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Reduce $\frac{a^2+7a+10}{a+5}$ into its lowest form

Find the proper subsets of $\{x:x^2-9x-10=0\}$

Match the two columns :
$\begin{array}{cc}Column-I& Column-II\\ \text{A) Sum of all the angles}& \text{P) Right angles}\\ \text{of a quadrilateral is}& \\ \text{B) In a}\parallel \text{gm, the angle}& \text{Q) Rectangle}\\ \text{bisectors of two adjacent}& \\ \text{angles intersect at}& \\ \text{C) Angle bisectors of}& R){45}^{\circ }\\ \text{a}\parallel \text{gm form a}& \\ \text{D) The diagonals of a}& \text{S) 4 right angles}\\ \text{square are equal and}& \\ \text{bisect each other at}& \\ \text{an angle of}& \end{array}$
Choose the correct option:

Identify the base in the given example: $5^3$

Base: ___

$\text{Find the value of}(66666{)}^2.$

Find the amount and the compound interest on Rs 2500 for 2 years at $10$ per annum, compounded annually.

How to find rational number between two rationls

If $ED$ is parallel to $AB,$ then angle $n$ is equal to ___ [in degrees]

The price of 1kg of potato is Rs. 60. 1 kg onions cost 10% less than 1 kg potato. If I pay Rs. 180 for potatoes, what will be the cost of onions (of the weight same as the weight of the potatoes)?

Odds in favor of different events are given. Select the events which are more likely to happen.

How to construct 85° angle without protector?

In division algorithm when should one stop the division process?

1. When the remainder is zero.

2. When the degree of the remainder is less than the degree of the divisor.

3. When the degree of the quotient is less than the degree of the divisor.

A principal of ₹40,000 is compound annually at a rate of 10% for 2 years. What is the compound interest?

Is compound interest greater than the simple interest for the same rate and at the same time?

The larger trapezium is made up of the four smaller trapeziums which are equal in size. If FD = 48 cm, then, select the statements that are true.

The rate of increase in population is 25%. What will be the population after 2 years if the initial population is 20000?

___

Two cylinders of the same volume have their radii in the ratio $1:6.$ Then, the ratio of their heights is

Find the value of x in the diagram below.

A sphere has ___ dimensions.

Eight students compete in the race. In how many ways first three prizes be given?

1) The densityof a liquid is 600g/cm³ . Express it in kg/ m³?

2) Calculate the density of a solid from the following data -

a) mass of solid =72g

b) Initial volume of water in measuring cylinder = 24ml.

A cyclist travels from a place A to a place B along the same route at a uniform speed on different days. The following table gives the speed of his travel and the corresponding time he took to cover the distance.

$\begin{array}{ccccc}Speedinkm/hr(x-axis)& 2& 4& 6& 10\\ Timeinhr(y-axis)& 60& 30& 20& 12\end{array}$

Draw the speed-time graph and use it to find

(i) The number of hours he will take if he travels at a speed of 5 km/hr

(ii) The speed with which he should travel if he has to cover the distance in 40 hrs.

Write the product $5\times 6\times 7\times 8\times 9$ in factorial notation.

There are about 100 million smartphones in the US. Ms. Maria has one smartphone. What share of US smartphones does Ms. Maria have? Express your answer using a negative power of 10.

Find the area of a square plot of land whose each side measures $8\frac{1}{2}$ metres.

In a direct impact, loss in kinetic energy is given by $△K=\frac{M_1{M}_2}{2(M_1+M_2)}.(V_1-V_2{)}^2(1-K^2)$ with usual

notations(except k). The quality k will have dimensional formula:

1. 4

Find value of $x$ in the given pair of equations.

$\frac{1}{x}+\frac{1}{y}=4$

$\frac{1}{x}-\frac{1}{y}=2$

A man invests ₹5000 at a certain rate of interest, compounded annually. At the end of one year, it amounts to ₹5600. The rate of interest per annum is

If $x$ and $y$ are distinct integers, then which of the following is true about $\frac{x+y}{2}$ ?

What is the probability of getting a 'composite number' when a die is rolled?