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If $m\ne n$ then $(m+n{)}^{-1}\times (m^{-1}+n^{-1})=$ ______

In a marathon, you started from checkpoint A and ran 5 km towards West. The checkpoint you reached was B. Then, you again ran for 12 km towards North and reached checkpoint C. Find the length of the shortest path which you must take to reach the finishing checkpoint A.
[4 MARKS]

Find the total number of 9 digit numbers which have all different digits.

The selling price of a table is more than its cost price by $25\%$ Then the cost price is less than selling price by

Question 9(c)
Use the sign of >, < or = in the box to make the statements true.
$23-41+11\square 23-41-11$

In the given figure, the value of 'z' is _______.

Days, weeks and months passed. After 117 days, the super batteries were charged fully. Jack said goodbye to William, and told that he was going to different country. Jack checked everything twice. He timed the time machine for 2015, his home and started. And when he came out of the portal, he finally found something familiar.

If instead of Time direction module, there was an inbuilt Time direction program which randomly assigns travel direction, what is the probability of ending up in future?

Akashi was playing with the numbers. She found that a number is divisible by both 7 and 12.

Which is the least number of which both of these will be divisible? [3 MARKS]

Which of the following is the greatest integer :

10, -20, -2, 0.

A pack of 2 kg of sugar contains $8\times {10}^6$ crystals and a sack contains 3 packs of sugar. How many crystals would 12 sacks contain?

The bar graph shows the favourite subjects of 20 students in class VI 'B'. How many more of them prefer Mathematics to Science?

FAVOURITE SUBJECTS OF 20 STUDENTS

Here the horizontal axis is x axis which represents subjects and vertical axis is y axis which represents number of students. x axis represents subjects and the scale y axis 1 cm = 1 student.

Which of the following statements is not true?

(a) Find the sum of $\frac{9}{16}$ + $\frac{9}{24}$.

(b) Arun walks $\frac{1}{3}$km from a place A towards East and then from there $1\frac{2}{3}$km towards west, where will he be now from A.

[3 MARKS]

If an isosceles triangle has a perimeter of $18cm$ and base $8cm$, then its area is ___ .

Sohail cycles on a circular track in anticlockwise direction. He travels with a speed ‘V’ to cover the path AB, next with speed ‘2V’ from B to C and with a speed of ‘3V’ from C to A. What is his average speed for the total journey? (AB = BC = CA)

1. 50

A pack of 2 kg of sugar contains 8×${10}^6$ crystals and a sack contains 3 packs of sugar. How many crystals would 12 sacks contain?

Question 90(iii)
The table below gives the data of tourists visiting 5 hills stations over two consecutive years. Study the table and answer questions that follow:

Which hill station was visited by least number of tourist in 2009?

Question 91(ii)
The table below gives the flavours of ice-cream liked by children (boy and girls) of a society.

Study the table and answer the following questions:
Which flavour is liked the most by the boys?

After rearranging the terms and solving the inequality 20x -45 > 35, we get ___ .

In a school hostel, a certain quantity of ration is consumed by 25 children in 30 days. However, 10 children did not return to the hostel after summer vacations. How long will the same amount of ration last now?

What is the angle between the minute and hour hands shown on the clock?

Question 4(d) :

Find the equivalent fraction of $\frac{3}{5}$ having:

numerator 27

Question 107

The given figure represents a weighing balance. The weights of some objects in the balance are given. Find the weight of each square and the circle.

The capacity of water jug is 500ml . The water level is 200ml below the top . Calculate the level of water in the jug.

Give reason why graph paper is used for measuring the volume of an irregular object

How many altitudes can a right angled triangle have?

A man invested Rs.45,000 in 15 % Rs.100 shares quoted at Rs.125. When the market value of these shares rose to Rs.140, he sold some shares, just enough to raise Rs.8,400.

Calculate the dividend that will be due to him on the remaining shares that he still holds.

When a negative integer is divided by a negative integer the result is:

Koushal, Abhilash and Nikhila jointly started a business. Koushal invested $\frac{1}{4}th$ of the total capital. Abhilash invested $\frac{1}{4}th$ of the total capital. Nikhila invested the remaining part of the capital. If the total profit is ₹ 2400 at the end of the year, find the profit earned by each of them .

$3\frac{1}{2}-4\frac{1}{2}$ = ______

One day Jhumpa noticed that the walls of her house were losing its shine and were getting deteriorated. So she called a painter and asked him to repaint their house. The painter took 3 days to complete one wall of her house. How many walls of the same size will the painter paint in 1 month if it is the month of April?

5(2-3x)-17(2y-5)=16

The coefficient of term $x{y}^2$ in expression $6x{y}^2+x^3-x^5+3x{y}^2+7x^4+4x+7$ is

Simplify : $37x-[5x+\{28x-(19x-7x)\left\}\right]$

What is the value of f?
Given, $f=z+\frac{2y}{(x+\frac{5}{x})z}+\frac{2}{3y}$; $x=5;y=2;z=1$

Consider the figure:

Let the number of faces be F, the number of edges be E and number of vertices be V. Then find the value of F + E + V.

Question 9

In $\Delta PQR$,

a) PQ - QR > PR
b) PQ + QR < PR
c) PQ - QR < PR
d) PQ + PR < QR

2x of its supplement

To mark $\left(\frac{1}{6}\right)th$ of a circle, what angle should be drawn at the center of the circle ?

If you walk at a speed of 20 km/hr from your house, you will reach your school at 9.05 a.m. If you walk at 30 km/hr, then you will reach by 8.55 a.m. Find the distance between your house and school.

The perimeter of a square courtyard is 144 m. Find, the cost of cementing it at the rate of $5 per m${}^2$ .