of getting a multiple of 2?
(ii) What is the probability of not getting a 1 or a 6?
(iii) What is the probability of getting a prime?

Negation of ‘Azra is in class X or Diya is in class XII’ is ___.

The sum of an angle and one third of its supplementary angle is ${90}^{\circ }$. The measure of the angle is
(a) ${135}^{\circ }$
(b) ${120}^{\circ }$
(c) ${60}^{\circ }$
(d) ${45}^{\circ }$

(a) Find the number of lines of symmetry of the following figure?

(b) How many angles of rotation will a regular polygon have if it has ‘n’ sides?
[4 MARKS]

If both $x-2$ and $x-\frac{1}{2}$ are factors of $p{x}^2+5x+r$ , then .

Exapanded form of 0.108 is _____.

Find the equations of the lines through the point (3, 2), which make an angle of ${45}^{\circ }$ with the line $x-2y=3$

Draw triangle of sides 6, 7 and 8 centimetres. Divide it into three triangles whose areas are in the ratio 1 : 2 : 3.

A rectangle is called congruent to a square of side 5 cm provided

Choose the pairs with equal volumes.

The mean of the following distribution is:

$$\begin{array}{ccccc}{x}_i& 15& 12& 18& 19\\ f_i& 2& 5& 7& 6\end{array}$$

The following histogram represents the age group of doctors enrolled in a certain program.

Find the number of doctors:

(i) who are in the age group between 25-35.

(ii) how many doctors belong to the age group between 45 - 50?

(iii) number of doctors below the age group of 25.

What is the simple interest rate per annum if Rs 1600 amounts to Rs 1900 in 2.5 years?

Let $x_1,x_2,\cdots ,x_n$ be n observations, and let $\overline{x}$ be their arithmetic mean and ${\sigma }^2$ be the variance.
Statement – 1: Variance of $2x_1,2x_2,\cdots ,2x_n\text{is}4{\sigma }^2$
Statement – 2: Arithmetic mean $2x_1,2x_2,\cdots ,2x_n\text{is}4\overline{x}$

1. 5

A hemispherical tank of radius 3 cm is full of milk. It is connected to a pipe, through which liquid is emptied at the rate of $\frac{1}{7}$ litre per second. The time taken to empty the tank completely is:

[Assume $\pi =\frac{22}{7}$]

A thin cylindrical thin can hold only one litre of paint. What is the height of the tin if the diameter of the tin is 14 cm? (One litre = 1000 cc)

Factorise:
$x^2+2\sqrt{3}x-24$

$\Delta ABC$ is an isosceles triangle in which $AB=AC$. Side $BA$ is produced to $D$ such that $AD=AB$. Show that $\angle BCD$ is a right angle.

What is the median of the following data: 1, 4, 7, 3, 9, 5, 3, 2, 7, 5.

1. 24

Can we draw an angle of 61 degrees?

Arrange the following polynomials in ascending order of the maximum number of zeros they can have.

Which of these is a condition for a parallelogram to be a rectangle?

1. 0

The measure of the angle whose supplement is 179° is ____.