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From among $30$ teachers in a school, one principal and one vice principal are to be appointed. In how many ways can this be done?

It is possible to construct a quadrilateral ABCD in which AB=5cm,BC=7.5cm,$\angle A={80}^{\circ },\angle B={140}^{\circ },\angle C={145}^{\circ }$?

Evaluate the exponential expression $x^5\times x^4$, for $x=2$

The point (2, 3) is a limiting point of a coaxial system of circles of which $x^2+y^2=9$ is a member. The co-ordinates of the other limiting point is given by

Two angles of a quadrilateral are 70° and 130° and the other two angles are equal. Find the measure of these two angles.

Express the following numbers in index form.
(1) Fifth root of $13$
(2) Sixth root of $9$
(3) Square root of $256$
(4) Cube root of $17$
(5) Eighth root of $100$
(6) Seventh root of $30$

Stoke's law states that the viscous drag force F experience by a sphere of radius a, moving with a speed v through a fluid with coefficient of viscosity $\eta$, is given by F =6$\pi$$\eta$av If this fluid is flowing through a cylindrical pipe of radius r, length l and a pressure difference of P across its two ends, then the volume of water V which flows through the pipe in time t can be written as

$\frac{V}{t}=k{\left(\frac{P}{l}\right)}^a{\eta }^b{r}^c$

Where k is a dimensionless constant. Correct values of a, b and c are

Try simplifying these:

(i) (3x + 2y) − (x + y)

(ii) (3x + 2y) − (x − y)

(iii) (x + y) − (x − y)

(iv) (x − y) − (x + y)

(v) (4x − 3y) − (2x − 5x)

Which of the following is not a polyhedron?

If I add a 2 digit number and the number formed by swapping digits, the number surely is divisible by ___

You have a 8 faced die having numbers from 1 to 8 on its 8 faces. What would be the probability of getting 8 on throwing it?

What per cent of $\frac{2}{7}$ is $\frac{1}{35}$? (a) 2.5 $\%$ (b) 10 $\%$ (c) 20 $\%$ (d) 25 $\%$

The sum of $\frac{-35}{11}$ and $\frac{12}{55}$ is ____________

Which one of the following is not an equivalent ratio of 2:3?

Factorise: $(2l+m{)}^2-8lm$

State the type of the underlined verb.

Samantha could read the minute print after the operation.

(X+4)(x-5)

The adjacent angles of a parallelogram add upto

Tap on the pythagorean triplets among the following.

Describe an experiment to show the pressure volume relationship in gases.

Suppose you are given a coordinate system. Determine the quadrant in which the following points lie:

(i) A(4, 5); (ii) B(−4, −5); (iii) C(4, −5).

Question 47

In the following question, fill in the blanks to make the statements true.

The standard from of 12340000 is ___ .

Diagonals of a rhombus

In a village six fruit merchants sold the following number of fruit baskets in a particular season:

Observe this pictograph and answer the following question:

The merchants who have sold 600 or more number of baskets are planning to buy a godown for the next season. Can you name them?

Question 6

Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:

$\begin{array}{cccccccccc}0& 1& 2& 2& 1& 2& 3& 1& 3& 0\\ 1& 3& 1& 1& 2& 2& 0& 1& 2& 1\\ 3& 0& 0& 1& 1& 2& 3& 2& 2& 0\end{array}$

Prepare a frequency distribution table for the data given above.